1. The Mechanics of Profit Maximization
CHAPTER 14
The Mechanics of Profit
Maximization
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2. Golden Rule of 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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3. Table 14.1 Characteristics of Selling Environments
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4. 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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5. 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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6. 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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7. 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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8. 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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9. Figure 14.1 The Commodity Market and Single Firm
The market demand and supply dictate the demand for the single firm in the perfectly competitive or commodity market.
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10. 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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11. Figure 14.2 Revenue, Cost, and Profit
Profit is maximized at the point where the marginal revenue and marginal cost are equal.
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12. Figure 14.2 Revenue, Cost, and Profit
Profit is maximized at the point where the marginal revenue and marginal cost are equal.
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13. 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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14. Business Insight Effects of Determinants of Demand
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15. Price Elasticity Point elasticity Arc 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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16. 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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17. Marginal Revenue Total revenue, TR = P × Q Marginal revenue
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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18. 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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19. 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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20. 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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21. 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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22. Operating Rules Minimize loss Compare revenue with variable costs
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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23. Figure 14.3
A Loss
Profit is maximized or loss is minimized at the point where the marginal revenue and marginal cost are equal.
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24. 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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25. 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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26. Sales Maximization Maximize total sales (total revenue) If MR > 0
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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27. 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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28. Figure 14.4 Revenue Maximization
The quantity at which revenue is maximized is the quantity where MR = 0.
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29. 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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30. The Cournot Model Assumptions Result
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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31. 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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32. 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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33. Figure 14.5 The Kinked Demand Curve
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.
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34. 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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35. 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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