For a firm, let total cost be TC(Q) = 10Q² and marginal cost be MC(Q) = 20Q. Which of the following is an expression for the output elasticity of total cost? A) ϵ_TC,Q = 10Q. B) ϵ_TC,Q = 2Q. C) ϵ_TC,Q = 2. D) ϵ_TC,Q = 20Q.

Question

Quizplus · Accepted Answer

The output elasticity of total cost is given by the formula:
ϵS1U1B1TC,QS1U1B0 = (dTC/dQ)(Q/TC)
Taking the derivative of TC(Q) with respect to Q, we get:
dTC/dQ = 10S1U1P12S1S1P0 + 10QS1U1P0
Substituting the value of marginal cost (MC) in the above equation, we get:
dTC/dQ = 20Q + 10QS1U1P0
Dividing this by TC(Q), we get:
ϵS1U1B1TC,QS1U1B0 = (20Q + 10QS1U1P0)/(10QS1U1P12S1S1P0)
Simplifying this, we get:
ϵS1U1B1TC,QS1U1B0 = 2 + (1/S1S1P1)
Since we have no information about the value of S1S1P1, the correct option is (C) ϵS1U1B1TC,QS1U1B0 = 2.

For a Firm, Let Total Cost Be TC(Q) = 10Q2

For a Firm, Let Total Cost Be TC(Q) = 10Q²