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A firm discovers that when it uses K units of capital and L units of labor...

A firm discovers that when it uses K units of capital and L units of labor it is able to

      produce q=4K^1/4 L^3/4 units of output.

a) Calculate the MPL, MPK and MRTS

b) Does the production function (q=4K^1/4 L^3/4) exhibit constant, increasing or decreasing returns to scale and why?

c) Suppose that capital costs $10 per unit and labor can each be hired at $40 per unit and the firm uses 225 units of capital in the short run. How much labor is used and what is the short-run total cost to produce 600 units of output?

d) Continue to assume that capital and labor can be hired at $40 per unit for labor and $10 for capital. In the long run if the firm produces 600 units of output, how much labor and capital will be used and what is the LR Total cost of production?

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