Suppose that a firm uses both labour (L) and capital (K) as inputs and has the long run production function q = LK - L, with MP_L = K - 1 and MP_K = L. Capital rents for $150 and labour can be hired for $75 per day.
i) Suppose that we are in the short-run and capital is fixed at K = 4. What is the production function?

If the firm wishes to produce q = 30, what combination of inputs should it use to produce as efficiently as possible?

ii) Calculate the MRTS when L = 3 and K=30? Briefly explain the meaning of MRTS for this production function.

iii) What is elasticity of substitution when the capital-labour ratio changes from 1/10 to 1/30?