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Find market demand for good x

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Reference no: EM132407180

This question will study the market for good x.

Suppose there is one consumer that is a price taker in all markets with the following preferences:

U(x, y) = 3x + y

This consumer has an income of I = 1000. There is one firm, which is a price-taker in the market for inputs and operates under perfect competition in the market for x. The firm follows the following production function, with inputs K and L, to produce good x:

f(K, L) = K 1/3L 1/3 Capital is fixed at K = 8. Wages and the rental rate for capital are w = 8/3 and r = 300, respectively. The price for good y is determined elsewhere at py = 300

(a) Find market demand for good x.

(b) Is f(K, L) increasing, decreasing or constant returns to scale?

(c) Find the short-run cost function for the firm producing good x.

(d) Find the short-run supply for x.

(e) What is the equilibrium market price and quantity for x.

(f) What is the equilibrium profit of the firm? Explain why the firm has incentives to keep operating.

Reference no: EM132407180

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