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ecomonics-chp-14.pptPowerPoint Slides prepared by: Andreea CHIRITESCU Eastern Illinois University
The Mechanics of Profit
Maximization
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CHAPTER 14
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Golden Rule of Profit Maximization
- Profit maximization
Continue expanding output until
The value society places on the last unit sold
Just equals the amount spent on resources to produce that unit of output
Marginal revenue = Marginal cost
MR = MC
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Table 14.1
Characteristics of Selling Environments
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Selling Environments: Market Structure
- Perfect Competition
A very large number of firms
Whatever any one firm does has no effect on the market
All firms sell an identical product
Anyone can begin a business or leave the business without difficulty
No cost to the consumer of going to a different place to make the purchase
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Selling Environments: Market Structure
- Monopoly
Only one firm supplies a good or service
No firm can enter the business and begin competing with the monopoly
- Monopolistic Competition
A large number of firms
Easy entry
Differentiated products
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Selling Environments: Market Structure
- Oligopoly
Just a few firms provide the good or service
Each firm is large enough to significantly affect the other firms
Differentiated
Or identical products
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The Graphics of Profit Maximization
- Market
Sum of all firms and all consumers
Downward-sloping demand curve
Upward-sloping supply curve
- Firm in a perfectly competitive market
Must sell its goods and services at the price determined in the market
“Price taker”
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© 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
The Graphics of Profit Maximization
- Firm in a perfectly competitive market
Horizontal demand
Marginal revenue = price
Demand curve = Marginal revenue curve
Maximize profit
Select the quantity where MR = MC
Demand = Price = Marginal revenue
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© 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
Figure 14.1
The market demand and supply dictate the demand for the single firm in the perfectly competitive or commodity market.
The Commodity Market and Single Firm
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The Graphics of Profit Maximization
- Firm in a market that is not perfectly competitive
Demand curve slopes down
To sell more the price must be lower
Firm has some degree of “market power”
Maximize profit:
Select the quantity where MR=MC
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Figure 14.2
Profit is maximized at the point where the marginal revenue and marginal cost are equal.
Revenue, Cost, and Profit
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Figure 14.2
Profit is maximized at the point where the marginal revenue and marginal cost are equal.
Revenue, Cost, and Profit
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Simple Mathematics of Profit Maximization
- Demand function
Function of variables that influence consumer spending
- Qx = f(Px, I, Py, T, Pex, N)
Px is the price of good x; I is income
Py is the price of other goods
T is tastes and preferences
Pe is the expected price of good x at some point in the future
N is the number of consumers
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Business Insight
Effects of Determinants of Demand
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Price Elasticity
- Point elasticity
Price changes that are extremely small
= ∂lnQ/∂lnP = [∂Q/∂P][P/Q]
- Arc elasticity
Price changes over some range of values that may be quite large
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Marginal Revenue
- Demand equation
Quantity demanded - a function of price and the determinants of demand
Q = g − hP
g and h are parameters
P is the product price
P = a − bQ
a is the vertical intercept
–b is the slope of the demand curve
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© 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
Marginal Revenue
- Total revenue, TR = P × Q
TR = P × Q = (a − bQ) × Q = aQ − bQ2
- Marginal revenue
Change in total revenue divided by the change in quantity
∂TR/∂Q = MR = a − 2bQ
a is the vertical intercept, same as the demand function
-2b is the slope of MR, twice the slope of the D curve
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The Calculus of Profit Maximization
- Profit, π = TR − TC = TR(Q) − C(Q)
- Maximize profit: MR = MC
∂π /∂Q = ∂TR(Q)/∂Q − ∂C(Q)/∂Q = 0
∂TR(Q)/∂Q is the marginal revenue
∂C(Q) /∂Q is the marginal cost
- Perfectly competitive firm
Price does not depend on the quantity
∂PQ/∂Q − ∂C(Q)/∂Q = P − MC = 0
P = MC
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© 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
The Calculus of Profit Maximization
- Firms not in a perfectly competitive market
Price does depend on the quantity, P = P(Q)
MR = ∂TR/∂Q = ∂P(Q)Q/∂Q = P + Q(∂P/∂Q)
MR = MC
P > MR, MR = MC
P > MC
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© 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
Business Insight
Convexity
- Assumption: convexity
- A convex set
Property that a collection that contains two items also contains an average of these two items
- Convexity – problem
When goods are indivisible
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© 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
Business Insight
Convexity
- In a convex environment
Minor adjustments, trial and error, and piecemeal improvements
Tend to make things better
- Assumption of convexity
Reasonable but does have weaknesses
There are no benefits from specialization
Management would move in increments
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Operating Rules
- Minimize loss
Select quantity where MR = MC
The loss is short run
- Compare revenue with variable costs
If P > AVC, operate
If P < AVC, shut down immediately
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© 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
Figure 14.3
Profit is maximized or loss is minimized at the point where the marginal revenue and marginal cost are equal.
