# Thursday, October 13: Short and Long Run Equilibria

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1 Amherst College epartment of Economics Economics 54 Fall 2005 Thursday, October 13: Short and Long Run Equilibria Equilibrium in the Short Run The equilibrium price and quantity are determined by the market demand and short run market supply curves. Market SS Short Run Market Supply Curve The short run market supply curve is the horizontal sum of each individual firm s short run supply curve. * Individual Firm s Short Run Supply Curve rofit Maximization: MR = SMC Marginal Revenue: The change in the firm s total revenue resulting from a one unit change in the quantity of output produced. * Short Run Marginal Cost: The change in the firm s total cost resulting in a one unit change in the quantity of output produced. rofit = TR STC Use calculus to find the profit maximizing quantity of output: drofit dtr = dstc = 0 dtr dstc = MR = SMC Short Run Marginal Cost Curve Shape: The short run marginal cost curve is upward sloping. Marginal Revenue and erfect Competition: MR = MR = dtr = d( q) since TR = q = + q d A perfectly competitive industry is composed of a large number of small firms. A single firm s production decisions will not significantly affect the price. Consequently, each firm is a price taker; each firm takes the price as a given, as a constant: q d = 0; therefore, MR = If =2.00 If =1.00 rofit maximizing quantity if =1.00 if =2.00 SMC MR=2.00 MR=1.00 q

2 2 Shutdown in the Short Run: < SAVC It is advantageous for a firm to shut down in the short run whenever the price is less than short run average variable costs. SMC SS Individual Firm s Short Run Supply Curve: The firm s marginal cost curve as long as price exceeds average variable cost; if price is less than short run average variable costs, the firm shuts down and produces nothing. Short Run Average Total Cost Curve Shape: The short run average total cost curve is U-shaped. if <SAVC MC, ATC if >SAVC SAVC q MC Short Run Average Total Cost Curve and Short Run Marginal Cost Curve Location: The short run average total cost curve intersects the marginal cost curve at minimum short run average total cost. ATC rofits in the Short Run rofit = TR STC = q SATC q since TR = q and SATC = STC q = ( SATC) q q Now, it is easy to determine sign of profit by comparing price and short run average total cost: < SATC = SATC > SATC SATC < 0 SATC = 0 SATC > 0 rofit < 0 rofit = 0 rofit > 0 Market Equilibrium, the Typical Firm, and Its rofit Market SS Typical Firm SMC SATC SATC * * MR=* * q* As a consequence of perfect competition, the horizontal axes have different scales. q Since < SATC at the profit maximizing quantity of output, profit is negative. uestions: How will the typical firm react in the long run?

3 3 Long Run Cost Curves The shape of a firm s long run cost curves depends on returns to scale: Increasing returns Constant returns ecreasing returns to scale to scale to scale LATC curve is LATC curve is LATC curve is downward sloping horizontal upward sloping LATC q Increasing Constant ecreasing Returns To Scale Short Run and Long Run Average Total Costs A short run average total cost curve (SATC) lies above the long run average total cost curve (LATC) except for a single point at which they just touch. The point where they touch represents the quantity at which the firm is able to use its cost minimizing combination of capital and labor. There is one short run average total cost curve for each amount of capital. SMC and SATC for different amounts of K LATC q Short Run Versus Long Run Short Run Firms can vary labor, but not capital; capital is fixed. Firms cannot enter or exit an industry. Long Run Firms can vary both labor and capital. Firms can enter or exit an industry. Unlike in the short run, in the long run firms can vary the amount of capital it uses; enter or exit the industry.

4 4 The Long Run: Entry, Exit, and the Sign of rofit Claim: As a consequence of the fact that economic profit includes both explicit and implicit costs, the sign of profits is key when deciding whether firms will enter or exit an industry in the long run. To justify this claim we shall review the argument given in your introductory course. Consider an owner operated firm. What are the explicit and implicit costs of such a firm? Explicit costs are the costs that come to mind immediately. The wages and salaries the firm pays to employees, the firm s electricity bill, telephone bill, heating bill, etc. In general, the explicit costs are what the owner of the firm must pay out to others. Implicit costs are more subtle; implicit costs are opportunity costs. In the case of an owner operated firm, implicit costs include the salary that the owner could earn if he/she did not operate the firm and worked for someone else. Total Costs = Explicit Costs + Implicit Costs What the owner Income the owner pays to others could earn if he/she worked for someone else Now, let us do a little algebra: rofits = Total Revenues Total Costs = Total Revenues (Explicit Costs + Implicit Costs) = (Total Revenues Explicit Costs) Implicit Costs Income the owner Income the owner actually earns when he/she could earn if he/she operates the firm worked for someone else Total revenues less explicit costs equals the income the owner takes home when he/she operates the firm. Implicit costs equal the income the owner could earn if he/she worked for someone else. rofit compares the income the owner actually earns when he/she operates the firm with the income he/she would earn if he/she worked for someone else: rofit < 0: Exit in the long run - income owner earns when operating the firm is less than the income he/she could earn by working for someone else. There is an incentive for firm owners in this industry to exit in the long run. rofit > 0: Entry in the long run income owners of firm in this industry exceeds what they could earn by working for someone else. This lures entrepreneurs into the industry. There is an incentive for entrepreneurs to enter the industry. rofit = 0: Long run equilibrium there is no incentive for exit or entry. Long Run Behavior: rice and Minimum Long Run Average Total Cost Claim: To determine what happen to an industry in the long run we compare the price and minimum long run average total cost: If rice < Minimum long run average total cost: exit occurs in the long run causing the price to rise. If rice > Minimum long run average total cost: entry occurs in the long run causing the price to fall. If rice = Minimum long run average total cost: a long run equilibrium exists.

