Firm 1 produces output X with a cost function C_1(X)=\frac{X^2}{200}. Firm 2 produces output Y with a cost function C_2(X, Y)=\frac{Y^2}{100}-2X. Both firms face competitive markets. The competitive price of X is 6 and the competitive price of Y is \$ 5. There is no entry or exit into this market. What is the socially optimal production of X?

800

Explanation:

The objective here is to determine the socially optimal production of X.

For this to occur ; it is crucial that both firm must merge together.

Therefore; the Profit will be = Total revenue - Total Cost

From the question; the total revenue = 6X + 5Y ;     &

The total cost is :

Now: The profit =

=

If the socially optimal production of X is the differential of the equation

(X) =

=

=

= 800

Thus the social optimal production of X = 800

was my answer wrong?

d) social security number

let me know if i am correct or not, so i can edit the answer.