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=500−10x−1.5y and Py=250−2.5y−x
The firm faces the total cost as follows: TC=6000+100x+50y
a. What bundle of products (x∗ , y∗ ) should the firm produce?
b. What prices will the firm be able to charge for each product give production at (x∗,y∗)?
c. What profits result in this instance?
d. At (x∗ ,y∗ ), what are the values of dTRydx and dTRxdy ? Provide a short (one- or twosentence) explanation of each value.