modeling firms’ behavior most economists treat the firm as a single decision-making unit the...

Modeling Firms’ Behavior

Most economists treat the firm as a single decision-making unit• the decisions are made by a single dictatorial

manager who rationally pursues some goal• profit-maximization

Profit Maximization

A profit-maximizing firm chooses both its inputs and its outputs with the sole goal of achieving maximum economic profits• seeks to maximize the difference between

total revenue and total economic costs

Output Choice

Total revenue for a firm is given byTR(q) = P(q)q

In the production of q, certain economic costs are incurred [TC(q)]

Economic profits () are the difference between total revenue and total costs

= TR(q) – TC(q) = P(q)q – TC(q)

Output Choice

The necessary condition for choosing the level of q that maximizes profits can be found by setting the derivative of the function with respect to q equal to zero

0

dq

dTC

dq

dTRq

dq

d)('

dq

dTC

dq

dTR

Output Choice

To maximize economic profits, the firm should choose the output for which marginal revenue is equal to marginal cost

MCdq

dTC

dq

dTRMR

Profit Maximization

output

revenues & costs

TRTC

q*

Profits are maximized when the slope ofthe revenue function is equal to the slope of the cost function

But the second-ordercondition prevents usfrom mistaking q0 asa maximum

q0

Marginal Revenue

If a firm can sell all it wishes without having any effect on market price, marginal revenue will be equal to price

If a firm faces a downward-sloping demand curve, more output can only be sold if the firm reduces the good’s price

Marginal Revenue

If a firm faces a downward-sloping demand curve, marginal revenue will be a function of output

If price falls as a firm increases output, marginal revenue will be less than price

Marginal Revenue Suppose that the demand curve for a sub

sandwich isq = 100 – 10P

Solving for price, we getP = -q/10 + 10

This means that total revenue isTR = Pq = -q2/10 + 10q

Marginal revenue will be given byMR = dTR/dq = -q/5 + 10

Profit Maximization

To determine the profit-maximizing output, we must know the firm’s costs

If subs can be produced at a constant average and marginal cost of $4, then

MR = MC

-q/5 + 10 = 4

q = 30

Average Revenue Curve

If we assume that the firm must sell all its output at one price, we can think of the demand curve facing the firm as its average revenue curve• shows the revenue per unit yielded by

alternative output choices

Marginal Revenue Curve

The marginal revenue curve shows the extra revenue provided by the last unit sold

In the case of a downward-sloping demand curve, the marginal revenue curve will lie below the demand curve


output

price

D (average revenue)

MR

q1

P1

As output increases from 0 to q1, totalrevenue increases so MR > 0

As output increases beyond q1, totalrevenue decreases so MR < 0


When the demand curve shifts, its associated marginal revenue curve shifts as well• a marginal revenue curve cannot be

calculated without referring to a specific demand curve

Short-Run Supply by a Price-Taking Firm

output

price SMC

SATC

SAVC

P* = MR

q*

Maximum profitoccurs whereP = SMC


output

price SMC

SATC

SAVC

P* = MR

q*

Since P > SATC,profit > 0


output

price SMC

SATC

SAVC

P* = MR

q*

If the price risesto P**, the firmwill produce q**and > 0

q**

P**


output

price SMC

SATC

SAVC

P* = MR

q*

If the price falls to P***, the firm will produce q***

q***

P***profit maximizationrequires that P = SMC and that SMCis upward-sloping

< 0


The positively-sloped portion of the short-run marginal cost curve is the short-run supply curve for a price-taking firm• it shows how much the firm will produce at

every possible market price

• firms will only operate in the short run as long as total revenue covers variable cost• the firm will produce no output if P < SAVC


Thus, the price-taking firm’s short-run supply curve is the positively-sloped portion of the firm’s short-run marginal cost curve above the point of minimum average variable cost• for prices below this level, the firm’s profit-

maximizing decision is to shut down and produce no output


output

price SMC

SATC

SAVC

The firm’s short-run supply curve is that portion of the SMC curve that is above minimum SAVC

Supply Function

The supply function for a profit-maximizing firm that takes both output price (P) and input prices (v,w) as fixed is written as

quantity supplied = q*(P,r,w)

• this indicates the dependence of output choices on these prices

Supply Function

The supply function provides a convenient reminder of two key points• the firm’s output decision is fundamentally a

decision about hiring inputs

• changes in input costs will alter the hiring of inputs and hence affect output choices as well

Producer Surplus in the Short Run A profit-maximizing firm that decides to

produce a positive output in the short run must find that decision to be more favorable than a decision to produce nothing

This improvement in welfare is termed (short-run) producer surplus• what the firm gains by being able to participate in

market transactions

Producer surplus is theshaded area below P*and above SMC

Producer Surplus in the Short Run

output

price SMC

P*

q*

If the market priceis P*, the firm will produce q*

Producer Surplus in the Long Run

By definition, long-run producer surplus is zero• fixed costs do not exist in the long run

• equilibrium profits under perfect competition with free entry are zero

modeling firms’ behavior most economists treat the firm as a single decision-making unit the...

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