A market leader in the RV industry sells RVs in both Europe and the United State
ID: 1165916 • Letter: A
Question
A market leader in the RV industry sells RVs in both Europe and the United States. Demand from Europe can be represented by PE=12,000-5QEand demand from North America can be represented by PN=60,000-30QN. The firm estimates marginal costs to be constant at $8,000 per RV.
Should the firm 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?
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 3rddegree price discrimination? Why or why not?
Explanation / Answer
Assuming re-sale is not possible across the markets, the firm should charge different price in each market, following third degree price discrimination. Profit is maximized when
MRE = MC and MRN = MC
For Europe,
PE = 12,000 - 5QE
Total revenue (TRE) = PE x QE = 12,000QE - 5QE2
Marginal revenue (MRE) = dTRE/dQE = 12,000 - 10QE
Equating with MC,
12,000 - 10QE = 8,000
10QE = 4,000
QE = 400
PE = 12,000 - (5 x 400) = 12,000 - 2,000 = 10,000
Since PE = 12,000 - 5QE, we have
5QE = 12,000 - PE
QE = 2,400 - 0.2PE
Own-price elasticity = (dQE/dPE) x (PE/QE) = - 0.2 x (10,000/400) = - 5
In North America,
PN = 60,000 - 30QN
Total revenue (TRN) = PN x QN = 60,000QN - 30QN2
Marginal revenue (MRN) = dTRN/dQN = 60,000 - 60QN
Equating with MC,
60,000 - 60QN = 8,000
60QN = 52,000
QN = 866.67
PN = 60,000 - (30 x 866.67) = 60,000 - 26,000 = 34,000
Since PN = 60,000 - 30QN, we have
30QN = 60,000 - PN
QN = 2,000 - (1/3)PN
Own-price elasticity = (dQN/dPN) x (PN/QN) = - (1/3) x (34,000/866.67) = - 13
Price is higher in North America where absolute value of own-price elasticity is higher, signifying demand is more elastic in North America. This is inconsistent with the concept of price discrimination because, higher price is charged in the less elastic market, and lower price is charged in the more elastic market.
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