Question

Chapter 10.9, Problem 1Q. How do you calculate the firms maximum profit for problem 9.1 in Chapter 10? Please show calculation.

The Jam Factory makes boutique jams that it sells in specialty stores in two different cities. In City 1, the daily inverse demand function is p1 = 12 - 0.5Q1 and the marginal revenue function is MR1 = 12 - Q1. In City 2, the inverse demand and marginal revenue functions are p2 = 20 - Q2 and MR2 = 20 - 2Q2. The firm’s cost function is C(Q) = 10 + 6Q, where Q = Q1 + Q2. Thus, the firm’s marginal cost of production is 6 per unit.

a. Create a spreadsheet with columns for Q1, Q2, p1, p2, MR1, MR2, and MC. Put the values 1 to 12 in increments of 1 in the Q1 column and put the same values in the Q2 column. Fill in the appropriate formulas in the other cells, noting that the MC column has the value 6 for each quantity. The Jam Factory price discriminates by charging a different price in each city. Find the profit-maximizing quantities and prices. Verify that the marginal revenues are the same in each city at the profit-maximizing quantities. Determine the firm’s profit.

Answer 1

For City 1,

For profit maximisation, MC = MR

We can see this from the table also. When Q₁ =6, MR =6 which is equal to MC.

For City 2,

For profit maximisation, MC = MR

We can see this from the table also. When Q₂ = 7, MR =6 which is equal to MC.

Therefore, the profit maximising quantities, (Q₁,Q₂) are (6,7) and the profit maximising prices, (P₁, P₂) are (9,13)

The maximum profit is 57