How much would the current firm have to produce to keep the potential firm out of the market?

1) In a market with the following demand curve: P=100-(Q1+Q2)

Q1 is the output of the current firm, Q2 is the output of the potential firm (to be entered into market) and P is the market price. The cost functions are given by:

TC = 40Q1 and TC = 40Q2+100 While 100 is an entering cost paid upon entering the market:

· a)  If the potential firm observes the current firm producing Q* units of output and expects this level to be maintained, what is the equation for the potential firm demand curve (remaining demand)?

· b)  If the potential firm maximizes profits using the remaining demand in (a), what output will be produced by the potential firm?

· c)  How much would the current firm have to produce to keep the potential firm out of the market? And At what price will sell this output?

2) Consider an exchange economy with only 2 consumers, Arnold and Brigitte, and 2 goods, X and Y. Arnold has utility function UA = X Y and Brigitte UB =min {X ,Y}.
Arnold has an initial endowment of (XA , YA) = (3, 0) and Brigitte has (XB , YB) = (0, 3).

· a)  Solve for the optimal allocation of goods. (XA , YA and XB , YB)

· b)  Find the price ratio and contact curve.

· c)  Sketch an Edgeworth box showing the initial endowments, pareto optimal solution, and contract curve.