5 5 First, consider the case in which the price falls short of minimum long run average total cost. Note that since the price falls short of minimum long run average total cost, the long run average total cost curve is always above the price: Market Typical Firm SMC SATC SS LATC * * MR=* * q* q NB: As a consequence of perfect competition, the scale of the horizontal axes are different. First, note that the firm is presently earning negative profits because short run average total cost exceeds the price: rofits = TR STC = ( SATC) q This is not the worst part of the news, however. Recall how the short and long run average total cost curves are related: a short cost average total cost curve lies above the long run average total cost curve except at a single level of production when the short run curve touches the long run curve. Regardless of how the firm adjusts the amount of capital it uses in the long run, the short run average total cost curve will lie above the price. Consequently, the firm will always earn negative profits because rofits = TR STC = ( SATC) q Since is always less than SATC profits are always negative. Negative profits cause firms to exit the industry. As firms exit the short run market supply curve shifts to the left causing the price to rise: Market SS Typical Firm SMC SATC LATC ** SS ** MR=** * * MR=* q NB: As a consequence of perfect competition, the scale of the horizontal axes are different.

6 6 When price falls short of minimum long run average total cost the following occurs in the long run: regardless of how firms in the industry adjust the amount of capital they use, they will earn negative profits; the negative profits causes firms to exit in the long run; the exit of firms shifts the short run market supply curve to the left causing the equilibrium price to rise toward minimum long run average total cost. Second, consider the case in which the price exceeds minimum long run average total cost. Note that since the price exceeds minimum long run average total cost, the long run average total cost curve dips below the price: Market SS Typical Firm SMC SATC LATC * * MR=* * q* q NB: As a consequence of perfect competition, the scale of the horizontal axes are different. Recall that the profits earned by the firm at the present time depend on the price and short run average total cost. In the above diagram, price is less than short run average total cost, profits are negative. Although at the present time the firm is incurring losses, the long run outlook is anything but bleak. Remember that unlike the short run, in the long run the firm can vary the amount of capital it uses; enter or exit the industry. Claim: by changing the amount of capital, the firm can move to a short run average total cost curve that dips below the price. To justify this claim recall how the short run and long run curves are related: a short cost average total cost curve lies above the long run average total cost curve except at a single level of production when the short run curve touches the long run curve. Since the long run average total cost curve dips below the price the firm can change the amount of capital it uses so that its short run average cost curve dips below the price.

7 7 Market SS Typical Firm SATC SMC LATC * * MR=* q** q NB: As a consequence of perfect competition, the scale of the horizontal axes are different. Since the short run average total cost curve dips below the price, it is now possible for the firm to earn positive profits: rofit = TR STC = ( SATC) q uestion: How much output will the firm now produce? Answer: The quantity of output that maximizes profit. The profit maximizing quantity of output is determined by marginal revenue and short run marginal cost. Note that the short run marginal cost curve and the short run average total cost curve intersect at minimum short run average total cost. q** is the profit maximizing level of output. At the profit maximizing level of output the firm is earning positive profits because the price exceeds short run average total costs. Where do we stand now? When the price exceeds minimum long run average total cost, a firm that is already in the industry can vary the amount of capital it uses to enable it to earn a positive profit. What will happen next? Entrepreneurs will recognize that there are positive profits to be earned in this industry. Consequently entry will occur. As firms enter the short run market supply curve shifts to the right because the short run market supply curve is the horizontal sum of each individual firm s short run supply curve. The rightward shift of the short run market supply curve causes the equilibrium price to fall. Market SS Typical Firm SATC SMC LATC SS * * MR=* ** ** MR=** q NB: As a consequence of perfect competition, the scale of the horizontal axes are different.

