1. Profit Maximization Rules
Dr. Jennifer P. Wissink
©2011 John M. Abowd and Jennifer P. Wissink, all rights reserved.

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 the behavior of total cost as q changes, is very important.
Define:
Marginal revenue (mr) = tr/q
Marginal cost (srmc) = srtc/q
NOTE: This procedure is good, no matter what type of firm considered.

3. Short Run Total Costs And Economic Profit
Short Run Total Costs include:
fixed costs and variable costs, which can be
explicit costs or implicit costs
Explicit costs: ones that go through a market transaction
remember... these can be fixed and variable
Implicit costs: opportunity cost of owned factors (such as the owner’s time, land, and equipment owned by the business)
Profit is Economic Profit:
the difference between total revenue from sales and total costs, as defined above.
Economic Profit vs. Accounting Profit
Accounting profit = total revenue – explicit costs
Economic profit = total revenue – explicit costs – implicit costs
Economic profit = accounting profit – implicit costs

4. 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.
(2)  (q*) is a maximum and not a minimum.
the second order condition, or s.o.c.
(3) at q* it is worth operating:  (q*>0)   (q=0).

5. Intuition For Rule (1): Why mr=mc At The Profit Maximizing q*
If mr > mc at q, then… by an incremental increase in q, profit will rise.
Suppose at q=5, profit = $244, mr=$15 and mc=$2.
If you take the next step and produce one more unit, revenue will increase by $15, costs will increase by $2, so profit will increase by $13.
Now profit is $257.
Note, the values of mr and mc need to be reconsidered and the same type of analysis performed.
If mr < mc at q, then… by an incremental decrease in q, profit will rise.
Suppose at q=25, profit = $555, mr=$5 and mc=$26.
If you take one step back and produce one less unit, revenue will decrease by $5, costs will decrease by $26, so profit will increase by $21.
Now profit is $576.
If mr = mc at q, then… you have (locally) maximized profit.
Very important to keep track of how marginal revenue and marginal cost change as you adjust your output level.

6. Intuition For Rule (2): Why At A Max And Not A Min
Profit, especially in the short run, starts negative because of fixed costs that need to be paid regardless of how much you produce, even if q=0.
So profit can get worse before it gets better.
Turns out to be the case that marginal revenue will equal marginal cost any time the profit function reaches a critical point.
So, you want to make sure you are at q1 and not q0.
In this class, you will be a the “max” provided you pick the larger of the two quantities.

7. Can you draw the picture of profits for each of these two situations?
Intuition For Rule (3): The Short Run Shut Down Decision
Can you draw the picture of profits for each of these two situations?
Suppose you have set mr=srmc and have picked the larger q, say q1, and it turns out that your profit is negative at q1.
What should you do? Produce q1? Shut down and set q=0 and then see what happens?
Do which ever one results in more profit (ok, so less loses!).
So produce q1 only if  (q1) ≥  (q=0).
 (q1) = tr(q1) – fc - vc(q1).
 (q=0) = -fc
If  (q1) ≥  (q=0), then tr(q1) – fc - vc(q1) ≥ -fc  tr(q1) ≥ vc(q1)  P ≥ sravc(q1).
So produce q1 at a loss as long as the price you sell your output for is at least as large as the value of short run average variable cost to produce q1, otherwise shut down and play dead until you figure out what to do and assess your future in this market.

8. Fixed Costs When You Shut Down
When q>0, fixed costs are fixed costs.
When q=0, we need to talk more about fixed costs. They can be either…
Sunk fixed costs or
Avoidable fixed costs.
This matters in the event you consider shutting down in the short run.
The rule we just stated (P≥sravc) for staying open when short run profit is negative assumes all your fixed costs are sunk.
If some of your fixed costs are avoidable fixed costs, then you will need MORE in revenue to justify staying open.
Look, if you close and set q=0, your loses are now less, since you now only lose the portion of your fixed costs that were sunk.

9. Rules For Profit () Maximization in the Long Run (pretty much the same)
If q* maximizes  , then
mr(q*) = lrmc(q*)
 (q*) is a maximum and not a minimum
at q* it is worth operating:  at q*  0
NOTE: This procedure is good, no matter what type of firm considered.

10. What’s Next
Apply understanding of profit maximization to perfectly competitive firms.