Question

Shower Power, Inc., a firm in monopolistic competition, produces shower radios. The company's economists know that it can sell no radios at $80, and for each $10 cut in price, the quantity of radios it can sell increases by 50 a day. This relationship continues to hold until the price falls to $20. The firm's total fixed cost is $3,000 a day. Its marginal cost is constant at $20 per radio.

a)Draw the demand curve faced by the firm and indicate shower power's marginal cost,  its marginal revenue curve and average total cost curves.

Answer 1

We are given that Quantity demanded increases by 50 units per $10 cut in price and quantity demanded is zero at a price of $80. With the help of given information, we can build P and Q in the following table.

Total Revenue =TR=P*Q

MR=Change in TR/Change in Q

Suppose we move from Q=0 to Q=50

MR=(3500-0)/(50-0)=$70

Suppose we move from Q=50 to Q=100

MR=(6000-3500)/(100-50)=$50

Similarly we can calculate other values.

Total Cost=Fixed Cost+Variable cost per unit*Output =3000+20*Q

(In this case variable cost per unit is marginal; Cost)

We can calculate TC for various values of Q

ATC=TC/Q

We can calculate ATC for various values of Q

MC=$20 (Given)

We have developed the following table with the help of given information and above formulas.

Q	TR=P*Q	MR=Change in TR/Change in Q	TC=3000+20*Q	ATC=TC/Q	MC
0	0		3000
50	3500	70	4000	80	20
100	6000	50	5000	50	20
150	7500	30	6000	40	20
200	8000	10	7000	35	20
250	7500	-10	8000	32	20
300	6000	-30	9000	30	20