Question

Seth owns a local business that provides email updates on surf conditions. He is the only supplier of these email updates in Santa Barbara and Goleta, which gives him a monopoly in both cities. The marginal cost of producing another update is zero (and we'll ignore fixed costs). The inverse demand for these updates in Santa Barbara is p = 67 - q and the inverse demand in Goleta is p = 31 - 4q. Suppose Seth charges different uniform prices in SB and Goleta. If Seth sets each price such that he is maximizing his total profits, what are Seth's total profits?

Answer 1

Answer :

given, MC = 0 and we will ignore fixed costs

Therefore TC = 0

Demand function in Santa barba is

p = 67 - q

MR = 67- 2q

Since Seth sets different uniform prices in two markets to maximises his profit therefore

MR = MC

67 - 2q = 0

2q = 67

q = 33.5

p = 67 - 33.5 = 33.5

Profit = pq - TC

= 33.5\times33.5 - 0

= 1122.25

Inverse demand finction Goleta is

p = 31 - 4q

MR = 31 - 8q

Likewise above

MR = MC

31 - 8q = 0

8q = 31  

q = 3.875  

p = 31 - 3.875 = 27.125

Profit = pq - TC

= 27.125\times3.875 - 0

= 105.109

Hence Seth's total profit = 1122.25 + 105.109

= 1227.35