8 8 When price exceeds minimum long run average total cost the following occurs in the long run: firms already in the industry will adjust the amount of capital they use so that they can earn positive profits; the positive profits lead to the entry of new firms in the long run; the entry of new firms shifts the short run market supply curve to the right causing the equilibrium price to fall toward minimum long run average total cost. Long run equilibrium Summary: what have we shown thus far? If the price falls short of minimum long run average total costs, firms will exit the industry in the long run causing the price to rise toward minimum long run average total cost. If the price exceeds minimum long run average total costs, new firms will enter the industry in the long run causing the price to fall toward minimum long run average total cost. Since the price rises in the long run whenever the price is less than minimum long run average total cost, and falls in the long run whenever the price is greater than minimum long run average total cost a long run equilibrium requires that the price to equal minimum long run average total cost. What amount of capital will the firm now use? Recall how short and long run average total cost curves are related: a short run average total cost curve lies above the long run average total cost curve except at a single level of production when the short run curve touches the long run curve. The best the firm can do is to adjust its amount of capital so that it earns a profit of 0: Market SS Typical Firm SMC SATC LATC * * MR=* * q* q NB: As a consequence of perfect competition, the scale of the horizontal axes are different.

9 9 Note that it is impossible for the firm to adjust the amount of capital it uses so as to earn a positive profit; at the present time even though the firm is maximizing its profit, it is earning a profit of 0 because price equals short run average total cost. Consequently, there is no incentive for new firms to enter the industry and also no incentive for firms already in the industry to exit. We have a long run equilibrium. Note that when a long run equilibrium is achieved, the price equals minimum long run average total cost. Long Run Supply Curve The long run supply curve provides the answers to the following series of hypothetical questions: If the price were, how much output would firms produce in the long run when the industry had achieved a long run equilibrium; that is, how much output would be produced after the industry achieves a long run equilibrium? Constructing the long run supply curve - constant cost industry First, begin with at a long run equilibrium as we described above. This provides us with one point on the long run supply curve: Market oint on LR Supply Curve SS Typical Firm SMC SATC LATC * * MR=* * q* q NB: As a consequence of perfect competition, the scale of the horizontal axes are different.

10 10 How do we find another point on the long run supply curve? Suppose that the market demand curve shifts to the right: Market oint on LR Supply Curve SS Typical Firm SMC SATC LATC ** ** MR * * MR=* * q* q** q NB: As a consequence of perfect competition, the scale of the horizontal axes are different. The equilibrium price increases for * to ** which causes the firm s marginal revenue curve to shift up from MR to MR. The firm s profit maximizing quantity of output increases from q* to q**. Note that the price now exceeds short run average total cost. The firm is earning positive profits. What will happen in the long run? The positive profits lure entrepreneurs into the industry; that is, firms will enter the industry. Entry shifts the short run market supply curve to the right and the equilibrium price falls. Market oint on LR Supply Curve SS SS Typical Firm SMC SATC LATC ** ** *** * * MR MR MR=* * q* q** q NB: As a conequence of perfect competition, the scale of the horizontal axes are different. So let us review what is happening here: emand Curve Shifts Rightward rice Increases rice > LATC rofits Can Earn ositive rofits

11 11 Consequently, Firms Enter SS Shifts Rightward rice Falls This process will continue until the price returns to minimum long run average total cost when the new long run equilibrium is established. So it looks like the price will return to its original level, *: Market oint on LR Supply Curve SS SS SS ** *** * * Typical Firm SMC SATC LATC MR MR MR=* * q* q** q NB: As a consequence of perfect competition, the scale of the horizontal axes are different. It looks like that the long run supply curve is just a horizontal line: This is true in a constant cost industry. In the analysis provided above we implicitly assume that the industry exhibited constant cost; that is, we implicitly assumed that as firms entered, the costs of the firms in the industry were not affected. Consequently, as firms entered, the cost curves of the firms in the industry did not shift. Summary: the long run supply curve is horizontal in a constant cost industry. The price must equal minimum long run average total cost to be in long run equilibrium. Since entry and exit does not cause the cost curves to shift in a constant cost industry, entry and exit will not change minimum long run average total cost. Consequently, the long run supply curve must be horizontal in a constant cost industry.

12 12 Constructing the long run supply curve - increasing cost industry Some industries do not exhibit constant costs, however. As entry occurs often costs are driven up. For example, if new firms enter the beer industry, the demand for brew masters will increase which in turn increases the wage paid to brew masters. Higher wages for brew masters increases the costs of beer firms. These industries are called increasing cost industries. We shall follow the same strategy as before to construct the long run supply curve of an increasing cost industry. Suppose that the demand curve shifts to the right. Market oint on LR Supply Curve SS Typical Firm SMC SATC LATC ** ** MR * * MR=* * q* q** q NB: As a consequence of perfect competition, the scale of the horizontal axes are different. Just as in the constant cost case, price rises and firms can earn positive profits. emand Curve Shifts Rightward rice Increases rice > LATC Firms Can Earn ositive rofits Again, just as before firms enter and the short run supply curve shifts to the right and the price falls. But in an increasing cost industry something else also begins to happen. As firms enter the costs of the firms are driven up and consequently, the long run average total cost curve shifts up Firms Enter LATC Shifts Up SS Shifts Rightward rice Falls Minimum LATC Increases

