Question

Suppose a textbook monopoly can produce any level of output at a constant marginal cost of $5. Assume that the monopoly sells its books in two different markets that are separated by some distance. The demand curve in the first market is given by Q1=55-P1 and the demand curve in the second market is given by Q2=70-2P2. 1. What are the optimal quantity and price produced in each market? (1.5 point for Q1, 1.5 point for Q2, 1.5 point for P1, 1.5 point for P2) 2. Using your results from previous question, calculate the price elasticity of demand e1 and e2 in each market. Which market has the less elastic demand? (1.5 point for e1, 1.5 point for e2). Clarity of the answers: 1 point. Show the essential steps of your work. Only partial credit will be given if work not shown.

Answer 1

Answer. To maximize profits, monoply choose the quantity at which, MR=MC.

For market 1,

TR = P*Q = (55-Q1)*Q1

So, MR = 55- 2Q1

Equating with MC,

55-2Q1 = 5

50= 2Q1

So, Q1 = 25 and P1 = 30.

For market 2,

TR = P*Q = (35-Q2/2)*Q2

So, MR = 35- Q2

Equating with MC,

35-Q2 = 5

30= Q2

So, Q2 = 30. and P2= 20.

2. For elasticity,

OdP - d OP

Market 1, Pe = 1 *(30/25) = 1.2

Market 2, Pe = 2* (20/30) = 1.33

So, market 1 has less elastic demand.