Question

Suppose that 3W is a representative firm operating in a perfectly competitive industry. 3W's total cost of production is given by TC = 100+q+. a. If the output price is $400, what is 3W's short-run profit-maximizing level of output? b. What is 3W's profit at that price? Graph your results from a) and b). (Hint: your graph needs to include the MR, MC, and ATC curves.)

Answer 1

MC = dTC/dq = 1 + 2q

(a) P= $400

Profit maximizing condition is where P=MC

1+2q = 400

2q = 399

q = 199.5 units

(b) Profit = TR- TC

TR = (400)(199.5)= $79,800

TC= 100+ (199.5) + (199.5)²

= $40099.75

Profit = $(79800 - 40099.75)

= $39700.25

(c) MR= P , so it is represented by the horizontal line at $400.

MC = 1 +2q

When q = 0, MC= 1

When q =50 , MC= 101

When q= 100 , MC= 201

When q= 150 , MC = 301

When q= 199.5 , MC = 400

ATC =TC/q = (100+ q+q²)/q

ATC = 100/q + 1 + q

When q =0 , ATC= 1

When ATC = MC then ,ATC is at its minimum , so

100/q + 1 +q = 1+2q

100- q² =0

q = 10 units

When q=10 , ATC = 100/10 + 1 + 10 = 21

And when q= 199.5 , ATC = 100/199.5 + 1+ 199.5

ATC = 201

By plotting this we get ATC, MC and MR curve as shown below :

Soo -P-MR yoo 300 200 50 los 150 200 250 199.5