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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?

Respuesta :

Answer:

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

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