EC202 Spring term problem sets 1-5

Monopolist Operation in a Market

Market Demand and Marginal Cost

• Demand function: P = 100 - 4Q (note: P is price, Q is quantity)

• Marginal cost (MC): Constant at £4

Profit Maximization

(a) Determining Quantity and Price

• To find the profit-maximizing quantity (Q) and price (P) for monopolist:**

  • Set Marginal Revenue (MR) = Marginal Cost (MC)

  • Derive MR from the demand function: MR = 100 - 8Q

  • Set MR = MC:

    • 100 - 8Q = 4

    • Solve for Q: 8Q = 96

    • Q* = 12

  • Calculate Price using the demand function:

    • P* = 100 - 4(12) = 52

(b) Graphical Illustration of Surpluses

• Consumer Surplus (CS): Area above price and below the demand curve.

• Producer Surplus (PS): Area below price and above the MC curve.

• Total Welfare (TW): CS + PS.

Total Welfare Maximization

(c) Price for Total Welfare Maximization

• In a perfectly competitive market, P = MC for total welfare maximization.

• Thus, for maximizing aggregate welfare: Set P = £4.

Consumer Surplus and Total Welfare Loss

(d) Losses from Monopoly

• Loss in Consumer Surplus: Difference between consumer surplus at competitive price vs monopoly price.

• Loss in Total Welfare: Area that represents the reduction in total welfare due to monopolistic pricing.

• Illustration: Graph showing reduction of areas representing consumer surplus and total welfare.

Demand for Cricket Bats

Market Characteristics

• Demand function: Q = 100 - P

• Cost function: C(Q) = 4Q² + 100

Profit Maximization for Cricket Bats

(a) Profit-Maximizing Output

• Deriving MR and setting it equal to MC to find optimal output.

(b) Profit-Maximizing Price

• Substitute optimal output into demand function to determine price.

(c) Calculating Profit

• Profit = Total Revenue - Total Cost at optimal output level.

Government Subsidy Impact

• If the government gives S per unit:

  • Calculate new MC, re-evaluate profit-maximizing output and price.

• To find S for P = MC: Set price equal to £(marginal cost).

Monopolist’s Advertising Impact

Market Demand Function with Advertising

• Demand: Q = A + 402 - P

  • Cost of advertising: A²

  • Production cost function: C(Q) = 10 + 2Q + Q²

Profit Maximization under Advertising

(a) Marginal Revenue Function

• Derived from demand function assuming influence from advertising (adjust based on A).

(b) Fixed Advertising Level

• Set A = 4 to find optimal Q* and corresponding price (P*) and profit.

(c) Flexible Advertising Levels

• Analyze profit-maximizing output and profit as function of A:

  • Explore impact of varying A on the monopolist’s decisions.

(d) Profit-Maximizing Level of Advertising

• Calculate based on prior findings to determine optimal advertising level for maximizing profits.