13 13 So, while the price is falling, minimum long run average total cost is increasing. Recall that a long run equilibrium is achieved whenever price equals minimum long run average total cost. The industry will now achieve a long run equilibrium sooner and the price will be greater than *. Therefore in an increasing cost industry, the long run supply curve will be upward sloping. Market oint on LR Supply Curve SS SS Typical Firm SMC SATC LATC LS *** ** * * MR MR=* * q* q NB: As a conequence of perfect competition, the scale of the horizontal axes are different.

16 3 If the price were \$150, Andy and Kate would buy an A. Andy would enjoy a surplus of \$75 (\$225-\$150); Kate a surplus of \$25 (\$175-\$150). If the price were \$150, total consumer surplus would equal \$100, the sum of Andy s and Kate s surplus. Geometrically, the total net benefit, the consumer surplus, equals the area beneath the market demand curve that lies above the price, \$150. If the price were \$100, Andy, Kate, and an would buy an A. Andy would enjoy a surplus of \$125; Kate a surplus of \$75; and an a surplus of \$40. If the price were \$100, total consumer surplus would equal \$240. Geometrically, the total net benefit, the consumer surplus, equals the area beneath the market demand curve that lies above the price, \$100. If the price were \$50, Andy, Kate, an, Liz, and Meg would buy an A. Andy would enjoy a surplus of \$175; Kate a surplus of \$125; an a surplus of \$90; Liz a surplus of \$25; Meg a surplus of \$10. If the price were \$50, total consumer surplus would equal \$425. Geometrically, the total net benefit, the consumer surplus, equals the area beneath the market demand curve that lies above the price, \$50. Andy: \$75 rice of an A Kate: \$ uantity of A s Andy rice of an A Kate an uantity of A s Andy: \$125 an: \$40 Meg: \$10 rice of an A Kate: \$75 Liz: \$ uantity of A s Surplus if rice equals Buyer Willingness to ay \$150 \$100 \$50 Andy \$225 \$75 \$125 \$175 Kate an Liz Meg arce Consumer Surplus \$100 \$240 \$425

17 4 Summary of Consumer Surplus The height of the demand curve reflects the benefit households enjoy from consuming each unit of the good. The benefit households enjoy from consuming each unit of the good (the height of the demand curve) less the expense households incur to purchase each unit (the price) is the surplus households enjoy. Geometrically, consumer surplus equals the area beneath the demand curve that lies above the price. Consumer surplus reflects the (net) benefit households enjoy from purchasing and consuming the good. roducer Surplus - Short Run roducer surplus in the short run reflects the net benefit firms enjoy from producing and selling the good. Geometrically, producer surplus is the area above the short run market supply curve that lies below the price. To justify this we shall first argue that the height of the market supply curve reflects the costs firms incur from producing each unit of output. * SS Recall that the short run market supply curve is the horizontal sum of each individual firm s short run supply * curve; geometrically, an individual firm s short run supply curve is its short run marginal cost curve. Firm A Firm B Short Run Market Supply for Beer If = 2.00 SS A SMC A SS B SMC B SS If = 1.50 If = 1.00 If =.50

18 5 If the price were \$1.50, suppose that Firm A produced 800 units and Firm B 600 units; consequently, the quantity supplied is 1400 units. Firm A Firm B Short Run Market Supply for Beer SS A SMC A SS B SS SMC B If = How much does it cost to produce the 1400 th unit? Claim: it costs \$1.50 to produce the 1400 th unit, an amount just equal to the height of the short run market supply curve. We can justify this claim easily. One of the firms must produce the 1400 th unit; suppose that Firm B produces the 1400 th unit. Note that the 1400 th unit in the market is the 600 th unit produced by Firm B. How much does it cost Firm B to produce its 600 th unit? The answer to this question is straightforward: an amount just equal to Firm B s short run marginal cost: Verbal definition: Short run marginal cost equals the change in the firm s short run total cost resulting from a one unit change in output. NB: Marginal cost only reflects variable cost because fixed costs never change. Consequently, the short run supply curve only reflects variable costs. What is Firm B s short run marginal cost for producing its 600 th unit. Look at Firm B s short run marginal cost curve on the diagram above. Its short run marginal cost of producing the 600 th unit is just \$1.50. We have shown what we set out to prove. We have justified our claim: the height of the market supply curve reflects the costs firms incur from producing each unit of output. The net benefit or surplus a firm enjoys from the production and sale of a unit equals the benefit it derives less the costs it incurs. The benefit derived from the sale of a unit just equals the price. Therefore, the gap between the price and the short run market supply curve reflects the net benefit firms enjoy from the production and sale of a unit of output. In total, producer surplus is just the area above the short run market supply curve that lies above the price. Summary of roducer Surplus in the Surplus The height of the short run supply curve reflects the costs firms incur in the short run from producing each unit of output. The revenues firms receive from selling each unit of output, the price, less the costs firms incur in the short run from producing each unit, the height of the supply curve, is the surplus firms enjoy. Geometrically, producer surplus in the short run equals the area above the short run supply curve that lies below the price. roducer surplus reflects the (net) benefit firms enjoy from producing and selling the good. * * SS

