PLEASE EXPLAIN STEP BY STEP ON A PAPER $.$

Consider an industry with two products A and B$.$ There are $100$ consumers who value product A

at vA $=150$ and product B at vB $=120.$ The incumbent firm $1$ produces both goods. Its marginal

cost of production for good A is cA $=90$ and cB$1=80$ for good B$.$

There is also a potential new entrant firm $2$ who only produces good B at a marginal cost of

cB$2$cB$1=80.$ Firm $2$ has a cost of entry of K $=1000.$ The timing of the game is as follows. First,

firm $1$ decides whether to sell good A and B in a bundle. Second, firm

$2$ decides whether to enter the industry. Third, all active firms name the price for their product.

a$)$ Suppose firm $2$ has not entered. Determine the monopoly profits of firm $1$ for both products.

Without entry, does firm $1$ make higher profits when selling the products in a bundle or separate?

b$)$ Assume firm $1$ offers the products individually and firm $2$ has entered the market for product

B$.$ Firms compete in prices. Determine the Nash equilibrium in prices in market

B and give the total profits of firm $1$ and firm $2$ as a function of cB$2.$

c$)$ Now assume firm $1$ supplies the products in a bundle. Give the Nash equilibrium in prices and

the profits of firm $1$ and firm $2$ as a function of cB$2.$

d$)$ Give the condition under which entry occurs with and without bundling.

e$)$ Give the conditions under which bundling is strictly profitable and deters entry from firm $2$ in

market B$.$ Explain this result.