ECON 21 Principles of Microeconomics (Summer 216) The Production Process and of Production Relevant readings from the textbook: Mankiw, Ch. 13 The of Production Suggested problems from the textbook: Chapter 13 Questions for Review (Page 275): 1, 3, 5, 6, and 7 Chapter 13 Quick Check Multiple Choice (Pages 275-276): 1, 3, and 4 Chapter 13 Problems and Applications (Pages 276-277): 1, 2, 3, 4, 5, 6, 7, 8, 9, and 1 Definitions and Concepts: Profit Total Revenues minus Total. Explicit inputs costs that require an outlay of money by the firm (i.e., costs associated with paying an out-of-pocket expense to acquire/use a factor of production). Implicit inputs costs that do not require an outlay of money by the firm (i.e., costs associated with incurring a non-monetary, opportunity cost to acquire/use a factor of production). Total Economic a notion of costs which includes all costs of hiring inputs, both explicit costs and implicit costs (i.e., Total Economic are equal to the sum of Explicit and Implicit ). Assume that (unless otherwise noted), Total refer to Total Economic (i.e., Total include not only Explicit but also Implicit ) Accounting Profit a measure of profit defined as the difference between Total Revenues and Total Explicit Economic Profit a measure of profit defined as the difference between Total Revenues and Total Economic Assume that (unless otherwise noted), Profit refers to Economic Profit Relation between Accounting Profit and Economic Profit. (Accounting Profit) = (Total Revenues) (Total Explicit ) (Economic Profit) = (Total Revenues) (Total Economic ) = (Total Revenues) (Total Explicit + Total Implicit ) = (Total Revenues) (Total Explicit ) (Total Implicit ) = (Accounting Profit) (Total Implicit ) (Accounting Profit) = (Economic Profit) + (Total Implicit )
Production Function the relationship between quantities of inputs used to make a good and the of output of the good produced. Marginal Product the increase in output resulting from using an additional unit of an input. Diminishing Marginal Product the property whereby the marginal product of an input declines in value as the used of the input is increased. Fixed costs that do not vary in magnitude as the of output produced is changed Variable costs that do vary in magnitude as the of output produced is changed (Total ) = (Variable ) + (Fixed ) Average Total Total divided by of output produced. [ATC=(TC)/(Q)] Average Variable Variable divided by of output produced. [AVC=(VC)/(Q)] Average Fixed Fixed divided by of output produced. [AFC=(F)/(Q)] Relation between different notions of Average. Since: (Total ) = (Variable ) + (Fixed ) It follows that: (Average Total ) = (Total )/(Quantity of Output) = (Variable + Fixed )/(Quantity of Output) = (Variable )/(Quantity) + (Fixed )/(Quantity) = (Average Variable ) + (Average Fixed ) That is: (ATC) = (AVC) + (AFC) Marginal a measure of the increase in Total of production associated with producing a greater amount of total output (typically defined as the change in total costs divide by the increase in of output ) General relation between an Average and the corresponding Marginal. Average Value will increase if and only if the current Marginal Value is greater than the previous average Average Value will decrease if and only if the current Marginal Value is less than the previous average
Efficient Scale the efficient scale of production refers to the of output at which Average Total of production are minimized. Short Run a period of time sufficiently short so that the amount hired/used of at least one input is equal to some predetermined level (based upon a previous decision) In the Short Run, the fixed inputs are being hired in predetermined quantities => fixed costs represent the predetermined costs of hiring these fixed inputs in their predetermined quantities Long Run a period of time sufficiently long so that the amount hired/used of every input can be varied In the Long Run the firm has the flexibility to hire zero units of every input => incur zero costs of production => fixed costs are equal to zero => all costs are variable Economies of Scale the property whereby average total costs of production decrease as the of output is increased [producing twice as much output costs less than twice as much ] Diseconomies of Scale the property whereby average total costs of production increase as the of output is increased [producing twice as much output costs more than twice as much ] Constant Scale Economies the property whereby average total costs remain constant as the of output is increased [producing twice as much output costs exactly twice as much ]
Graphical Relation of Average Variable to Marginal : Recall, AVC = (Variable )/(Quantity) For the first unit of output, variable costs are equal to simply marginal costs of the first unit => AVC must start out equal to MC Further: AVC declining MC < AVC AVC increasing MC > AVC MC(q) Minimum level of Average Variable AVC(q) Quantity of output at which Average Variable are minimized Thus, MC(q) intersects AVC(q) at the minimum of AVC(q) (implying that MC(q)=AVC(q) at the level of output at which AVC(q) achieves it s minimum)
Graphical Relation of Average Total to Marginal : Minimum level of Average Total ATC = (Total )/(Quantity) = (Variable )/(Q) + (Fixed )/(Q) Note that total costs for the first unit consist of more than just variable costs of the first unit => as a result, ATC will start out above MC But, since Marginal measure how Total change as more output is produced, we still have ATC declining MC < ATC ATC increasing MC > ATC MC(q) ATC(q) Efficient Scale Again, MC(q) intersects ATC(q) at the minimum of ATC(q) (implying that MC(q)=ATC(q) at the level of output at which ATC(q) achieves it s minimum) Efficient Scale the efficient scale of production refers to the of output at which Average Total of production are minimized.