19 6 roducer Surplus and rofits First, review the definition of profits; profit equals total revenue less short run total cost: rofit = TR STC Recall that in the short run we can divide total costs into two components: short run fixed costs and short run variable costs; that is, short run total costs equal short run variable costs plus short run fixed costs rofit = TR (SVC + SFC) Simplifying, rofit = TR SVC SFC Next, recall that the height of the short run market supply curve reflects the costs of producing each unit of output. oes the height of the short run market supply curve reflect fixed or variable costs? Clearly, the answer is variable costs; the height of the supply curve tells us by how much costs rise when the firm produces each unit of output. Therefore, the area beneath the short run supply curve reflects the short run variable costs of all firms: Area Beneath the Supply Curve = SVC of all firms What does * * equal? * * equals the total revenues collected by all firms. Focusing attention on the diagram to the right, recall that producer surplus equals the area above the short run supply curve that lies below the price. Geometrically, producer surplus is just the area of the * * rectangle less the area beneath the short run supply curve: * SS Area Beneath roducer Surplus = * * the Supply Curve TR SVC = Collected by Incurred by All Firms All Firms * Now, recall that rofit = TR STC = TR SVC SFC Hence, rofit TR SVC SFC Earned by = Collected by Incurred by Incurred by All Firms All Firms All Firms All Firms Substituting in for producer surplus: rofit SFC Earned by = roducer Surplus Incurred by All Firms All Firms

20 7 Welfare Maximizing uantity of Output From the perspective of society as a whole, how much output should be produced? Economists take two approaches to answer this question: consumer and producer surplus approach; areto efficiency approach. Both approaches end up with the same conclusion, but they use different means to get there. We shall discuss the surplus approach here; in the last two weeks of the course, we shall consider the areto approach. Equilibrium in the Market In equilibrium, the quantity demanded equals the quantity supplied. We shall argue that the equilibrium quantity maximizes the welfare of society as a whole. To do so, recall that the height of the market demand curve and short run market supply curves provides important information: The height of the market demand curve reflects the benefit households enjoy from consuming each unit of the good. The height of the short run market supply curve reflects the costs firms incur from producing each unit of the good. * * SS Equilibrium uantity Is the Welfare Maximizing uantity We shall argue that the equilibrium quantity is the welfare maximizing quantity in two steps: if less than the equilibrium quantity were produced, society as a whole would be made better off by producing more; if more than the equilibrium quantity were produced, society as a whole would be made better off by producing less. First, suppose that less than the equilibrium quantity were produced. Consider all the units between this quantity and the equilibrium quantity. Since the height of the market demand curve exceeds the height of the short run market supply curve, the benefits household would receive from the consumption of each of these units exceeds the costs firm would incur from producing them. From the standpoint of society as a whole these units should be produced. In other words, if less than the equilibrium quantity were produced, society as a whole would be made better off by producing more. * SS Second, suppose that more than the equilibrium quantity were produced. Consider all the units between this quantity and the equilibrium quantity. Since the height of the short run market supply curve exceeds the height of the market demand curve, the costs firms are incurring from the production of each of these units exceeds the benefits households are receiving from consuming them. From the SS *

21 8 standpoint of society as a whole these units should not be produced. In other words, if more than the equilibrium quantity were produced, society as a whole would be made better off by producing less. roducer Surplus - Long Run roducer surplus in the long run reflects the returns earned by the inputs (labor, capital, etc.). Geometrically, producer surplus in the long run is the area above the long run supply curve that lies below the price. To justify this we shall review what we learned about the long run supply curve. Recall the shape of the long run supply curve depends on what happens to input prices when entry or exit occurs. * LS Constant cost industry: horizontal long run supply curve In a constant cost industry, the cost of inputs is not affected by entry or exit; that is, entry and exit does not affect the returns to inputs. uestion: how will an increase in demand affect long run producer surplus? For a constant cost industry, long run producer surplus is unaffected. Since the long run supply curve is horizontal producer surplus is 0 before and after the increase in demand. Constant Cost Industry Entry oes Not Affect Input rices Returns to Inputs Unaffected Long Run roducer Surplus Unaffected * * * ** LS

