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Profit maximization by firms - PowerPoint PPT Presentation

Profit maximization by firms. ECO61 Udayan Roy Fall 2008. Revenues and costs. A firm’s costs (C) were discussed in the previous chapter A firm’s revenue is R = P  Q

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Profit maximization by firms

ECO61

Udayan Roy

Fall 2008

• A firm’s costs (C) were discussed in the previous chapter

• A firm’s revenue is R = P  Q

• Where P is the price charged by the firm for the commodity it sells and Q is the quantity of the firm’s output that people buy

• We discussed the link between price and quantity consumed – the demand curve – earlier

• Now it is time to bring revenues and costs together to study a firm’s behavior

Profit-MaximizingPrices and Quantities

• A firm’s profit, P, is equal to its revenue R less its cost C

• P = R – C

• We assume that a firm’s actions are aimed at maximizing profit

• Maximizing profit is another example of finding a best choice by balancing benefits and costs

• Benefit of selling output is firm’s revenue, R(Q) = P(Q)Q

• Cost of selling that quantity is the firm’s cost of production, C(Q)

• Overall,

• P = R(Q) – C(Q) = P(Q)Q – C(Q)

9-3

• Noah and Naomi face weekly inverse demand function P(Q) = 200-Q for their garden benches

• Weekly cost function is C(Q)=Q2

• Suppose they produce in batches of 10

• To maximize profit, they need to find the production level with the greatest difference between revenue and cost

9-4

Note that [50 – Q]2 is always a positive number. Therefore, to maximize profit one must minimize [50 – Q]2. Therefore, to maximize profit, Noah and Naomi must produce Q = 50 units. This is their profit-maximizing output.

When Q = 50, π = 2  502 = 5000. this is the biggest profit Noah and Naomi can achieve.

• In general marginal benefit must equal marginal cost at a decision-maker’s best choice whenever a small increase or decrease in her action is possible

• Here the firm’s marginal benefit is its marginal revenue: the extra revenue produced by the DQ marginal units sold, measured on a per unit basis

9-9

• An increase in sales quantity (DQ) changes revenue in two ways:

• Firm sells DQ additional units of output, each at a price of P(Q). This is the output expansion effect: PDQ

• Firm also has to lower price as dictated by the demand curve; reduces revenue earned from the original Q units of output. This is the price reduction effect: QDP

9-10

Price reduction effect of output expansion: QP. Non-existent when demand is horizontal

Output expansion effect: PQ

9-11

• The output expansion effect is PDQ

• The price reduction effect is QDP

• Therefore the additional revenue per unit of additional output is MR = (PDQ + QDP)/DQ = P + QDP/DQ

• When demand is negatively sloped, DP/DQ < 0. So, MR < P.

• When demand is horizontal, DP/DQ = 0. So, MR = P.

9-12

• Two-step procedure for finding the profit-maximizing sales quantity

• Step 1: Quantity Rule

• Identify positive sales quantities at which MR=MC

• If more than one, find one with highest P

• Step 2: Shut-Down Rule

• Check whether the quantity from Step 1 yields higher profit than shutting down

9-14

• Profit equals total revenue minus total costs.

• Profit = R – C

• Profit/Q = R/Q – C/Q

• Profit = (R/Q - C/Q) Q

• Profit = (PQ/Q - C/Q) Q

• Profit = (P - AC) Q

Profit-maximizing price

E

B

profit

Average cost

Average

D

C

cost

Demand

Marginal revenue

QMAX

Profit: downward-sloping demand of price-setting firm

Costs and

Revenue

Quantity

0

• Recall that profit = (P - AC) Q

• Therefore, the firm will stay in business as long as price (P) is greater than average cost (AC).

Demand

Shut down because P < AC at all Q:downward-sloping demand of price-setting firm

Costs and

Revenue

Quantity

0

profit by producing

the quantity at which

MC

marginal cost equals

marginal revenue.

MC

2

AC

=

=

=

=

P

MR

MR

P

AR

MR

1

2

MC

1

Q

Q

Q

1

MAX

2

Profit Maximization: horizontal demand for a price taking firm

Costs

and

Revenue

Quantity

0

AC

Shut down because P < AC at all Q: horizontal demand for a price taking firm

Costs

and

Revenue

ACmin

=

=

P

AR

MR

Quantity

0

• Price takers are firms that can sell as much as they want at some price P but nothing at any higher price

• Face a perfectly horizontal demand curve

• not subject to the price reduction effect

• Firms in perfectly competitive markets, e.g.

• MR = P for price takers

• Use P=MC in the quantity rule to find the profit-maximizing sales quantity for a price-taking firm

• Shut-Down Rule:

• If P>ACmin, the best positive sales quantity maximizes profit.

• If P<ACmin, shutting down maximizes profit.

• If P=ACmin, then both shutting down and the best positive sales quantity yield zero profit, which is the best the firm can do.

9-21

• We have seen how the price is determined in the case of price setting firms that have downward sloping demand curves

• But how is the price that price taking firms use to guide their production determined?

• For now think of it as determined by trial and error. Pick a random price. See what quantity is demanded by buyers and what quantity is supplied by producers. Keep trying different prices whenever the two quantities are unequal

• The market equilibrium price is the price at which the quantities supplied and demanded are equal