Modeling Firms’ Behavior

1. Modeling Firms’ Behavior • Most economists treat the firm as a single decision-making unit • the decisions are made by a single dictatorial manager who rationally pursues some goal • profit-maximization

2. Profit Maximization • A profit-maximizing firm chooses both its inputs and its outputs with the sole goal of achieving maximum economic profits • seeks to maximize the difference between total revenue and total economic costs

3. Output Choice • Total revenue for a firm is given by TR(q) = P(q)q • In the production of q, certain economic costs are incurred [TC(q)] • Economic profits () are the difference between total revenue and total costs  = TR(q) – TC(q) = P(q)q – TC(q)

4. Output Choice • The necessary condition for choosing the level of q that maximizes profits can be found by setting the derivative of the  function with respect to q equal to zero

5. Output Choice • To maximize economic profits, the firm should choose the output for which marginal revenue is equal to marginal cost

6. Profits are maximized when the slope of the revenue function is equal to the slope of the cost function But the second-order condition prevents us from mistaking q0 as a maximum q0 q* Profit Maximization revenues & costs TC TR output

7. Marginal Revenue • If a firm can sell all it wishes without having any effect on market price, marginal revenue will be equal to price • If a firm faces a downward-sloping demand curve, more output can only be sold if the firm reduces the good’s price

8. Marginal Revenue • If a firm faces a downward-sloping demand curve, marginal revenue will be a function of output • If price falls as a firm increases output, marginal revenue will be less than price

9. Marginal Revenue • Suppose that the demand curve for a sub sandwich is q = 100 – 10P • Solving for price, we get P = -q/10 + 10 • This means that total revenue is TR = Pq = -q2/10 + 10q • Marginal revenue will be given by MR = dTR/dq = -q/5 + 10

10. Profit Maximization • To determine the profit-maximizing output, we must know the firm’s costs • If subs can be produced at a constant average and marginal cost of $4, then MR = MC -q/5 + 10 = 4 q = 30

11. Average Revenue Curve • If we assume that the firm must sell all its output at one price, we can think of the demand curve facing the firm as its average revenue curve • shows the revenue per unit yielded by alternative output choices

12. Marginal Revenue Curve • The marginal revenue curve shows the extra revenue provided by the last unit sold • In the case of a downward-sloping demand curve, the marginal revenue curve will lie below the demand curve

13. Marginal Revenue Curve As output increases from 0 to q1, total revenue increases so MR > 0 price As output increases beyond q1, total revenue decreases so MR < 0 P1 D (average revenue) output q1 MR

14. Marginal Revenue Curve • When the demand curve shifts, its associated marginal revenue curve shifts as well • a marginal revenue curve cannot be calculated without referring to a specific demand curve

15. P* = MR Maximum profit occurs where P = SMC q* Short-Run Supply by a Price-Taking Firm price SMC SATC SAVC output

16. Since P > SATC, profit > 0 Short-Run Supply by a Price-Taking Firm price SMC SATC P* = MR SAVC output q*

17. P** If the price rises to P**, the firm will produce q** and  > 0 q** Short-Run Supply by a Price-Taking Firm price SMC SATC P* = MR SAVC output q*

18. If the price falls to P***, the firm will produce q*** P*** q*** Short-Run Supply by a Price-Taking Firm price SMC SATC P* = MR SAVC profit maximization requires that P = SMC and that SMC is upward-sloping output q*  < 0

19. Short-Run Supply by a Price-Taking Firm • The positively-sloped portion of the short-run marginal cost curve is the short-run supply curve for a price-taking firm • it shows how much the firm will produce at every possible market price • firms will only operate in the short run as long as total revenue covers variable cost • the firm will produce no output if P < SAVC

20. Short-Run Supply by a Price-Taking Firm • Thus, the price-taking firm’s short-run supply curve is the positively-sloped portion of the firm’s short-run marginal cost curve above the point of minimum average variable cost • for prices below this level, the firm’s profit-maximizing decision is to shut down and produce no output

21. The firm’s short-run supply curve is that portion of the SMC curve that is above minimum SAVC Short-Run Supply by a Price-Taking Firm price SMC SATC SAVC output

22. Supply Function • The supply function for a profit-maximizing firm that takes both output price (P) and input prices (v,w) as fixed is written as quantity supplied = q*(P,r,w) • this indicates the dependence of output choices on these prices

23. Supply Function • The supply function provides a convenient reminder of two key points • the firm’s output decision is fundamentally a decision about hiring inputs • changes in input costs will alter the hiring of inputs and hence affect output choices as well

24. Producer Surplus in the Short Run • A profit-maximizing firm that decides to produce a positive output in the short run must find that decision to be more favorable than a decision to produce nothing • This improvement in welfare is termed (short-run) producer surplus • what the firm gains by being able to participate in market transactions

25. If the market price is P*, the firm will produce q* P* Producer surplus is the shaded area below P* and above SMC q* Producer Surplus in the Short Run SMC price output

26. Producer Surplus in the Long Run • By definition, long-run producer surplus is zero • fixed costs do not exist in the long run • equilibrium profits under perfect competition with free entry are zero