22 9 Increasing cost industry: upward sloping long run supply curve The cost of inputs is driven up by entry; consequently, entry increases the returns to inputs. uestion: how will an increase in demand affect long run producer surplus? For an increasing cost industry, long run producer surplus increases. Since the long run supply curve is upward sloping, an increase in demand will increase producer surplus. Increasing Cost Industry Entry Increases Input rices Returns to Inputs Increases Long Run roducer Surplus Increases ** * * ** LS Supply Elasticities Recall that when we calculate elasticites we are always concerned with percent changes. Short Run rice Elasticity of Supply (E SS, ) Verbal efinition: E SS, reflects how sensitive the short run quantity supplied of a good is to the good s price. E SS, = the percent change in the short run quantity supplied resulting from a 1 percent change in the good s price percent change in short run quantity supplieded = percent change in the good's price Substituting in the expressions for the percent changes: Δ E SS, = 100 Δ 100 Simplfying, E SS, = Δ Δ = Δ Δ Taking limits as Δ approaches 0: E SS, = d d

23 10 Long Run rice Elasticity of Supply (E LS, ) Verbal efinition: E LS, reflects how sensitive the short run quantity supplied of a good is to the good s price. E LS, = the percent change in the long run quantity supplied resulting from a 1 percent change in the good s price percent change in long run quantity supplieded = percent change in the good's price Following the same logic as before E LS, = d d

24 Amherst College epartment of Economics Economics 54 Fall 2005 Thursday, October 20: Tax Incidence and Monopoly Application of Consumer and roducer Surplus - Tax Incidence Before Tax Equilibrium In equilibrium, uantity emanded = uantity Supplied. SS Effect of a Tax: Two Notions of the rice When a tax is imposed, two notions of the price emerge: one notion from the viewpoint of the households and a second from the viewpoint of the firms. These two notions of the price differ by the amount of the tax. To understand this, consider the gasoline tax. The legal * incidence of the gasoline tax is borne by the firm; that is, the firm is legally obligated to send the gasoline tax revenue to the government. In Massachusetts, the Federal and state tax now totals about \$.40 per gallon. For every gallon of gasoline the firm sells, it must sent \$.40 to the government. How is the price seen through the eyes of the firm, F, related to the price seen through the eyes of the household, H. The price seen from the viewpoint of the firm is just \$.40 less than the price seen from the viewpoint of the household because for each gallon sold, the firm must send \$.40 of what the household pays to the government: F = H.40 In general, F = H t where t = the tax rate * Illustrating the New Equilibrium How can we illustrate the new equilibrium? First, note that two conditions must be met at the new equilibrium F = H t uantity emanded = uantity Supplied Second, note that the quantity demand and the quantity supplied are sensitive to different notions of the price: uantity demanded is sensitive to the price as seen from the viewpoint of the household, H ; uantity supplied is sensitive to the price as seen from the viewpoint of the firm, F. To illustrate the new equilibrium, start at the old equilibrium and then reduce the quantity by moving to the left until the vertical gap between the market demand curve and market supply curve equals the amount of the tax, t. This quantity equals the new equilibrium quantity, **. The point on the market demand, ** H, is the new equilibrium price from the viewpoint of the households; the point on the market supply curve, ** F, is the new equilibrium price from the viewpoint of the firm. ** H ** F t ** SS Sensitive to F Sensitive to C

25 2 To argue that this illustrates the new equilibrium, we must show that ** F = ** H t and quantity demanded = quantity supplied First, it is easy to show that ** F = ** H t. This follows directly from the fact that the vertical gap between the market demand and market supply curve equals t. The above diagram clearly illustrates that ** F = ** H t Second, we must show that quantity demanded equals quantity supplied. Recall that the quantity demanded is sensitive to the price seen from the viewpoint of the household and the quantity supplied is sensitive to the price seen from the viewpoint of the firm: Household s viewpoint Firm s viewpoint rice = ** H rice = ** F uantity demand = ** uantity supplied = ** Both the quantity demand and the quantity supplied equal **. How does the tax affect households, firms, and the government? SS SS SS t ** H Consumer Surplus ** F roducer Surplus ** Tax Revenue = t ** Households and firms are hurt by the tax; the government is helped. Since the price paid by households rises as a consequence of the tax, consumer surplus falls. The shaded red area in the left diagram illustrates the fall in consumer surplus; that is, the shaded red area reflects how much consumers are hurt by the tax. Since the price received by firms falls as a consequence of the tax, producer surplus falls. The shaded blue area in the center diagram illustrates the fall in producer surplus; that is, the shaded blue area reflects how much firms are hurt by the tax. The government is helped by the tax, since it collects more revenues. uestion: how much revenue does the government collect from this tax? Answer: t **. The shaded green area in the right diagram reflects the tax revenue collected from the tax; that is, the shaded green area reflects how much the government is helped by the tax.

