Question

1. 1 :36 - 45 0 19273-26 9 . 12 A firm produces a product in a competitive industry and has a total cost function C+50 + 40 +29' and a marginal cost function MC = 4 +4q. At the given market price of $20, the firm is producing 5 units of TR4204 output. Is the firm maximizing its profit? What quantity of output should the firm produce in the long EMR=20 run? 2 4149=20 974 STRIAIS VD

Answer 1

1. We know a competitive firm maximizes it's output when :

P = MC

As, P = $20 and MC = 4 + 4q

So, 20 = 4 + 4q

20 - 4 = 4q

4q = 16

q = 16/4

q = 4

Hence, At 4 units output firm maximizes it's profit

So, Firm will not maximize its profit at 5 units of output.

Long run equilibrium under perfect competition is at the point where :

$\frac{\partial AC}{\partial q} = 0$

We can see

C = 50 + 4q + 2q²

So, Average Cost (AC) = C/q = (50 + 4q + 2q²)/q

So, AC = 50/q + 4 + 2q

So,

$\frac{\partial \;\frac{50}{q} + 4 + 2q}{\partial q} = 0$

$-\frac{50}{q^{2}} + 2 = 0$

$2 = \frac{50}{q^{2}}$

$q^{2} = \frac{50}{2} = 25$

$q = \sqrt25$

$q = 5 \;\;\;\;\;\;\;\;\;\;\;\;\;\;\; or \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; q = -5$

As, Output can't be negative. So q = 5

So, Quantity of Output produced in the long run is 5 units