# Equilibrium

### Contents

page 1 of 3

#### Profit

In the unit on supply, we established that sellers derive their utility from profits, or the amount of money that they actually make from a sale. Roughly speaking, this means that when the price of a good goes up, the seller will be happier, but there is more to profit than the sale price of a good. For instance, we would think that Kenny, who sells shirts, would be happier if the selling price went from \$20 a shirt to \$25 a shirt. If nothing else changes, then that's true: he will be happier at the higher price. If with the higher sale price his costs change, however, from an initial cost of \$10 a shirt to a cost of \$17 a shirt, then he would have been happier at the lower price, since his profits now are actually decreased.

Profit = Total Revenue (TR) - Total Cost (TC)
Kenny's initial profit per shirt is:
Profit = 20 - 10 = \$10 a shirt
After the change in both selling price and costs, however, his new profit per shirt is:
Profit = 25 - 17 = \$8 a shirt
This is a very basic look at why there is more to seller utility than just selling price. If we look more closely, we can find better ways to represent costs, revenue, and profits.

The following graphs shows different ways of looking at revenue:

Figure %: Revenue
Total revenue (TR)is the total amount of money that a firm gets for selling a certain amount of goods. To find TR, multiply the price of the goods by the quantity of goods sold:
TR = pq
Average revenue (AR) is the average amount of money that the firm gets per unit of goods. This is equal to p, the market price, since the firm cannot decide how much people will pay for its goods.
AR = TR/q
AR = p
Marginal revenue (MR) is the extra amount of revenue generated by selling one additional unit of goods. It is equal to the slope of the TR curve:
MR = (change in TR)/(change in q)
MR will also be equal to p, since we assume that the firm is not big enough to significantly affect the market through its actions. That is, the firm will not affect the market price of a good, no matter how much or how little it sells. Thus, for every additional unit it sells, its marginal revenue will be p:
MR = p
Note that we can draw the graph of market equilibrium next to the graph of marginal revenue and average revenue. Extending the revenue line into the equilibrium graph, we see that this line hits right at the equilibrium point.

The following graph shows different ways of measuring and representing costs of production:

Figure %: Costs

Total cost (TC) is the sum of all the different costs they incur when producing and selling their product.

Average cost (AC) is the total cost divided by the quantity of goods:
AC = TC/q
Marginal cost (MC) is the extra cost incurred in producing one more of the product. This can be found by measuring the slope of the TC curve:
MC = (change in TC)/(change in q)
Costs can also be broken down into types of costs:
1. Total variable costs (TVC) refers to costs which vary with the amount of goods a firm makes and sells. An example of TVC could be the cost of chocolate chips, if the firm makes chocolate chip cookies.
2. Total fixed costs (TFC) refers to costs THAT a firm has to pay, no matter how much or how little it produces. One example might be the monthly rent on a store.
Added together, TVC and TFC are equal to TC:
TVC + TFC = TC
TVC and TFC, when divided by q, yield average variable cost (AVC) and average fixed cost (AFC):
AVC = TVC/q
AFC = TFC/q
Added together, AVC and AFC are equal to AC:
AVC + AFC = AC
We can also find the marginal variable cost (MVC) and the marginal fixed cost (MFC) by taking the slopes of the two curves. Because fixed costs don't change with quantity, however, the MFC will be 0:
MVC = (change in TVC)/(change in q)
MFC = (change in TFC)/(change in q) = 0
Added together, MVC and MFC are equal to MC, but since MFC is 0, the marginal cost is equal to the marginal variable cost:
MVC + MFC = MC
MVC + 0 = MC
MVC = MC

If we can combine a firm's costs and revenues, we can calculate the firm's profits. Using the variables we have been working with, we can represent profit as:

Profit = TR - TC
TR - TC = q(AR - AC) = q(P - AC)
Profit = q(P - AC)
Firms will try and maximize their profits, since it is through increasing profits that firms increase their utility. To maximize profits, firms will choose to sell the quantity at which the marginal cost is equal to the marginal revenue. Why is this true? If MC were greater than MR, then the firm would be losing money for each additional unit of product. If MR were greater than MC, the firm would be losing out on extra profit by not making another unit. The following graph shows this ideal quantity as q*. The shaded region is the amount of profit that the firm generates:
Figure %: Calculating Profit
The amount of profit will appear as a rectangle whose length is the distance between average cost and average revenue (since that reflects the average amount gained per unit) and whose width is the number of units sold. To calculate the actual amount of the profits, you would multiply the length (dollars per unit) and the width (quantity) of the shaded rectangle. It is possible for profits to be negative (in the case that the "profit" rectangle is above the average revenue curve, instead of below it.

If the firm is making profits, that is, if P is greater than the average cost, then all is well, they will continue producing and selling goods. If P is less than AC, however, the firm is losing money.

P < AC : the firm is losing money
How will the firm respond to this? Firms make decisions differently for the short run and the long run.

In the short run, (in economic terms, the immediate future), it is not feasible to "close shop" immediately. There are leases to end, bills to pay, creditors to pay off, and other concerns to take care of first. In such a case, the firm can make two choices: either to continue producing and selling goods for the time being (in order to minimize losses), or to stop production altogether (to cut losses). How does a firm decide which path to take? This decision is based on the firm's variable costs. If the price is still higher than the average variable cost, it will continue production, if the price is lower than the average variable cost, it will shut down.

P > AVC : continue production in the short run

P < AVC : stop production in the short run
Why is this? Think about it this way: in the first case, the firm is losing money in the big picture. Each unit that they make incurs some variable cost, but because that cost is lower than the price, they keep producing, since they can still recoup some of their losses by continuing production.