26 3 The amount by which households and firms are hurt by the tax exceeds the amount by which the government is helped. The net harm done to society as a whole is called the excess burden or dead weight loss of the tax. The shaded area to the right illustrates the excess burden. ** F roducer Surplus - Long Run roducer surplus in the long run reflects the returns earned by the inputs (labor, capital, etc.). Geometrically, producer surplus in the long run is the area above the long run supply curve that lies below the price. To justify this we shall review what we learned about the long run supply curve. Recall the shape of the long run supply curve * depends on what happens to input prices when entry or exit occurs. ** H t ** SS LS * Constant cost industry: horizontal long run supply curve In a constant cost industry, the cost of inputs is not affected by entry or exit; that is, entry and exit does not affect the returns to inputs. uestion: how will an increase in demand affect long run producer surplus? For a constant cost industry, long run producer surplus is unaffected. Since the long run supply curve is horizontal producer surplus is 0 before and after the increase in demand. Constant Cost Industry Entry oes Not Affect Input rices Returns to Inputs Unaffected Long Run roducer Surplus Unaffected * * ** LS

27 4 Increasing cost industry: upward sloping long run supply curve The cost of inputs is driven up by entry; consequently, entry increases the returns to inputs. uestion: how will an increase in demand affect long run producer surplus? For an increasing cost industry, long run producer surplus increases. Since the long run supply curve is upward sloping, an increase in demand will increase producer surplus. Increasing Cost Industry Entry Increases Input rices Returns to Inputs Increases Long Run roducer Surplus Increases ** * * ** LS

28 5 Monopoly review: Review of Key oints rofit Maximization: rofits = TR STC To find the profit maximizing quantity of outputs, differentiate profits with respect to quantity and set the derivative equal to 0: drofit = dtr dstc = 0 Clearly, to maximize profits, dtr = dstc MR = SMC Marginal Revenue Verbal definition: Marginal revenue equals the change in the firm s total revenue resulting from a one unit change in output. Calculus definition: Marginal revenue equals the derivative of total revenue with respect to quantity: MR = dtr Total revenue equals price times quantity: TR = q. Now, apply the rules of differentiation, MR = dtr = + qd What does d equal? That is, how does the quantity of output the firm produces affect the price. There are two polar cases: erfect competition Monopoly Large number of small firms One large firm No single firm s production The monopoly produces a decisions can significantly quantity and charges a price that affect the price lies on the market demand curve Each firm takes the price as To sell more output, the given; that is, each firm considers monopolist must reduce the price to be a constant the price d = d 01 < 0 Thus far, we have focused on the perfect competitive case. Now, we shall turn to monopoly. We have not yet justified the statements we make about monopoly. 1 We mentioned before this argument cheats a little; we shall address this shortly.

29 6 Notation First, a word about the notation we use. We have been consistent with our use of and q. We have used upper case to represent quantity in the entire market; we have used lower case q to represent production by a single firm. In the case of a monopoly, however, there is no need to differentiate between lower and upper case because there is only one firm in the industry. Consequently, in the monopoly case we can use upper case and lower case q interchangeably. Also, traditionally there is little distinction made between the short run and the long run when discussing monopoly. The reason for this is that for whatever reason if an industry is a monopoly, entry has not occurred. If we initially have a monopoly and entry occurs, suddenly we do not have a monopoly any more. Therefore, we typically drop references to short and long run when we discuss monopoly. Monopoly, the Market emand Curve, and Market Clearing Claim: A monopoly will always choose a market clearing price; that is, a monopoly will always produce a quantity and charge a price that lies on the market demand curve; that is, a monopoly will always clear the market. To justify this claim in two steps: First, we shall argue that a profit maximizing monopolist would never choose a price that would create a shortage; that is, a monopolist would never operate at a point below the market demand curve. Second, we shall argue that a profit maximizing monopolist would never choose a price that would create a surplus; that is, a monopolist would never operate at a point above the market demand curve. Why would a monopoly never operate at a point below the market demand curve? To explain why, suppose that it did. A profit maximizing firm would not be content with this situation. The firm could raise the price to the point on the market demand curve lying directly above and still sell all the quantity of output it was producing. Since the firm produces the same amount of output, total costs would not be affected. At the higher price, the firm would now collect more revenues. With higher revenues and the same costs, the firm s profits would rise. Why would a monopoly never operate at a point above the market demand curve? To explain why, suppose that it did. A profit maximizing firm would not be content with this situation. The firm is not able to sell all the output it is producing. Why incur the costs of producing something when it cannot be sold? The firm could reduce the quantity of output to the point on the market demand curve lying directly to the left with no change in the total revenues it collects. Since the firm is producing less, costs would fall. With the same total revenues and lower costs, the firm s profits would rise.

