ECN 150 - Firm Profit-Maximization Problem Guide
Ryan Safner
Fall 2015
In order to figure out how to maximize a firm’s profits, follow these simple steps:
1
Price-Taker or Price-Searcher?
Is the firm a price-taker or a price-searcher?
a. If there are many firms in the market all selling the same product, and no firm has the ability
to affect the market price (as competitors will switch to other firms), then the market is competitive and the firm is a price-taker
COMPETITIVE
FIRM
COMPETITIVE
MARKET
P($)
P($)
Sm
P*
P*
Df
Dm
Q
Q
The firm will take the market price (set by market supply and market demand) as its own
demand curve.
1
b. If there is only one firm in the market, then that market is a monopoly, with the firm being a
price-searcher
MONOPOLIST
P($)
D f = Dm
Q
t
The firm will face the entire market demand curve and will be able to choose the price.
2
Find the Profit-Maximizing Output Quantity
Profits are maximized where Marginal Cost = Marginal Revenue. The ONLY two curves that will
matter are the marginal cost (MC) curve and the marginal revenue (MR) curve.
a. If the firm is a price-taker in a competitive market, then the firm’s demand curve is also its
marginal revenue curve. Find the quantity where the marginal revenue equals the marginal
cost (where the MC and MR (or Demand) curves intersect). That quantity is the profit maximizing quantity.
COMPETITIVE FIRM
P($)
MC
P*
D = MR
Q*
Page 2
Q
b. If the firm is a price-searcher in a monopoly, then the firm’s demand curve is different from
its marginal revenue curve. The marginal revenue (MR) curve will start at the same point
and be twice the slope of the demand curve. Find the quantity where the marginal revenue
equals the marginal cost (where the MC and MR curves intersect). That quantity is the profit
maximizing quantity.
MONOPOLY
P($)
MC
D
Q*
MR
Page 3
Q
ff
3
Find the Profit-Maximizing Price
Profits are maximized where Marginal Cost = Marginal Revenue. The ONLY two curves that will
matter are the marginal cost (MC) curve and the marginal revenue (MR) curve.
a. If the firm is a price-taker in a competitive market, then the firm can only charge the market
price. Charging above the market price will lose the firm all of its customers. Charging lower
than the market price will not maximize profits.
COMPETITIVE FIRM
P($)
MC
P*
D = MR
Q
Q*
b. If the firm is a price-searcher in a monopoly, then the firm is able to charge as much as
consumers are willing to pay. This is given by the market demand curve, so the firm will
charge whatever the market demand curve is at the profit-maximizing quantity.
MONOPOLY
P($)
MC
P*
D
Q*
MR
Page 4
Q
4
How Much Profit is Earned?
Only now do we need to bring in the average cost to determine the firm’s profits. Average profit
(profit per unit) is equal to the average revenue (revenue per unit, a.k.a. the price) minus the average
cost (cost per unit); Qπ = AR−AC = P−AC. Total profit is equal to the total revenue (average revenue,
or price x quantity) minus the total costs (average cost x quantity), or average profit x quantity;
π = TR − TC.
Thus, simply compare where the price (demand curve) is at the profit-maximizing quantity, with
the average cost curve is at that same quantity. The difference will be the profit.
COMPETITIVE FIRM
MONOPOLY
P($)
P($)
MC
MC
AC
AC
AC
P*= AR
D = MR
P*= AR
AC
D
Q*
Q
Q*
MR
Q
If the price is lower than the average cost (as here in the competitive firm), the firm will suffer
losses of (P − AC) per unit, for a total loss of (P − AC) ∗ Q. If the price is higher than the average
cost (as here in the monopoly), the firm will earn profits of (P − AC) per unit, for a total profit of
(P − AC) ∗ Q.
5
Should The Firm Exit in the Long Run?
The long run is when all firms are able to enter and exit an industry.
a. If a firm is earning positive profits (P − AC > 0), it should stay in the market.
b. If a firm is earning negative profits, or losses (P − AC < 0), it should exit the market.
c. If a firm is earning zero profits (P − AC = 0 Ô⇒ P = AC), then the firm is indifferent
between staying or leaving (assume it will stay).
This is the same regardless of what type of firm it is, and average variable cost has no role to play
here.
Page 5
6
Should a Firm Earning Losses Continue to Produce in the Short
Run?
In the short run, even before a firm earning losses is able to exit the market, it may still find it favorable to produce. A firm must pay its fixed costs regardless of whether or not it chooses to produce.
This will depend on whether or not it is able to cover its variable costs at the profit-maximizing
quantity. Note, we assume the firm will always and only produce at the profit-maximizing quantity
Q*!
1. If the firm is earning losses but price is higher than its average variable costs (P > AVC),
then it is able to pay its workers and resource owners in order to produce (cover its variable
costs) and earn enough revenues to pay some of its fixed costs. Thus, it will still produce
because although it will still earn losses, it will earn smaller losses by producing compared
to larger losses by not producing at all (and earning no revenues to pay the fixed costs). The
competitive firm below provides an example.
2. If the firm is earning losses but price is lower than its average variable costs (P < AVC),
then it is unable to pay its workers and resource owners in order to produce (cover its variable
costs), and thus it will not produce. The monopoly below provides an example.
COMPETITIVE FIRM
MONOPOLY
P($)
AC
P($)
MC
MC
AC
AVC
AC
AVC
AVC
P*= AR
AC
P*= AR
D = MR
AVC
D
Q*
Q
Page 6
Q*
MR
Q