Profit Maximization

1. Profit Maximization Lecture 13

2. Today’s Topics Long Run Profit Maximization Should I be in this market? How much should I produce? Short Run Profit Maximization Should I shut down? How much should I produce?

3. Profit Maximization Firms are organized to produce a profit (surplus) for the owners of the organization. Remember in the long run, the opportunity costs of the manager as well as the owners of capital are included in the total costs of the firm. Total costs represent minimum costs. Profits are the difference between Total Revenues (TR) and Total Costs (TC) Profits = ? = TR - TC Assume that Firms are risk neutral Market is competitive, output sold by the firm will not affect the price of the good

4. Average Revenue: AR = TR/Q = PQ/Q = P Marginal Revenue: If the average is constant then the marginal must be equal to average. Revenue

5. Profit Maximization Managers will want to consider the following condition when choosing their output. The change in profits given a change in output equals: Hence The only difference between Long Run and Short Run pertains to the relevant costs: LR or SR. Note this ‘first order’ condition only states that at what level of output one should produce to maximize (or minimize) profits. One has to determine ‘second order’ conditions to determine whether one is making profits or not.

6. Long Run If the price is Po, will the firm produce? At Q* and Q**, Po = MC, however, at both output levels, the firm is not covering their costs Po < LRAC The firm won’t produce at this price and won’t produce until P = min LRAC

7. Long Run If the price is P, will the firm produce? At Q* and Q**, P = MC, however, at Q* the firm is not covering their costs P < LRAC But at Q**, the firm will make a profit and will produce at this level if the price is P.

8. Long Run Supply The portion of the LRMC where Q exceeds the level of output associated with minimum LRAC. In the LR, will a firm produce in the increasing returns to scale portion of their technology? If the market is competitive, what price should the firm expect if all firms have access to the same technology and face the same input prices?

9. Long Run Price Expectations If all firms (existing and potential competitors) have access to the same technology then they will have the same cost structure. In the long run, if the price exceeds the min LRAC then the profits should attract competitors and hence drive down the price until no profits exist. Hence if these conditions exist then the firm should expect P = min LRAC In general, the firm should expect the long run price to equal the minimum of the minimum LRAC of its competitors. If the firm can expect to maintain a long run cost advantage over its competitors then the firm can expect in the long run to make a surplus (revenues will exceed the firm’s opportunity costs)

10. In the long run, the firm will expect the price (PE) to equal minimum LRAC and consequently put in place a capital stock (KLR) that is both technically and cost efficient to produce QLR. What if price deviates from PE? How will the firm change its decision of how much to produce? Remember in the short run, the firm can’t change its capital stock. It can only change its output and work force.

11. If the price exceeds PE, the firm will want to expand its output but will it expand its output until P = LRMC?

12. At Q=QLR: SRATC = LRAC SRMC = LRMC At Q>QLR: SRATC > LRAC SRMC > LRMC Produce at P = SRMC(Q) ==> QSR Note, output rises but not as much as it would in the long run.

13. Will they produce at P = SRMC(Q) ==> QSR? Note in the LR, they would choose not to produce and ‘get out’ of the business if P remained at this level.

14. In the short run, what is their opportunity cost of being this market? Their total costs or just their labor costs? It is just their labor costs because their capital is ‘fixed’ in this business in the short run. Hence they will remain in business and operating at QSR if they can cover their opportunity costs (variable costs) P = min SRAVC They will shut down in the short run if P < min SRAVC

15. In the LR, if the firm expects P = min LRAC then the LRS is the ‘inverse’ of the LRMC above min LRAC. LRS is the ‘green’ relationship. In the SR (given the firm’s LR expectations) the SRS is the ‘inverse’ of the SRMC above min SRAVC. This is the ‘black’ relationship in the picture. Why is the LRS show more price responsiveness than the SRS?

16. Question about Firm Behavior How will the firm respond to a permanent decline in average revenues (P) if it continues to operate in both the SR and LR? If the price declines, the firm will reduce its output in the short run by laying off workers until P = SRMC or P = w/MPL. In the long run if the price remains low, the firm will restrict its output even further by shedding capital and perhaps even more labor (effect on labor is unclear).

17. More or Less Labor?

18. Questions about Firm Behavior Is it possible for the firm in response to a permanent decline in average revenues to Continue to operate in SR but shut down in LR? Yes if min LRAC > P > min SRAVC Shut down in SR and reopen in LR? Yes if min SRAVC > P > min LRAC