Question

A firm has short run TC:

TC = 100 + 2 Q + Q2 with MC = 2 + 2 Q

1) Find ATC and AVC functions

2) If P = 25, how much will the firm produce in the SR?

3) If P = 20, how much will the firm produce in the SR?

4) Assuming the firm has the same cost curves in the LR, how much will it produce in the LR?

Answer 1

TC = 100 + 2Q + Q^2, MC = 2 + 2Q.

1) $ATC = TC/Q = 100/Q + 2 + Q.$

AVC = VC/Q = 2 + Q.

2) If P = 25, then the firm will produce the next Q in the SR:

P = MC,

2 + 2Q = 25,

Q = 11.5 units.

3) If P = 20, then the firm will produce the next Q in the SR:

P = MC,

2 + 2Q = 20,

Q = 9 units.

4) If the firm has the same cost curves in the LR, then it will produce the next Q in the LR:

MC = ATC,

100/Q + 2 + Q = 2 + 2Q,

Q - 100/Q = 0,

$Q^2 = 100,$

Q = 10 units.