A Loss
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Operating Rules
- Breakeven
When total revenue equals total cost
Total Cost: TC = TFC + TVC
Total Variable Cost, TVC = AVC * Q
TC = TFC + AVC * Q
Total Revenue, TR = P * Q
TR = TC: P * Q = TFC + AVC * Q
Breakeven output level: Q = TFC/(P − AVC)
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Operating Rules
- Breakeven
P – AVC = the contribution margin per unit
Portion of the selling price that can be applied to cover the fixed costs of the firm and provide for profit
Shutdown point: P = AVC
If P > AVC, the firm will be operating
If P < AVC, the firm will shut down
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© 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
Sales Maximization
- Maximize total sales (total revenue)
Find the quantity and price where marginal revenue is zero
- If MR > 0
Additional sales could be obtained by lowering price
- If MR < 0
Additional sales could be obtained by raising price
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Sales Maximization
- A firm’s market share
Percentage of the market’s sales (or revenue) constituted by that firm
market share = revenue/market size
∂market share/∂Q = 0
Yields ∂TR/∂Q = 0
Assuming market size constant
If one firm increases its sales other firms lose sales
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Figure 14.4
The quantity at which revenue is maximized is the quantity where MR = 0.
Revenue Maximization
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Oligopoly
- Oligopoly
Presents special problems because of the interdependence of firms
The Cournot Model
The Kinked Demand Model
The Cartel Model
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The Cournot Model
- Assumptions
Two firms selling an identical good
MC = 0
Each firm, while trying to maximize profits
Decides that the other firm holds its output constant at the existing level
- Result
Each firm moves and then countermoves
Until an equilibrium is reached
Each supplies one-third of the market
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The Cournot Model
- Market demand: Q = a − bP
b = 1 and zero total costs
- Firm A’s decision to supply
Depends on what firm B does
Supply one-half of the difference between Q = a and the amount offered by firm B
QA = (a −QB)/2
- Firm B – the same: QB = (a −QA)/2
- QA = QB = a/3
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The Kinked Demand Model
- Firms in an oligopoly
May not know the shape of the demand curve for their product
The shape depends on how their rivals react to one another
Have to predict how their competitors will respond to a price change
To know what their demand curve looks like
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Figure 14.5
The price and quantity for the firm pictured is given by the point where MR = MC, price P1, and quantity Q1. The marginal cost declines, so the firm decides to lower price. Since other firms match the price decrease, sales don’t increase, whereas without the other firms following the price decline, sales would increase from Q1 to Q2.
The Kinked Demand Curve
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The Cartel Model
- Cartel
Arises when rival firms agree to cooperate
And determine price and quantity
To maximize joint profits
Knowing firms’ demand and marginal cost functions
Knowing market demand function
Calculate cartel’s marginal cost function
Horizontally sum the marginal cost functions
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The Cartel Model
- Cartel
Calculate MR for the cartel
Find profit maximizing quantity for the cartel: MR = MC
Find price from the demand equation
Optimal output for each firm
Substitute the cartel’s equilibrium MC into the individual firm’s MC functions
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