Mathematical Economics
dr Wioletta Nowak
Lecture 7-8
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Total Costs, Average Costs,
Marginal Costs,
Long-run Costs, Short-run Costs,
Cost Curves, Long-run and Short-run Cost
Curves,
• Monopoly
Total Costs
Average Costs
• The average cost function measures the cost per unit of
output
• Average costs (AC) = average variable costs (AVC) +
average fixed costs (AFC)
• Average fixed costs always decline with output, while
average variable costs tend to increase. The net result is a
U-shaped average cost curve.
Marginal Costs
• The marginal cost curve lies below the average
cost curve when average cost is decreasing, and
above when they are increasing.
• The marginal costs are equal average costs at the
point of minimum average costs.
Long-run Average Costs and Short-run Average Costs
Long-run Average Costs and Short-run Average Costs
Monopoly
• Monopoly is a price-maker.
• A monopolist has market power in the sense
that amount of output that is able to sell
responds continuously as a function of the
price it charges.
The monopolist’s profit maximization problem can be
posed as
The first-order conditions for the profit maximization
problem are
The monopolist’s profit maximization problem can be
posed as
The first-order condition for the profit maximization
problem is
Monopoly with a Nonlinear Demand Function
Monopoly with a Linear Demand Function
Example
Inefficiency of Monopoly
Mathematical Economics
dr Wioletta Nowak
Lecture 9-10
• Oligopoly
• Cournot equilibrium
• Quantity leadership – Slackelberg model
• Exchange
• Market Equilibrium
Cournot equilibrium
The first-order conditions for the profit maximization
problems are:
• The first-order condition for firm 1 determines firm 1’s
optimal choice of output as a function of its beliefs about firm
2’s output choice. This relation is known as firm 1’s reaction
curve. It depicts how firm 1 will react given various beliefs it
might have about firm 2’s choice.
Quantity leadership – Slackelberg model
The follower’s problem
The leader’s problem
• The Stackelberg equilibrium – Firm 1, the leader, chooses the
point on the firm 2’s reaction curve that touches firm 1’s
lowest possible isoprofit line, thus yielding the highest
possible profits for firm 1.
Example 1
a) Calculate the Cournot equilibrium amount of output for each
firm and firms’ profits.
b) If firm 2 behaves as a follower and firm 1 behaves as a
leader, calculate the Stackelberg equilibrium amount of
output for each firm and firms’ profits.
c) If firm 1 behaves as a follower and firm 2 behaves as a
leader, calculate the Stackelberg equilibrium amount of
output for each firm and firms’ profits.
• Partial equilibrium: how demand and supply
are affected by the price of the particular good.
• General equilibrium: how demand and
supply conditions interact in several markets to
determine the prices of many goods.
• General equilibrium refers to the study of how
the economy can adjust to have demand equal
supply in all markets at the same time.
Market Equilibrium
Example 2
Example 3
Example 4