1 Chapter 13-14: Marginal Product, Costs, Revenue, and Profit Production Function The relationship between the quantity of inputs (workers) and quantity of outputs Total product (TP) is the total amount of output that is produced during a given period of time Average product (AP): (of a variable factor) is the TP divided by the number of units the variable factor used to produce it. Since labor is usually the most important variable factor in the short run, we usually talk of the average product of labour: AP = TP / L Marginal Product increase in output (TP) arising from an additional unit of that input, holding all other inputs constant helps firms decide whether they can produce more from more inputs MP = TP / L slope of the production function (TP); diminishes as L rises because TP gets flatter Law of diminishing returns: if increasing amounts of a variable factor are applied to a given quantity of the fixed factor, eventually the marginal product of the variable factor declines. - Ex: a worker who does everything required to manufacture a product. As more workers are added, each can specialize on one task, and marginal product rises. BUT if there is a fixed amount of physical capital, eventually the marginal product begins to decline (could be negative) Relation between AP and MP 1) MP > AP, MP rising then law of diminishing returns kicks in: MP falls while AP keeps rising 2) When MP = AP, it is the maximum of AP. (if the marginal thing = average, average won t change) 3) When MP < AP, AP falls as the MP of each additional worker is less than average, pulling down AP Relation between TP and MP 1) When TP is rising at an increasing rate (concave up), MP is positive and rising 2) When TP is rising at a decreasing rate (concave down), MP is positive and falling 3) When TP is at its maximum, MP is at 0 in the short run 4) When TP is falling, MP is negative (below Q Labour axis) Cost function Relationship between Q and cost of production The curve gets steeper as Q increases because of diminishing marginal product Total cost = fixed cost + variable costs Average total cost = AFC + AVC = (FC + VC) / Q - ATC curve U-shaped because initially, falling AFC pulls ATC down, then rising AVC pulls ATC up. Fixed cost: do not vary with Q produced average fixed cost: AFC = FC / Q - This is a sunk cost: a cost that has already been committed and cannot be recovered. You must pay them regardless of your choice. A firm must pay its fixed costs whether it shuts down or not.
2 - If you bought a ticket for $10, and value a movie for $15, buy another one even if you lose it Variable costs: vary with Q average variable cost: AVC = VC/Q rises as Q rises, eventually - Example: fixed cost would be the cost of land, variable cost would be the wages or material cost - Find the variable costs at different quantities Economies of scale: ATC falls as Q increases (more common when Q is low) - Occurs when increasing production allows greater specialization and more efficiency Constant returns to scale: ATC stays the same as Q increases Diseconomies of scale: ATC rises as Q increases (more common when Q is high) - Due to coordination problems in large organizations Marginal Cost The increase in TC from producing one more unit supply curve = Q willing to supply at any P - P is value to buyers of the marginal unit decide whether it s worth the cost to produce more In the short run, competitive firms (equilibrium) produce where P(market price) = MC MC = TC / Q usually rises as Q rises Relation between MC and ATC The MC curve crosses the ATC curve at the ATC curve s minimum - At low levels of output, MC < ATC, so ATC is falling. - But when the 2 curves cross, MC = ATC at minimum ATC = efficient scale (break even; 0 profit) - MC > ATC, so ATC must start to rise at this level of output. If where MC = ATC is less than the market price, (firm is producing at lower costs) the firm should produce more, at the market price produce at P where D = MC Costs in the Short run and Long run Short run: some inputs are fixed costs of these are the FC (fixed costs) Long run: all inputs are variable; curve is much flatter due to more flexibility factory size variable In LR, ATC at any Q is cost per unit using the cost efficient mix of inputs for that Q - minimums of each SRATC curve form the points of the LRATC firm s LR cost curve uses the most efficiency factory size with the lowest ATC - efficient scale: level of production with lowest ATC
3 Characteristics of Perfect Competition 1. Many buyers and many sellers 2. The goods offered for sale are largely the same 3. Firms can freely enter or exit the market no barriers (government does not restrict # firms) 1 and 2 means that each buyer and seller is a price taker: takes the price as given Competitive firm has an upward sloping total revenue curve and horizontal demand In the LR, supply curve is horizontal and in SR demand is horizontal? Revenue of a Competitive Firm Total revenue = P x Q - Because everyone s a price taker, Q doesn t affect P, and hence TR is proportional to Q. Average revenue (AR) = TR / Q = P Marginal revenue (MR): TR / Q; the change in TR from selling one more unit - For a competitive firm (can keep increasing its output without affecting the market price), each one-unit increase in Q causes