The cost and demand conditions for residential water consumption are shown below.If there are 450,000 residential water customers,then develop an optimal two-part pricing scheme and answer the question. At the optimal user fee,the water utility company will lose _______ per month.

Question

The cost and demand conditions for residential water consumption are shown below.If there are 450,000 residential water customers,then develop an optimal two-part pricing scheme and answer the question.  At the optimal user fee,the water utility company will lose _______ per month.

Quizplus · Accepted Answer

First, we need to find the optimal price to charge per unit of water consumed. This is found by setting the marginal cost equal to the marginal revenue:

MC = 0.0002Q + 10
MR = 0.004Q - 2

0.0002Q + 10 = 0.004Q - 2
0.0038Q = 12
Q = 3157.89

So the optimal price to charge per unit is $10 + $0.0002(3157.89) = $10.63.

Now we need to find the optimal fixed fee to charge each customer. This is found by setting the quantity demanded equal to zero and solving for the fixed fee:

0.004(0) - 2 = -F + $10.63
F = $8.63

So the optimal two-part pricing scheme is to charge each customer a fixed fee of $8.63 plus $10.63 per unit of water consumed.

To find out how much the water utility company will lose per month, we need to calculate the total revenue and total cost:

Total revenue = ($8.63)(450,000) + ($10.63)(Q)
Total cost = (0.0001Q^2 + 10Q)(450,000)

Total revenue = ($8.63)(450,000) + ($10.63)(3157.89) ≈ $6,850,806.47
Total cost = (0.0001(3157.89)^2 + 10(3157.89))(450,000) ≈ $8,290,806.47

So the water utility company will lose $8,290,806.47 - $6,850,806.47 = $1,440,000 per month. Therefore, the answer is B.

The Cost and Demand Conditions for Residential Water Consumption Are