Question

Suppose Margaret and Thomas are the only two homeowners in the neighborhood. Margaret's demand for clean streets is Q = 50 - 2P. Thomas's demand for clean streets is Q = 40 - P. What is the socially optimal number of clean streets if the marginal cost of cleaning them is $35?

Answer 1

Answer:

20 is the socially optimal number

Explanation:

In this question, we are asked to calculate the socially optimal number of clean streets given the marginal cost of cleaning them.

To solve this problem, we employ a mathematical approach as follows:

Market demand = Sum of Individual demand

Magaret demand = p = (50-Q)/2 = 25-0.5Q

Thomas demand = P = 40-Q

Market demand = 25-0.5Q + 40-Q = 65-1.5Q

MC = 35

Socially optimal number = MC = Market demand

35 = 65-1.5Q

30 = 1.5Q

Q = 20

Answer 2

The socially optimal number of clean streets when the marginal cost of cleaning them is $35 will be 20.

Based on the information given, the demand for Margaret will be:

P = (50 - Q) / 2 = 25 - 0.5Q

The demand for Thomas is P = 40 - Q

The market demand will be gotten by adding both demands. This will be:

= 25 - 0.5Q + 40 - Q

= 65 - 1.5Q

Therefore, MC = 65 - 1.5Q

35 = 65 - 1.5Q

1.5Q = 65 - 35.

1.5Q = 30

Q = 30/1.5

Q = 20

Therefore, the socially optimal number of clean streets is 20.

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