Coach Industries is a market leader in the RV industry and s

Coach Industries is a market leader in the RV industry and sells RVs in both Europe and the United States. Demand from Europe can be represented by P_E=15,000-5Q_E and demand from North America can be represented by P_N=50,000-25Q_N. The firm estimates marginal costs to be constant at $10,000 per RV.

a) Should Coach charge the same price in each market? What price(s) should it charge? How much should it plan to sell in each market at these prices?

b) Calculate the own-price elasticities in each of these markets at the optimal quantities chosen in part a). Are these prices consistent with what you know about 3^rd degree price discrimination? Why or why not?

Solution

Total Revenue in Europe = Q(15000 - 5Q) = 15000Q - 5Q²

^{Marginal Revenue in Europe =} 15000 - 10Q

Equating marginal cost to marginal revenue: 10000 = 15000 - 10Q

Q = 5000/10 = 500

Total Revenue in America = 50000Q - 25Q²

Marginal Revenue in America = 50000 - 50Q

Equating marginal revenue to marginal cost: 10000 = 50000 - 50Q

Q = 40000/50 = 800

Thus, the equilibrium quantity in Europe is 500 and 800 in America.

Price charged in Europe: 15000 - 5(500) = 12500

Price charged in America: 50000 - 25(800) = 30,000

Thus, a higher price should be charged in America.

Coach should not charge same price in both the places.

Price elasticity in Europe = dP/Dq = -5

Price elasticity in America = dP/Dq = -25

These prices are constant with third degree price discrimination. This is because we can see that different prices are charged in different segments of markets (Europe and America) for the same product by the company.