Profit maximization by firms

1
Profit maximization by firms

• ECO61
• Udayan Roy
• Fall 2008

2
Revenues and costs

• A firms costs (C) were discussed in the previous
  chapter
• A firms 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
  firms 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 firms behavior

3
Profit-MaximizingPrices and Quantities

• A firms profit, P, is equal to its revenue R
  less its cost C
• P R C
• We assume that a firms 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 firms revenue, R(Q)
  P(Q)Q
• Cost of selling that quantity is the firms cost
  of production, C(Q)
• Overall,
• P R(Q) C(Q) P(Q)Q C(Q)

9-3
4
Profit-Maximization An Example

• 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
5
Profit-Maximization An Example
Note that 50 Q2 is always a positive number.
Therefore, to maximize profit one must minimize
50 Q2. Therefore, to maximize profit, Noah
and Naomi must produce Q 50 units. This is
their profit-maximizing output.
When Q 50, p 2 ? 502 5000. this is the
biggest profit Noah and Naomi can achieve.
6
Figure 9.2 A Profit-Maximization Example
9-6
7
Choice requires balance at the margin

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

8
Example
9
Marginal Revenue

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

9-9
10
Marginal Revenue and Price

• 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
11
Figure 9.4 Marginal Revenue and Price
9-11
12
Marginal Revenue and Price

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

9-12
13
Demand and marginal revenue
14
Profit-Maximizing Sales Quantity

• Two-step procedure for finding the
  profit-maximizing sales quantity
• Step 1 Quantity Rule
• Identify positive sales quantities at which MRMC
• 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
15
Profit

• 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

16
Profit downward-sloping demand of price-setting
firm
Costs and
Revenue
Quantity
0
17
Profit downward-sloping demand of price-setting
firm

• Recall that profit (P - AC) ? Q
• Therefore, the firm will stay in business as long
  as price (P) is greater than average cost (AC).

18
Shut down because P lt AC at all Q
downward-sloping demand of price-setting firm
Costs and
Revenue
Quantity
0
19
Profit Maximization horizontal demand for a
price taking firm
Costs
and
Revenue
Quantity
0
20
Shut down because P lt AC at all Q horizontal
demand for a price taking firm
Costs
and
Revenue
ACmin


P
AR
MR
Quantity
0
21
Supply Decisions

• 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 PMC in the quantity rule to find the
  profit-maximizing sales quantity for a
  price-taking firm
• Shut-Down Rule
• If PgtACmin, the best positive sales quantity
  maximizes profit.
• If PltACmin, shutting down maximizes profit.
• If PACmin, then both shutting down and the best
  positive sales quantity yield zero profit, which
  is the best the firm can do.

9-21
22
Price determination

• 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