Answer to Question #287927 in Economics for Likenaw

Question

. A monopolist has the following weekly total revenue and total cost function (R) = 30Q- Q^2 and (C )= Q^3 -15Q^2+10Q+100, respectively in dollars.

a) Find the level of output that maximizes the profit?

b) Find the maximum weekly profit?

c) Find the point elasticity of demand at equilibrium level of output?

Answer 1

a) The level of output that maximizes the profit is:

MR = MC,

MR = R'(Q) = 30 - 2Q,

$MC = C'(Q) = 3Q^2 - 30Q +10,$

$3Q^2 - 30Q +10 = 30 - 2Q,$

$3Q^2 - 28Q - 20 = 0,$

Q = (28 + 32)/6 = 10 units.

b) The maximum weekly profit is:

$TP = R - C = (30×10 - 10^2) - (10^3 - 15×10^2 + 10×10 +100) = 500.$

c) The point elasticity of demand at equilibrium level of output is:

P = 30 - Q = 30 - 10 = 20,

Q = 30 - P, then:

Ed = -1×20/10 = -2, so the demand is elastic.