Question

Suppose that the competitive firms are facing the following cost function and revenue function, C = 14 + q2,revenue function: = 20q -q². (a) Find profit function (b)Find marginal cost function. (c) Find marginal revenue function (c)Find output (q) that maximize profit (d)find total Profit

Answer 1

a) Profit function

=TR-TC

$20q-q^2-(14+q^2)= 20q-q^2-14-q^2$

$=20q-2q^2-14$

b) Marginal cost

$=\frac{\delta TC}{\delta q}= 2q$

c) Marginal revenue function

$=\frac{\delta TR}{\delta q}= 20-2q$

d) Output that maximizes profit

MR=MC

2q=20-2q

4q= 20

q= 5

e) Total Profit

$=20q-2q^2-14$

$=20(5)-2(5^2)-14= 100-50-14$

$= 36$