The Vancouver Paper Company, located in Vancouver, British Columbia, produces newsprint and packaging materials in a fixed 1:1 ratio, or 1 ton of packaging materials per 1 ton of newsprint. These two products, A (newsprint) and B (packaging materials), are produced in equal quantities because newsprint production leaves scrap by-products that are useful only in the production of lower-grade packaging materials.

The total cost function for Vancouver can be written: TC = 2000 + 50Q + 0.01Q² where Q is a composite package or bundle of output consisting of 1 ton of product A and 1 ton of product B.

a. Given current market conditions, demand curves for each product are as follows:

PA= 400 0.01QA

PB= 350 0.015QB

What is the profit maximizing level of output, price of each product, and total profit?

(show your work both graphically and mathematically)

b. Suppose that an economic recession causes the demand for product B (packaging materials) to fall dramatically, while the demand for product A (newsprint) and marginal cost conditions hold steady. Assume new demand for product B is: PB= 290 0.02QB

what is the profit maximizing level under these circumstances, price of each product, and total profit? (show your work both graphically and mathematically)