30 7 Since a profit maximizing monopoly would never create a shortage by operating at a point below the market demand curve or create a surplus by operating at a point above the market demand curve there is only one alternative left. The monopoly will always choose a market clearing price by operating at a point on the market demand curve. How will the quantity of output the monopoly produces be related to the price it charges? When the monopoly produces more, it must lower the price to sell the additional output; that is, when the monopoly produces more, it must charge a lower price to remain on the market demand curve: We can express this relationship in terms of a derivative: d d < 0 d where d is the derivative of the market demand curve Monopoly, Marginal Revenue, and Market emand What does this suggest about marginal revenue for a monopoly? Recall that MR = dtr d where TR = Clearly, MR = + q d d Since d d < 0, whenever the quantity of output is positive marginal revenue is less than price: MR < whenever >0 Let us summarize what we have just learned. For a given quantity of output, the monopolist will charge a price that lies on the demand curve and marginal revenue will be less than this price (whenever the quantity of output is positive). rice Marginal Revenue < rice We can now draw a monopoly s marginal revenue curve. MR

31 8 Monopoly s rofit Maximizing uantity Now, rofit = TR TC To find the profit maximizing quantity of outputs, differentiate profits with respect to quantity and set the derivative equal to 0: drofit d = dtr d dtc d = 0 Clearly, to maximize profits, dtr d = dtc d MR = MC The profit maximizing quantity of output is the quantity of M MC output at which marginal revenue equals marginal cost. What price will the monopoly charge? Remember that the monopoly will always operate at a point on the market demand curve. So, once we determine the profit maximizing quantity of output, we look to the market demand curve to determine the price. M MR How much profit is the firm now earning? The above diagram does not provide the information that we need to determine how much profit the monopoly firm is earning. Recall that profit depends on the relationship between price and average total cost. ATC = TC Multiplying by q: ATC = TC Since TR = and TC = ATC, we can substitute for TR and TC in the profit equation: rofit = TR TC = ATC Next, factor a q from both terms: rofit = ( ATC) Recall that when we draw the average total cost curve, we must be certain that it intersects the marginal cost curve at minimum average total cost. If the diagram to the right is accurate, the monopoly would be earning a positive profit. M ATC for q* units M MR MC ATC What is bad about a monopoly? Excess rofits - The opular Notion Most people believe a monopoly is bad because it earns obscenely high profits. While economists recognize that it is possible for a monopoly to earn high positive profits, it need not always be true. In other words, the view that the existence of a monopoly guarantees high profits is simply incorrect. To understand why, recall that rofit = ( ATC) ATC for q* units M M MR MC ATC

32 9 If when maximizing profits, the price falls short of average total cost; in the case, a monopoly will be incurring losses. The above diagram illustrates this. Consequently, since the existence of a monopoly does not guarantee high profits, high profits cannot be the reason that a monopoly is bad. Monopoly Leads and Excess Burden (ead Weight Loss) What If uestion: If the monopoly, for whatever reason, believed that it was one of many firms in a perfectly competitive industry, what quantity and price would result? In a perfectly competitive industry, the equilibrium quantity and price are determined by the market demand and market supply curve. the market supply curve is the horizontal sum of each firm s individual supply curve; an individual firm s supply curve is its marginal cost curve. If the monopoly really believed that it was one of many firms in a perfectly competitive industry, its individual supply curve would be its marginal cost curve. Since there is only one firm in a monopoly, the market supply curve would be the monopoly s individual supply curve. Consequently, the market supply curve would be the monopoly s marginal cost curve. The competitive price would be C and competitive quantity would be C. C C MC "S" Comparing the monopoly and competitive case. The monopoly firm is better off in the monopoly case because its profits are maximized when M units are produced. Since more than M units are produced in the competitive case, profits in the competitive case must be less than profits in the monopoly case. Households are better off in the competitive case. The competitive price, C, is less than M C the monopoly price, M. Households would clearly prefer to purchase the good at a low rather than a high price. How is society as a whole affected? The firm benefits from monopoly while households are hurt. We need to measure the magnitude of the benefit experienced by the monopoly firm and the harm done to households. Consumer and producer surplus allows us to do this. M C MR MC "S"

33 10 Competition Consumer surplus roducer surplus M MC "S" M MC "S" C C MR M C MR M C Monopoly Consumer surplus roducer surplus M MC "S" M MC "S" C C MR M C MR M C From Competition to Monopoly M Consumer surplus Lost MC "S" M roducer surplus Gained Lost MC "S" C C MR M C MR M C Some, but not all of the loss in consumer surplus is compensated by a gain in producer surplus. In net, there is a loss. In other words, the gain experience by the monopoly firm is less than the loss experienced by households. This represents the excess burden or dead weight loss of a monopoly. M C MC "S" MR M C

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