Consider an industry in which firms produce undifferentiated commodity for which demand is given by X = 100 - P. A number of firms produce the item in question, all of whom have production function
where Y is the level of output and a is some constant from (0, 1), K is the amount of capital employed, and L is the amount of labor employed. The prices of capital and labor are fixed at $1 throughout. All firms have fixed costs of $16.
(a) Suppose precisely six firms are in this industry, all of which maximize profits taking prices as given. What is the equilibrium in this case?
(b) Suppose there is free entry into this industry, with all of the firms having the production function given above. What is the equilibrium in this case?
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