As the result of a merger, you are now CEO of a company that operates in 2 regio
ID: 1124282 • Letter: A
Question
As the result of a merger, you are now CEO of a company that operates in 2 regions, East and West. The markets are somewhat different. The West has the following demand and MR:
Qd = 200 - 4P
MR = 50 - 0.5Q
While the East is a larger and less price sensitive market:
Qd = 300 - 2P
MR = 150 - Q
a) The area manager from the East suggests you use a strategy that charges each market a separate price. If you operate in separate markets, the variable cost associated with each unit is $5, and fixed costs are $2000. What is this strategy called? Calculate your profits using this strategy.
b) The area manager from the West points out that there are certain scale economies that can be achieved by treating the regions as one big market--variable cost per unit would decrease to $4, while fixed costs remain $2000. What is your profit with this strategy? Which do you choose?
Explanation / Answer
Total cost (TC) = Fixed cost + Variable cost = 2,000 + Variable cost
(a) This pratice is called third-degree price discrimination strategy. In this strategy, MR of each market is equated with marginal (unit variable) cost (MC).
For West market,
50 - 0.5Q = 5
0.5Q = 45
Q = 90
From demand function,
Q = 90 = 200 - 4P
4P = 110
P = 27.5
For East market,
150 - Q = 5
Q = 145
From demand function,
Q = 145 = 300 - 2P
2P = 155
P = 77.5
Total revenue from both markets = (27.5 x 90) + (77.5 x 145) = 2,475 + 11,237.5 = 13,712.5
Total cost = 2,000 + 5 x (90 + 145) = 2,000 + 5 x 235 = 2,000 + 1,175 = 3,175
Total profit = Total revenue from both markets - Total cost = 13,712.5 - 3,175 = 10,537.5
(b) This strategy is called single price strategy where a single price is used in both markets.
Aggregate (market) quantity (Q) = Q(West) + Q(East) = 200 - 4P + 300 - 2P = 500 - 6P
6P = 500 - Q
P = (500 - Q) / 6
Total revenue (TR) = P x Q = (500Q - Q2) / 6
MR = dTR/dQ = (500 - 2Q) / 6
Equating with MC,
(500 - 2Q) / 6 = 4
500 - 2Q = 24
2Q = 476
Q = 238
P = (500 - 238) / 6 = 262 / 6 = 43.67
Total revenue = P x Q = 43.67 x 238 = 10,392.67
Total cost = 2,000 + 5 x 238 = 2,000 + 1,190 = 3,190
Profit = Total revenue - Total cost = 10,392.67 - 3,190 = 7,202.67
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