A two product monopoly faces the following demand and cost functions:

?(?sub1)^d [not an exponent]= 40 ? 2?sub1 ? ?sub2

??sub2^d = 35 ? ?sub1 ? ?sub2

?? = ?sub1^2 + 2?sub2^2 + 10

a. Find the pair of prices, psub1 and p2sub, that satisfy the first-order necessary conditions for a local maximum of the profit function: ?(?sub1, ?sub2 ) = ?sub1?sub1^? (?1,?2) + ?sub2?sub2^? (?1,?2) ? ((?sub1^? (?sub1,?sub2))^2 + 2(?sub2^? (?sub1,?sub2))^2 + 10)

b. Confirm that the second-order, sufficient condition for a local maximum is met at that pair of prices. Can you conclude that the local maximum you have identified is also a global maximum? Explain.

c. How much of each product will be produced and sold? What will the firm's profit be?

6. A two product monopoly faces the following demand and cost functions: a. C. ' qf=40-2p1pz - q=35p1p2 - c=qf+2q+10 Find the pair of prices, p1 and P2, that satisfy the first-order necessary conditions for a local maximum of the profit function: 7:091, p2) = plqplpz) + p2q(p1,p2) (613101.992 + 26:? (p1.p2)2 + 10) Confirm that the second-order, sufficient condition for a local maximum is met at that pair of prices. Can you conclude that the local maximum you have identied is also a global maximum? Explain. How much of each product will be produced and sold? What will the firm's profit be