Graphical Relation between Average Variable and Average Total : Recall that ATC=AVC+AFC Since AFC are positive, it immediately follows that at every level of output ATC are greater than AVC Since AFC = (Fixed )/(Quantity) it follows that AFC are decreasing in of output (i.e., AFC become smaller as more output is produced) By definition, Fixed do not change as more output is produced Thus, when AFC are computed at a higher level of output, Fixed are spread over more units => AFC must be smaller Since ATC = AVC + AFC => AFC = ATC AVC Graphically, AFC is the vertical distance between ATC and AVC Since AFC decreases as (q) increases => red curve and blue curve must get closer to each other at higher levels of output AFC at Low ATC(q) AVC(q) AFC at High Low High
Illustration of Total based upon ATC curve: Recall that ATC = (Total )/(Quantity) It follows that (Total ) = (Quantity)(ATC) Visually, the (Total ) of producing an arbitrary level of output can be illustrated as the area of the rectangle from the ATC curve back to the origin (the base of this rectangle is equal to the of output on which we are focusing and the height of this rectangle will be equal to the ATC of producing the of output on which we are focusing) If ATC of producing 5, units are 6., then TC of producing 5, must be (5,)(6) = (3,) Total of producing 5, units => equal to yellow area ATC(q) 6. A 5,
Illustration of Variable based upon AVC curve: Likewise, AVC = (Variable )/(Quantity) It follows that (Variable ) = (Quantity)(AVC) Visually, the (Variable ) of producing an arbitrary level of output can be illustrated as the area of the rectangle from the AVC curve back to the origin (the base of this rectangle is equal to the of output on which we are focusing and the height of this rectangle will be equal to the AVC of producing the of output on which we are focusing) If AVC of producing 5, units are 5., then VC of producing 5, must be (5,)(5) = (25,) Variable of producing 5, units => equal to green area 5. AVC(q) 5,
Illustration of Variable based upon MC curve: Suppose that the AVC of producing 4, are 4. => previous approach would allow us to calculate that VC of producing 4, are (4,)(4) = (16,) What we want to recognize at this point, if that the Variable could also be obtained by focusing on the area below the Marginal Cost curve up to 4, units of output (i.e., adding up the additional costs of producing the next unit of output for each of the first 4, units produced ) Variable of producing 5, units => equal to pink area MC(q) 4. AVC(q) 4,
Relation between Long Run and Short Run : For simplicity, first suppose that the input which will be fixed in the Short Run (say, retail store size ) can take on one of only three values (e.g., we could have either a small store, a medium size store, or a large store ) In essence, there will be a distinct Short Run Average Total Cost Curve for each of these three different values of store size ATC Small (q) ATC Mid (q) ATC Big (q) Big ATC Small ATC In the Short Run the producer is essentially stuck with one of these three Average Total Curves (based upon the retail store size which he chose last period, when he signed the lease) (2,) (2,) ATC Mid (q) ATC Big (q) Mid ATC (2,) 2,
Relation between Long Run and Short Run (continued): In contrast, in the Long Run the producer has the flexibility to choose the curve along which they will operate To produce 2, units in the Long Run, the producer would clearly choose the medium size store => when choosing similarly at all levels Long Run Average Cost Curve is essentially the Lower Envelope of all of the corresponding Short Run Average Total Cost Curves ATC Big (q) ATC Small (q) ATC Mid (q) If the input/factor which is fixed in the Short Run can only be hired/used in discrete quantities, then the LRAC will be scallop-shaped as illustrated above If instead this input/factor could be hired/used in a continually varied, then the LRAC will be a nice smooth curve as illustrated below (where at each point there is a Short Run ATC curve which just touches the LRAC curve) Long Run Average Cost Curve as the Lower Envelope of infinitely many Short Run Average Total Cost Curves ATC 789 ( q) ATC 23 ( q) ATC 412 ( q)
Visual illustration of Economies of Scale and Diseconomies of Scale: Economies of Scale the property whereby average total costs of production decrease as the of output is increased [producing twice as much output costs less than twice as much ] Diseconomies of Scale the property whereby average total costs of production increase as the of output is increased [producing twice as much output costs more than twice as much ] Constant Scale Economies the property whereby average total costs remain constant as the of output is increased [producing twice as much output costs exactly twice as much ] Long Run Average Economies of Scale Constant Scale Economies Diseconomies of Scale
