A firm makes two products, x and y. Inverse demand for each shows that pricing i

Question

A firm makes two products, x and y. Inverse demand for each shows that pricing in one market depends on sales in the other according to the equations:

Px = 1000 -20x + 3y and Py = 500 – 5y + x.

The firm faces joint fixed cost of $12000 and constant marginal cost of production in each product segment, MCx =$200, and MCy = $100.

A. What bundle of products (x*, y*) should the firm produce?

B. What price will the firm be able to charge for each product given production at (x*, y*)?

C. What profits result in this instance?

Explanation / Answer

Px = 1000 -20x + 3y

Profit fonction for the firm will be

Profit = TRx + TRy - TC

= Px.X + py.Y - 12000 - MCx.X - MCy.Y

= (1000 -20x + 3y)x + (500 – 5y + x).y - 12000 - 200x - 100y

dProfit/dx = 1000 - 40X + 3y + y - 200

Putting dProfit/dx = 0

40x - 4y - 800 = 0

dProfit/dy = 500 - 10y + x + 3x - 100

Putting dProfit/dy = 0

4x - 10y + 400 = 0

Solving two equations for x and y

96y = 3200

y* = 33.33

X* = 16.67

B. Px = 1000 - 20*16.67 + 3*33.33 = 766.59

Py = 500 - 5*33.33 + 16.67 = 350.02

c. Profit = 766.59*16.67 + 350.02*33.33 - 12000 - 200*16.67 - 100*33.33

= 5778.22

If you don't understand then comment, I'ill revert back on the same. :)

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