the revenue to rise by P. Hence, MR = P = AR (NOT TR) Total revenue is maximized when MR = 0 Profit Maximization Profit = TR TC = (P ATC) x Q Explicit costs: require an outlay of money (ex: paying wages to workers) Implicit costs: do not require a cash outlay (ex: opportunity cost of the owner s time) Accounting profit: total revenue minus total explicit costs - ignores implicit costs, so it is higher than economic profit Economic profit: total revenue minus total costs (explicit AND implicit) - Shows the relationship between the quantity of inputs used to produce a good (x-axis), and the quantity of output of that good (y-axis) - Can be represented by table, equation, or graph profit maximizing Q is at P = MC (and remember P = MR = AR) in perfect competition - this means that changing Q would lower profit no matter what - if you think at the margin and make incremental adjustments to the level of production, you re naturally led to produce the profit-maximizing quantity. If increase Q by one unit, revenue rises by MR, and cost rises by MC. 3 rules for profit maximization: 1. If MR > MC, (under the MR = MC) then increase Q to raise profit 2. If MR < MC, (over MR = MC) then reduce Q to raise profit 3. Profit maximization is where MR = MC profit/loss is the rectangular area between P=MC and ATC (height = ATC P, width = Q) - loss: when P = MC is below ATC = MC (P<ATC) - Profit: When P=MC > ATC=MC (P>ATC)
4 Shutdown, Exit, New entrants Shutdown: a short run decision not to produce anything because of market conditions - Revenue falls by TR, Costs fall by VC - Firm should shut down if TR < VC P < AVC (TR/Q < VC/Q) - If P > AVC, then firm produces Q where P(MR) = MC - sunk costs should not affect decision, as you must pay them anyway - firm s SR supply curve is the portion of its MC above AVC Exit: a long run decision to leave the market - Revenue falls by TR, Costs fall by TC - Firm should exit if TR < TC P < ATC - Does not have to pay costs at all, fixed or variable. - Firm s LR supply curve is the portion of MC above ATC New entrants: LR: new firm will enter the market if TR > TC P> ATC Exit vs. new entrants Firm s LR supply curve is the portion of its MC curve above LRATC If existing firms earn positive economic profit: - New firms enter - SR market supply shifts right P falls, reducing profits - Entry stops when firms economic profits have been driven to zero If existing firms incur losses - Firms exit the market - SR market supply curve shifts left P rises, reducing remaining firms losses - Exit stops when firms economic losses have been driven to zero LR equilibrium: process of entry or exit is complete remaining firms earn 0 economic profit - the zero-profit condition is P = ATC - Since firms produce where P = MR = MC, then P = ATC = MC - MC intersects ATC at minimum ATC therefore, in the LR, P = minimum ATC Why firms stay in business if profit = 0 Recall that economic profit is total revenue minus all costs - This includes implicit costs, such as opportunity cost of owner s time and money In the zero-profit equilibrium, firms earn enough revenue to cover these costs
5 Market Supply Assumptions 1. All existing firms and potential entrants have identical costs 2. Each firm s costs do not change as other firms enter/exit the market 3. The number of firms in the market is (most reasonable assumption) - Fixed in the short run (due to fixed costs) - Variable in the long run (due to free entry and exit) The SR market supply curve in a competitive market A firm s SR supply curve is the portion of its MC curve above AVC As long as P >= AVC, each firm produces its profit maximizing quantity, where MR = MC At each price, the market QS is the sum of QS by each firm supply curve is a sum of costs? The LR market supply curve (with entry and exit) In LR, the typical firm earns 0 profit LR supply is horizontal at P = minimum ATC = efficient scale The LR market supply curve is horizontal if 1. All firms have identical costs (P of good = ATC of producing good) 2. Costs do not change as other firms enter or exit the market If either of these assumptions is not true, LR supply curve slopes up 1. Firms have different costs (P > ATC) As P rises, firms with lower costs enter the market before those with higher costs Only further increases in P make it worthwhile for higher-cost firms to enter the market (more profit to satisfy high costs), which increases market QS. Hence, LR market supply curve slopes upward At any P: o for the marginal firm, P= minimum ATC and profit = 0 (would leave if P was lower) o for lower-cost firms, profit > 0
6 2. costs rise as firms enter the market in some industries, supply of a key input is limited (ex: fixed amount of land suitable for farming) the entry of new firms increases demand for this input, causing its price to rise this increases all firms costs hence, an increase in P is required to increase the market QS, so the supply curve slopes up SR and LR effects of an increase in demand A firm begins in long run equilibrium, but then an increase in demand raises P In the short run, entry is not possible, so an increase in demand increases firms profits Leading to SR profits for the firm profits induce entry, shifting S right in the LR - reducing P, driving profits to 0 and restoring LR equilibrium