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 = 74-q and the inverse demand in Goleta is p = 39 - 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?

Question

Mason Terrell

Business

6 October, 18:46

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 = 74-q and the inverse demand in Goleta is p = 39 - 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?

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Answers (1)

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Makayla Hancock · Answer 1

Seth's total profits is $1,535.359

Explanation:

According to the given data we have the following:

MC = 0 and we will ignore fixed costs

Therefore TC = 0

Demand function in Santa barbara is

p = 74 - q

MR = 74 - 2q

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

MR = MC

74 - 2q = 0

2q = 74

q=37

p = 74 - 37 = 37

Profit = pq - TC

= 37*37 - 0

= $1,369

Inverse demand finction Goleta is

p = 39 - 4q

MR = 39 - 8q

MR = MC

39 - 8q = 0

8q = 39

q = 4.875

p = 39 - 4.875 = 34.125

Profit = pq - TC

= 34.125*4.875 - 0

= $166.359

Therefore, Seth's total profits = $1,369 + $166.359

Seth's total profits = $1,535.359

Seth's total profits is $1,535.359