A firm with market power faces the following estimated demand and average variable cost functions: where is quantity demanded,P is price,M is income,and is the price of a related good.The firm expects income to be $40,000 and to be $2.Total fixed cost is $100,000.What is the estimated demand function for the firm?

Question

A firm with market power faces the following estimated demand and average variable cost functions:   where  is quantity demanded,P is price,M is income,and  is the price of a related good.The firm expects income to be $40,000 and  to be $2.Total fixed cost is $100,000.What is the estimated demand function for the firm?

Quizplus · Accepted Answer

We know that the estimated demand function for the firm is of the form: Q = a + bP + cM + dPrel, where Q is quantity demanded, P is price, M is income, and Prel is the price of a related good. 
Given information about the firm, we know that M = $40,000 and Prel = $2. We also know that total fixed cost is $100,000, which means that average fixed cost is $10 per unit of output (since AFC = TFC/Q). 
To find the estimated demand function, we need to use the information provided in the question and solve for the coefficients a, b, c, and d:

Q = a + bP + cM + dPrel
Q = a + 500bP + 70c + 200d

We can rearrange the demand function to isolate price:

Q - 70c = a + 500bP + 200d 
(Q - 70c - a - 200d)/500 = bP

Now we can substitute in the given values and solve for b:

39,000 = a + 500b(800) + 70(40,000) + 200d 
100,000/Q = 10 + 500b(200) + 2b 
100,000/Q = 1,000b 
b = 100

Substituting this back into the demand function:

Q = a + 500(100)P + 70(40,000) + 200d 
Q = a + 50,000P + 2,800,000 + 200d

We know that when P is zero, the quantity demanded is 70,000:

70,000 = a + 0 + 2,800,000 + 200(0) 
a = -2,730,000

Therefore,

Q = -2,730,000 + 50,000P + 2,800,000 + 200d 
Q = 70,000 + 50,000P + 200d

So the estimated demand function for the firm is Q = 70,000 + 50,000P + 200d.

Therefore, the correct answer is C, which matches this equation.

A Firm with Market Power Faces the Following Estimated Demand