1. Lecture 8 Short Run Profit Maximization Long Run Cost Curves
Sources:  
Case, Fair, Oster, Introduction to Microeconomics
Case, Fair, Principles of Microeconomics

2. Short Run Profit Maximization
Profit () = total revenue (tr) - total cost (srtc).
Profit depends on the firm’s output level (q).
So…  (q) = tr(q) - srtc(q).
Firm’s problem:
choose q* to maximize  (q) = tr(q) - srtc(q).
Note the behavior of total revenue as q changes and total cost as q changes is very important.
Define:
Marginal revenue (mr) = tr/q
Marginal cost (srmc) = tc/q

3. Rules For Profit () Maximization in the Short Run
Firm’s problem:
choose q* to maximize  (q) = tr(q) - srtc(q).
Define:
Marginal revenue (mr) = tr/q
Marginal cost (srmc) = tc/q
If q* maximizes  , then:
(1) mr(q*) = srmc(q*)
the first order condition, or f.o.c.
Very important note: for a price-taking firm, P=mr at all values of q.
Therefore, for a perfectly competitive firm, at q*, P = srmc.
(2)  (q*) is a maximum and not a minimum.
the second order condition, or s.o.c
(3) at q* it is worth operating (stay open ie. Not shut down):  (q*>0)   (q=0)

4. Intuition: Why mr=mc at the Profit Maximizing q*
If mr > mc at q, then…
If mr < mc at q, then…
If mr = mc at q*, then…
Note again: For a perfectly competitive firm, P=mr at every q,
so if mr=mc at q*  P=mc at q*.

5. Short Run Profit Maximization in a Perfectly Competitive Output Market
Introduce some “new” notation.
Ahmet’s output: q
The aggregate output of the entire apple market: Q
The market price for apples: P
Ahmet is a “price taker”.
Ahmet’s perceived demand for HIS apples (δ) will be the prevailing market price P.
So… for Ahmet, δ = P = marginal revenue.

6. Ahmet’s Profit Maximizing Move When P=$528

7. q
In the short-run, it is possible for an individual firm to make an economic profit. This situation is shown in this diagram, as the price or average revenue, denoted by P, is above the average cost denoted by C.

8. q
However, in the long period, economic profit cannot be sustained. The arrival of new firms or expansion of existing firms in the market causes the (horizontal) demand curve of each individual firm to shift downward, bringing down at the same time the price, the average revenue and marginal revenue curve. The final outcome is that, in the long run, the firm will make only normal profit (zero economic profit

9. Three Long Run Cost Curves
Consider the following… q = f(K, L) where q is firm output, K is firm capital and L is firm labor and where PK is the unit price of capital and PL is the unit price of labor.
There are three long run cost curves for the firm:
long run total cost lrtc = PLL*(q) + PKK*(q)
long run average total cost lratc = lrtc/q
long run marginal cost lrmc = lrtc/q
The most important is the lratc curve.

10. The Long Run Average Total Cost
In the long run, all inputs (factors of production) are variable. Consequently, a firm's output and costs are unconstrained in the sense that the firm can produce any output level it chooses by employing the needed quantities of inputs (such as labor and capital) and incurring the total costs of producing that output level.
The Long Run Average Cost, LRAC, curve of a firm shows the minimum or lowest average total cost at which a firm can produce any given level of output in the long run (when all inputs are variable).
In the long run, a firm will use the level of capital (or other inputs that are fixed in the short run) that can produce a given level of output at the lowest possible average cost. Consequently, the LRAC curve is the envelope of the short run average total cost (SR ATC) curves, where each SR ATC curve is defined by a specific quantity of capital (or other fixed input).

11. Getting the Long Run Average Total Cost Curve for Three Different Levels of K

12. q

13. When the lratc curve is falling it is said to exhibit internal economies of scale.
When the lratc curve is rising it is said to exhibit internal diseconomies of scale.

15. If the long run price were to be above the minimum LRATC, firms in the market will be making a profit
(remember, if P > ATC, there is profit).
This would attract new firms to enter the market.
The output of these new entrants would lower the price, thus removing the economic profit.
The result will be a long run equilibrium, in which the price must be equal to the minimum long run average total cost.
The producers in the market will thus make zero economic profit in the long run (there still may be temporary short run profit for brief periods, however).

16. q

17. Why Are There Zero Economic Profits in the Long Run?
Zero economic profits means that all factors used in production make exactly their opportunity cost.
Purchased factors receive their market price, which is equal to their opportunity cost.
Owned factors receive the same compensation that they would receive in their next best use, which is also equal to their opportunity cost.
Thus, no firm wants to enter the market because it cannot make any more money than it is currently making.
Similarly, no firm wants to leave the market because it cannot make any more money in any other business.

18. Long Run Equilibrium in Perfectly Competitive Markets
All the short run equilibrium properties hold.
But also add… no firms wish to exit the market nor do firms want to enter.
Given: market demand, factor prices and technology
Get: (P*, Q*, q*)
Note: For there to be neither entry or exit, need economic profit to be zero. This is a long run equilibrium requirement.

19. Long Run Equilibrium Position with Identical Firms
Firms are profit maximizing  mr = mc at q* for each firm.
Zero profit required  P* = lratc at q* for each firm.
Since the firm is perfectly competitive,  P* = mr at all values of q for the firm.
By substitution, at q*, P* = mc and P* = lratc.
Therefore, at q*, mc = lratc.
Therefore, q* is at the minimum of the typical firm’s lratc curve.
P* must be the price consistent with the minimum value on the typical firm’s lratc curve.