Question

Suppose that a local firm faces the following demand curve: Q = 70 - (1/11)P

The firm had to make an upfront investment of $2000 and it costs them $220 to produce each unit of output.

1) Graph the demand curve

2) Derive expression for marginal revenue. Graph it on the same figure as (1).

3) Derive expressions for the average cost and marginal cost. Graph on the same figure as (1) and (2).

4) Which Q should the firm produce and what price P should it charge to maximize profit?

5) Calculate profit, Can you use the figure from (1) to show it graphically?

Answer 1

The demand curve is: Q = 70 - (1/11)P. Find the inverse demand function as

(1/11)P = 70 - Q

P = 70*11 - Q*11 or P = 770 - 11Q

The firm had to make an upfront investment of $2000 which becomes its fixed cost and its variable or marginal cost is therefore $220 per unit

1) Graph of the demand curve is provided below

2) From the inverse demand function, find total revenue as TR = PQ

TR = 770Q - 11Q^2

Now MR is the derivative of TR

dTR/dQ = 770 - 22Q

This is the equation for marginal revenue.

3) Note that the average cost is C/Q and the marginal cost is dC/dQ. Here cost function is C = 2000 + 220Q. AC = (2000/Q + 220) and MC = 220.

4) Profit maximation results when MR = MC

770 - 22Q = 220

550 = 22Q

Q = 25 and price P = 770 - 11*25 = 495.

5) Profit is 4875 and is shown in the graph as (495 - 300)*25 OR (P - ATC)*Q