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Profit maximization by firms

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Check whether the quantity from Step 1 yields higher profit than shutting down. 9-14 ... shutting down maximizes profit. If P=ACmin, then both shutting down ... – PowerPoint PPT presentation

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Title: 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
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