Question

A firm has the production function Q =x1^1/2 * x2In the short run, it must use exactly 15 units of factor 2. The price of factor 1 is $75 per unit and the price of factor 2 is $2 per unit. The firm’s short-run marginal cost function is

	a.	MC(Q) = 30 + 75Q^2.
	b.	MC(Q) = 30Q^1/2.
	c.	MC(Q) = 2Q.
	d.	MC(Q) = 15Q^1/2.
	e.	MC(Q) = 10Q/15.

Answer 1

Q = X₁^1/2 X₂

In the short run, it must use exactly 15 units of factor 2. It means capital is fixed in short run at 15 units so put this in production function, we get

Q = X₁^1/2 (15)

X₁^1/2 = Q/15

X₁ = (Q/15)²

X1 = Q² / 225 ---- Put this value in the cost function,

Cost function: C = X1*( Price of factor 1) + X2*(price of factor 2)

C = [Q² / 225]* (75) + 15*2

C = [Q² / 3] + 30 -- total cost

MC = d(C)/ dQ

MC = 2Q/3 + 0

MC = 2Q/3

Ans is MC = 2Q/3 Which is also equal to 10Q/15 [ if we simplify 10Q/15, we get 2Q/3]

So correct ans is e) MC = 10Q/15