1.[Firm selling product of two qualities]

A firm produces two different types and of a commodity.

The cost of producingunits of andunits ofis

(,)=(4/100)2+(1/100)+(1/100)2+4+2+250.

Suppose the firm sells it's output in a perfectly competitive market with a per unit price of$15for typeand$9for.

Find the profit maximizing output levelsandand also the maximum profit.

2.[Multi-product Monopoly Profit Maximization]

A monopoly firm sells two different brands of a product for which the demand functions are

1=500.251,

2=1002, and the cost function for the firm is

(1,2)=0.51^2+412+2^2+100.

Find the profit maximizing output levels1and2and also the maximum profit.

3.[Profit Maximizing Input Demand]

Consider a competitive firm with the following profit function

=,

where=1and=1and

(,)=3^1/3^2/3

(a) Find the input quantitiesand that satisfy the first order conditions for the profit maximization.

(b) Find the output price for which

(i) there is no solution to the profit maximization problem;

(ii) there are infinitely many solutions to the profit maximization problem; and

(iii) there is unique solution to the profit maximization problem.

(c) In (ii) and (iii) above find the profit maximizing input bundle(s)(,)