Profit Maximization. Econ 410: Micro Theory. Profit Maximization. Recall from last time. Firm Profit Maximization and Competitive Supply. q 0.
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1 lide 1 lide 3 Econ 410: Micro Theory Firm Profit Maximization and Competitive upply Wednesday, November 14 th, 2007 Profit is positive when R(>C( Profit Maximization ince profit is equal to the difference between revenue and costs, firms want to maximize this distance. Graphically: $ 0 B A q 0 q* C( R( ( Profit is maximized where R( C( is maximized This occurs where MR (slope at A) and MC (slope at B) are equal lide 2 lide 4 Recall from last time We assume that a firm s goal is to maximize profits Profit ( ) = Total Revenue - Total Cost Total Revenue (R) = P q A competitive firm Chooses output to maximize its profit function Takes prices for both inputs and outputs as given ( R( C( Profit Maximization Profit is maximized at the point at which an additional increment to output leaves profit unchanged. Why? If MR>MC. If MR<MC. Mathematically ( R( C( Firms choose quantity to maximize their profit function (differentiating w.r.t. R C 0 MR MC 0 MR MC q q q
2 lide 5 lide 7 Competitive Firms We know a competitive firm is a price taker. How does this affect the relationship between a competitive market demand curve and the demand curve for an individual firm? The demand curve faced by an individual firm is a horizontal line. Why? A firm s sales have no effect on market price The demand curve faced by an entire market is downward sloping. Why? hows amount of goods all consumers will purchase at different prices These facts tell us that a perfectly competitive firm maximizes profit when: = MR = MC( But, it is not always true that the optimal choice for a firm results in short run economic profits. A firm will incur losses if P < ATC for the profit maximizing quantity We can find total profit by finding the profit per unit and multiplying by q. If P<ATC, profit per unit is negative lide 6 lide 8 Competitive Firms $1 Firm For a perfectly competitive firm, P=MR. Why? d $1 Industry How would we find the firm s profits or losses? Losses = (P- AC) x q * or area ABCD C D At q * : MR = MC and P < ATC B A MC AVC ATC P = MR D ( 100,000 (Q) q *
3 lide 9 lide 11 Competitive firms and profit If P > ATC, the firm is making profits If P < ATC, the firm is experiencing losses Why would a firm produce at a loss? could be expected to increase soon. hutting down and starting up is costly A firm has two choices in the short run: Continue producing hut down temporarily Firms will compare the profitability of each choice ample Exam Question Bette's Breakfast, a perfectly competitive eatery, sells its "Breakfast pecial" for $5.00. The costs of waiters, cooks, power, and food average out to $3.95 per meal; the costs of the lease, and insurance averages out to $1.25 per meal. Bette should: a) Close her doors immediately. b) Continue producing in the short and long run. c) Continue producing in the short run, but plan to go out of business in the long run. d) Raise her prices. e) Lower her output. lide 10 lide 12 When should a firm shut down? If AVC < P < ATC, the firm should continue producing in the short run This enables the firm to cover all of its variable costs and some of its fixed costs If AVC <ATC< P, the firm should shut down In this case, the firm cannot cover its variable costs or any of its fixed costs Recall that a supply curve indicates the quantity of a good that will be produced at every possible price What does a supply curve for a competitive firm look like in the short run? A competitive firms supply curve is the portion of the marginal cost curve that lies above the AVC curve. Why? Graphically
4 lide 13 lide 15 ($ per unit) P 2 P 1 A firm chooses the output level where P = MR = MC, as long as P > AVC. Because of this, a firm s short run supply is the portion of MC lying above AVC MC ATC AVC $1 avings to the firm from reducing output MC 2 MC 1 How could we show an increase in inputs costs on this graph? As input cost increases, MC shifts to MC 2 and q falls to q 2. P = AVC q 1 q 2 q 2 q 1 lide 14 lide 16 Why is the firm s supply curve upward sloping? Diminishing returns How does the firm s output change in response to a change in the price of an input? We can show how an increase in marginal costs will affect a firm s output decisions graphically and mathematically How can we find the supply curve for the entire market? By summing the supply curves of all the individual producers in the market Changes in & Market upply As the price of a good rises, output increases But, in the short run, supply could be less responsive to price. Why? Increased demand for inputs raises their price This could cause a firm s marginal cost to increase, lowering optimal output
5 lide 17 lide 19 $ per unit P 3 P 2 P 1 MC MC MC 3 The short-run industry supply curve is the horizontal summation of the supply curves of each firm Q Elasticity of upply Perfectly inelastic short-run supply arises when An industry s plant and equipment are so fully utilized that output can t be increased without building more factories Perfectly elastic short-run supply arises when Marginal costs are constant Why? lide 18 lide 20 Elasticity of upply Elasticity of Market upply Measures the sensitivity of industry output to market price The percentage change in quantity supplied in response to 1-percent change in price, or: E s ( Q / Q) /( P / P) Changes in Marginal Cost and Elasticity When MC increases rapidly in response to increases in output, supply is relatively inelastic. When MC increases slowly, supply is more elastic A Producer urplus A firm s producer surplus is: The sum over all units produced of the difference between the market price of the good and the marginal cost of production Area above supply curve to the market price MC AVC Producer urplus B & AVC P Is producer surplus the same as profit? Producer urplus q *
6 lide 21 lide 23 ample Exam Question The decision of a firm to shut down can be restated in terms of producer surplus by saying that a firm should produce in the short run as long as: a) Revenue exceeds producer surplus. b) Producer surplus is positive. c) Producer surplus exceeds fixed cost. d) Producer surplus exceeds variable cost. e) Profit and producer surplus are equal. For next time We ll look at how competitive markets change in the long run Please Read: Pages and sections of your textbook Problem et Reminder Exercises 2-4 on page 260 of your textbook #2 and #3 are worth 2 points each, and #4 is worth 6 points Due Date: Monday, November 26 th lide 22 Producer urplus How would we find producer surplus for an entire market? By adding up the surplus for all producers Equal to the area below the market price and above the supply curve P * Producer urplus D Q *
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