PROFIT MAXIMIZATION QPTR I will continue using the demand example, which was -- We will use a new cost example based on two numbers: Fixed Cost = $80 Variable Cost per Unit = $40 Those numbers imply -- QAFCvcpuATC 0#N/A40#N/A

Let’s combine the two tables QPTRAFCvcpuATC ###40### Question: Is it possible for this firm to make a positive profit? Put another way, the question is, “Should this firm be in business?”

QPTRAFCvcpuATC ###40### Answer: Yes, the firm can make a positive profit. The easiest way to see it from these numbers is by noting that there exists some output for which Price is greater than Average Total Cost. If price exceeds ATC, there is a positive profit: Each unit is sold for more than it cost to make. So, yes, the firm should be in business. Next question, what price/quantity combination maximizes profit? Can this firm make a positive profit?

QPTRAFCvcpuATCTCProfit ###40### What price/quantity combination maximizes profit? Let’s add two more columns on the end. From this it appears that output of 3, at a price of $70 is the best choice and indeed it is. The question is, “What makes that price/quantity combination the best.”

QPTRTCProfit OK, let’s get rid of some columns for a minute. We want to find a rule for maximizing profit. Consider the choice to produce 3 units instead of 2. That decision caused revenue to rise, cost to rise and profit to rise. Since we want profit to rise this was a good choice. Now consider the choice to produce 4 units instead of 3. That decision caused revenue to rise, cost to rise and profit to FALL! Since we want profit to rise this was a bad choice. In what way was the decision to go from Q = 2 to Q = 3 different from the decision to go from Q = 3 to Q = 4? In both cases revenue and cost both rose, but profit rose in one case and fell in the other case.

QTR Change of TRTC Change of TCProfit OK, let’s try looking at the changes of Revenue and Cost. We can now get the rule for profit maximization: You should increase output if __________________________________ Revenue will rise more than cost will rise You should reduce output if __________________________________ Revenue will fall less than cost will fall

We arrive at a conclusion You should operate at the point at which the change of revenue from producing one more unit is as close as possible to the change of cost from producing one more unit. This is such an important conclusion that we will introduce one of economics’ favorite words. The word is marginal and it used to describe the amount by which something changes as you do more or less of an activity. The term marginal cost (MC) describes the additional cost to produce one more unit. The term marginal revenue (MR) describes the additional revenue received from selling one more unit.

Let’s look at the terms MC and MR. So what we’ve called “vcpu” will now be renamed MC for “marginal cost.” In the simple cost example we’ve been using, marginal cost is what has been called “variable cost per unit.” This is because vcpu is the amount needed to produce an extra unit. Notice you can ignore fixed costs – they do not change when you produce more and we are now only concerned about the changes of cost. In order to produce an extra unit, you only need the cost of wages and materials to make that unit. Land and capital are already paid for.

Marginal revenue is a bit trickier. Let’s look at our demand example again. QPTRMR We will introduce an odd trick. When we write marginals, we will write them between the lines. Think of marginal revenue as the change of revenue as you go from one quantity to another As we go from Q = 0 to Q = 1, Total Revenue changes by $90 (from 0 to 90). Marginal Revenue is $90. As we go from Q = 1 to Q = 2, Total Revenue changes by _______ 160 – 90 = $70 As we go from Q = 2 to Q = 3, Total Revenue changes by _______ 210 – 160 = $50 As we go from Q = 3 to Q = 4, Total Revenue changes by _______ 240 – 210 = $30 10 As we go from Q = 4 to Q = 5, Total Revenue changes by _______ 250 – 240 = $ As we go from Q = 5 to Q = 6, Total Revenue changes by _______ -$10 (falls by $10)

QPTRMRMC Recall that the marginal cost of producing each item is $ Start at Q = 0 and ask, “Should I produce the next unit?” It will raise my revenue by $90 and raise my costs by $40. No matter how well I was doing I’ll be doing $50 better if I produce the next one. So, Yes, I should produce Q = 1. Now ask, “Should I produce the next one? Go to Q = 2?” Again since MR > MC, the answer is, “Yes.” When does the answer become, “No?” When you consider producing the 4 th unit. At this point the next unit will add more to your cost than it will add to your revenue. Don’t do it! So the profit maximizing quantity is ______. The profit maximizing price is _______. Q = 3 P = $70

GRAPHING D = P MR P* Q* $/Q Q MC Making it easier: Get rid of MR P* is half-way between MC and the intercept of the Demand curve D = P P* Q* $/Q Q MC Demand intercept Q* occurs where MC = MR