Reference no: EM13761011

12. 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 equation:
Px=1000 - 20x + 3y and Py = 500 - 5y + x.
The firm faces joint fixed cost of $12,000 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 prices will the firm be able to charge for each product given production at (x*, y*)?
c. What profits results in this instance?
d. At (x*, y*) what the values of ∂TRy / ∂x and ∂TRx / ∂y? Provide a short (one or two sentence) explanation for each value.
e. Check you work by determining the profits that result if x and y are one unit more or less than optimal and fill in the following table.
π =given production near optimal (x*, y*)

y/x Value of x
Value of y π at (x,y) X*-1 X* X*+1
Y*+1
y*
Y*-1