Question

A firm has estimated their demand curve and cost function to be. P=4000-2Q TC= 1,000,000 - 1500Q + 3.5Q2

a. Find the equation for Marginal Revenue (MR) as a function of Q.

b. What price would a monopolist charge?

c. Calculate the amount of economic profit she would make.

d. Suppose that the monopolist was able to engage in first-degree price discrimination. What quantity would she be willing to produce?

e. What is the range of prices that she would charge her various buyers? Briefly explain. From _________ to __________.

f. Calculate the economic profit she would make in this case. Compare this to the regular monopoly case and briefly discuss where this additional profit comes from.

ONLY NEED PART E AND F PLEASE. Thank you!

Answer 1

e) If  the monopolist was able to engage in first-degree price discrimination

So it would charge each consumers their maximum willingness to pay for the good. It means the price range is start from maximum willingness to pay till the willingness to pay at P = MC

MC = -1500+ 7Q = 7Q -1500

P = 4000 - 2Q

P = MC

4000 - 2Q = 7Q - 1500

5500 = 9Q

Q = 611.11

P (at Q = 611.11) = 4000 - 2 x 611.11 = 4000 - 1222.22 = 2777.78 -- the minimum price

The maximimum price the is where Q = 0,

P = 4000-2*0 = 4000

the range of prices that she would charge her various buyers is 4000 to 2777.78

Marginal cost at Q = 0,

MC = -1500

f) In this case, she would make the profit = (1/2)*(4000- (2777.78))*611.11 + (1/2)*(2777.78 - (-1500))*611.11 - total fixed cost

= 1680552.5- 1,000,000

= 680,552.5

Before price discrimination,

**as you have answer of 1st four part so you must know how this profit come**

Profit = TR - TC = 1,500,000 - 1,125,000 = 375,000

this additional profit of 680552.5 - 375,000 = 305552.5 is come from consumer surplus and dead weight loss which both was not coming to monopoly when he is not charging on the basis of first degree price discimination.