Answer to Question #243019 in Microeconomics for Danish

Question

Firm l produces x and Firm 2 produces y. Each firm is a price taker. The price of x is $2, and the price of y is $3.
The cost function of x is given by
x^÷100 and the cost function of y is given by y^÷100_x .How much subsidy per unit of production in x will induce a socially efficient supply?
A $0.75
B. $1.00
C. $1.22
D. $1.50​

Answer 1

Solution:

The correct answer is D. $1.50

Socially efficient supply is where MSB = MSC

Firm 1 MSB (X) = 2

Firm 2 MSB (Y) = 3

Firm 1 MSC =$\frac{\partial TC} {\partial X} = \frac{X} {50}$

Firm 2 MSC = $\frac{\partial TC} {\partial Y} = \frac{Y} {50}$

Firm 1 socially efficient supply: MSB = MSC

= 2 = $\frac{X} {50}$

X = 100

Firm 2 socially efficient supply: MSB = MSC

= 3 = $\frac{Y} {50}$

Y = 150

Subsidy per unit of production in x that will induce a socially efficient supply =$\frac{Y} {X} = \frac{150} {100} = 1.50$