Problem: 1. Consider a firm operating in the Short Run. All inputs are fixed other than labor. The first three columns in the table below provide a partial summary of the Short Run Production Function of this firm (the relation between number of workers hired per week and output per week). The remaining columns provide a partial summary of Short Run of this firm. Based upon the values provided, correctly fill in all empty cells in this table (for non-integer values, report your answer to two digits beyond the decimal ). Number of Workers Quantity of Output Marginal Product of Labor Fixed Variable Total Average Fixed 1 4 2 2 5 3 7 4 78 5 84 6, 6 4 7 3 8 2 9 94 1 945 Average Variable Average Total Marginal Multiple Choice Questions: 1. If a firm made an Accounting Profit of 65, last year, then the Economic Profit of the firm A. must have been greater than 65,. B. must have also been equal to 65,. C. must have been less than 65, (but had to have been positive). D. must have been less than 65, (and could have been either positive or negative). 2. refer(s) to input costs that do not require an outlay of money by the firm. A. Profit B. Implicit C. Explicit D. Accounting 3. The Efficient Scale of Production refers to A. the level of output above which all Fixed can be avoided. B. the level of output which minimizes Average Fixed of production. C. the level of output which minimizes Average Total of Production. D. the level of output at which Marginal of Production become negative.
4. In the Short Run, the only variable input which Company X hires is labor. Suppose that the Marginal Product of Labor is always positive. When increasing the amount of labor hired from 99 units to 1, output increases from 2 units to 21 units. If the production process of this firm exhibits a Diminishing Marginal Product of Labor, then units of output would be produced if 11 units of labor were hired. A. fewer than 21 B. more than 21 but fewer than 22 C. exactly 22 D. more than 22 5. In his first game as a professional quarterback for the Atlanta Falcons Matt Ryan threw for 161 yards. In his second game he threw for 158 yards. From this information alone it follows that his average number of yards per game A. was higher after the second game than after the first game. B. was lower after the second game than after the first game. C. did not change after the second game (that is, the average after the second game was exactly equal to the average after the first game). D. became negative after the second game. 6. Average Fixed costs of Production A. measure the increase in total costs of production associated with producing a greater amount of total output. B. are defined as Fixed of Production divided by of output produced. C. are equal to Average Total of Production minus Average Variable of Production. D. More than one of the above answers are correct. 7. If a firm is currently operating at a point where costs of production exhibit Economies of Scale, then as the firm increases its level of output A. Average Total of Production must decrease. B. Average Total of Production must increase. C. Average Fixed costs of production must remain constant. D. Total of Production must decrease. 8. The is defined as a period of time sufficiently long so that the amount hired/used of every factor of production can be varied. A. Profitability Stage B. Efficient Scale C. Short Run D. Long Run
For questions 9 through 12, consider a firm with costs of production as illustrated below: 9. ATC(q) 6. 5. 4.4 AVC(q) 5 1,4 2, 9. Based upon the graph above, this firm is currently operating in the A. Long Run, since no Marginal Cost Curve has been drawn. B. Medium Run, since Average Variable are clearly positive at all levels of output. C. Short Run, since Marginal of production are clearly positive. D. Short Run, since Fixed of Production are clearly positive. 1. The Marginal Cost of producing the 5 th unit of output must be A. less than 5.. B. equal to 5.. C. greater than 5., but less than 9.. D. equal to 9.. 11. The Efficient Scale of production is equal to units of output. A. B. 5 C. 1,4 D. 2, 12. If this firm were to produce 5, units of output, Fixed of Production would be equal to A. 4. B. 2,. C. 5,. D. 12,.
