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A firm uses two inputs x1 and x2 to produce output y. The production function is...

A firm uses two inputs x1 and x2 to produce output y. The production function is f(x1, x2) = (x13/2+ x2)1/2. The price of input 1 is 1 and the price of input 2 is 2. The price of output is 10.

(a) Calculate Marginal Products for each input. Are they increasing or decreasing? Calculate Marginal Rate of Technical Substitution. Is it increasing or diminishing?

(b) Draw two or more isoquants. Does this production function exhibit increasing, decreasing or constant returns to scale?

(c) Solve the firm’s cost minimization problem. Derive the firm’s cost function c(y). And find the profit-maximizing choice of inputs x1* and x2* and output y*. Calculate the firm’s profit from these choices.

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