Question

Suppose a firm with cost structure c(y)= y2 + 2y +4 is the only producer of the good in the market. Market demand is given as y(p)= 40 - 2p What is the profit-maximizing quantity for this firm?

Answer 1

1)

c(y) = y2 + 2y + 4

MC = c'(y) = 2y + 2

y = 40 - 2p

2p = 40 - y

p = 20 - y/2

MR = 20 - y  

since firm is only producer so profit maximising condition is

MR = MC

20 - y = 2y + 2

20 - 2 = 2y + y

18 = 3y  

y = 18/3

y = 6

profit maximising quantity is 6

2)

p = 20 - y/2

p = 20 - 6/2

p = 20 - 3

p = 17

3)

Total cost

c(y) =   y2 + 2y + 4

c(6) = (6)2 + 2(6) + 4

= 36 + 12 + 4

= 52

4)

TR = py  

= 17(6) = 102

Profit = TR - TC

= 102 - 52 = 50