Answer to Problem: 1. The cells which contain values that were given have been shaded in yellow in the table below. Number of Workers Quantity of Output Marginal Product Fixed Variable Total Average Fixed Average Variable Average Total Marginal of Labor 3, 3, 1 4 4 3, 1,2 4,2 7.5 3 1.5 3 2 6 2 3, 2,4 5,4 5 4 9 6 3 7 1 3, 3,6 6,6 4.29 5.14 9.43 12 4 78 8 3, 4,8 7,8 3.85 6.15 1 15 5 84 6 3, 6, 9, 3.57 7.14 1.71 2 6 88 4 3, 7,2 1,2 3.41 8.18 11.59 3 7 91 3 3, 8,4 11,4 3.3 9.23 12.53 4 8 93 2 3, 9,6 12,6 3.23 1.32 13.55 6 9 94 1 3, 1,8 13,8 3.19 11.49 14.68 12 1 945 5 3, 12, 15, 3.17 12.7 15.87 24 Focusing first on the columns labeled Quantity of Output and Marginal Product of Labor, recall that Marginal Product of Labor provides a measure of the amount by which Quantity of Output increases when an additional unit of labor is hired. It follows that Quantity of Output when 2 workers are hired must be 4+2=6. Likewise, when 6, 7, and 8 workers are hired the respective levels of output are 84+4=88, 88+3=91, and 91+2=93. It then follows that the MPL of the first worker hired is 4-=4. Similarly, the MPL for the 3 rd, 4 th, 5 th, 9 th, and 1 th workers are (respectively) 7-6=1, 78-7=8, 84-78=6, 94-93=1, and 945-94=5. Next note that Average Fixed are 5 when 2 workers are hired and 6 units of output are produced. Since AFC=F/q, this implies that F=(q)(AFC)=(6)(5)=3,. Since Fixed do not change, we have that Fixed are equal to 3, in each row. From here we can determine the AFC at every level other than 2 workers, by calculating AFC=(3,)/(q). For example, when 1 worker is hired and 4 units are produced: AFC=(3,)/(4)=(7.5). Similarly, when 1 workers are hired and 945 units are produced: AFC=(3,)/(945)=3.17. Note that the Variable of hiring 5 workers is 6,. This implies that the wage rate of each worker is (6,)/(5)=1,2. It follows that the Variable in every other row are simply (1,2)(Number of Workers). For example, when hiring 2 workers Variable are (1,2)(2)=2,4. Marginal are defined as (Change in )/(Change in Output) as additional output is produced. In the current context, this ratio can be expressed as (Per Unit Wage Rate of Labor)/(MPL)=(1,2)/(MPL). For example, the Marginal Cost of hiring the 4 th worker and increasing output from 7 to 78 is (1,2)/(8)=15. Total are simply the sum of Variable and Fixed. For example, when hiring 6 workers TC=7,2+3,=1,2. AVC=(VC)/(q) and ATC=(TC)/(q). For instance, when hiring 2 workers and producing 6 units, AVC=(2,4)/(6)=4 and ATC=(5,4)/(6)=9.
Answers to Multiple Choice Questions: 1. D 2. B 3. C 4. B 5. B 6. D 7. A 8. D 9. D 1. A 11. D 12. B