In the market for product X, there are 800 identical consumers with a utility function given by U = X^0.5Y^0.5.

400 of these consumers have an income of $1,500 each, 300 have an income of $2,500 , while the rest have an income of $4,000.

Consider that price of good "Y" is $10.

On the other hand, it's known that a firm's production function is q = 10*L^0.5K^0.5.

In the short run K = 100. The prices of labor (L) and capital (K) are $20 and $100 respectively, per unit of input.

The industry consists of 20 firms.

Determine:

(a) Market demand for X

b) The firm's cost and supply curve.

c) Market supply for X

d) Market equilibrium price and quantity

e) What will be the firm's profit and quantity produced-sold?

f) What is the long-run behavior of the firms in the industry (do they exit or stay?)?

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