Question

Spanner Co. the nation’s number one manufacturer of widgets faces the following monthly demand curve of Q? = 80 − 2? and can manufacture widgets at a monthly cost of ?(?)= 10?

1. Is Spanner Co. a price taker? Explain.

2. What are Spanner Co.’s profit-maximizing price and quantity?

3. What is Spannar Co.’s revenue-maximizing quantity?

Answer 1

Q=80-2P

P= 40-0.5Q

MR=40-Q

Cost= 10Q

MC=dC/dQ= 10

a. No, Spanner co. is not a price taker as the firm faces a downward sloping demand curve. So Firm is price maker.

b. Profit will be maximized when MR= MC.

40-Q=10

Q*=50

P*= 40-0.5*50=15

Profit maximising price=$15

Quantity= 50.

c. Revenue maximising output: 40

Revenue= Price*Quantity= 40Q-0.5Q^2

To find the value fo Q where Revenue is maximum, Differentiate revenue with respect to Q and equate it to zero.

dTR/dQ= 40-Q=0

Q**=40

Revenue will be maximum at Q=40.