Uniform Pricing Monopolist I

Given an inverse demand function: P = a – bQ; where a = 170, b = 1, and the short-run cost function is C(Q) = eQ + f, where e = 30 and f = 200, if the monopolist is maximizing profit:

a. Solve for Q*, P*, total revenue, marginal revenue, total cost, marginal cost, profit, price elasticity of demand, consumer surplus and producer surplus.

Uniform Pricing Monopolist II

Given an inverse demand function: P = a – bQ; and the short-run cost function is C(Q) = eQ + f, where e = 30 and f = 200, if the monopolist is maximizing profit:

Solve for Q*, P*, total revenue, marginal revenue, total cost, marginal cost, profit, price elasticity of demand, consumer surplus and producer surplus where a = 340 and b = 1.

Solve for Q*, P*, total revenue, marginal revenue, total cost, marginal cost, profit, price elasticity of demand, consumer surplus and producer surplus where a = 170 and b = 2.

Compare your results with the results 2a and 2b with 1a above.

Uniform Pricing Monopolist III

Given an inverse demand function: P = a – bQ; where a = 170, b = 1, and the short-run cost function is C(Q) = eQ + f, where e = 30 and f = 200, if the monopolist is maximizing revenue:

Solve for Q*, P*, total revenue, marginal revenue, total cost, marginal cost, profit, price elasticity of demand, consumer surplus and producer surplus.

Compare your results with the results from 1a above.

Group Pricing

Given an inverse demand function: P = a1 – b1Q; where a1 = 25, b1 = 0.05, and the short-

run cost function is C(Q) = eQ + f, where e = 10 and f = 0: Solve for Q*, P*, total revenue, marginal revenue, total cost, marginal cost, profit, consumer surplus and producer surplus.

Given an inverse demand function: P = a2 – b2Q; where a2 = 50, b2 = 0.10, and the short-

run cost function is C(Q) = eQ + f, where e = 10 and f = 0: Solve for Q*, P*, total revenue, marginal revenue, total cost, marginal cost, profit, consumer surplus and producer surplus.

Given an inverse demand function: P = a – bQ; where a = 33.33, b = 0.033, and the

short-run cost function is C(Q) = eQ + f, where e = 10 and f = 0: Solve for Q*, P*, total

revenue, marginal revenue, total cost, marginal cost, profit, consumer surplus and producer surplus.

Compare the outputs, prices, profits and sum of CS and PS from 4a and 4b with the results in 4c.

Two-Part Pricing: Identical Customers

Given an inverse demand function: P = a – bQ; where a = 170 and b = 1, and the short-run cost function is C(Q) = eQ + f, where e = 30 and f = 200, if the monopolist is maximizing profit:

a. Solve for Q*, P*, optimal fee, total revenue, marginal revenue, total cost, marginal cost, profit, and consumer surplus minus the fee.

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