Question

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 – Q 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, 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. b. Add two columns to your spreadsheet showing the price elasticity of demand in each city for each price-quantity combination. Verify that your results are consistent with Equation 10.5. (Hint: The price elasticity of demand for City 1 is E1 = -2p1/Q1 and for City 2 is E2 = -p2/Q2.) Please explain and share the formulas used in each cell of the Spreadsheet.

Answer 1