Question 1 Consider the following production function: y = F(L, K) = 40=K3 where L and K are the amount of labour and capital used in the production process, and y is the output. Throughout this question, the output price p is 3 and the rental rate of capital r is 1. We will first consider a firm in the short run, where the amount of capital is fixed at K = 64. The fixed cost is therefore 64. (a) (Level A) Is there diminishing returns to labour? Explain. (b) (Level A) Suppose the wage rate w is 1. Find the profit-maximising choice of L. Calculate the profit-maximising output level and the maximised profit. (There is no need to check the second order condition - but of course you can check if you want to.) (c) (Level A) Now suppose w increases to 2. Find the profit-maximising choice of L. Calculate the profit-maximising output level and the maximised profit. (There is no need to check the second order condition.) You can leave your answers in square roots. (d) (Level A) What is the change in L when w increases from 1 to 2 in the short run? You can leave your answers in square roots.Now consider the rm in the long run, where K is variable and can be chosen by the rm. {e} {level A) Does the production function exhibit increasing, decreasing or constant returns to scale? Explain. {f} {level B) Suppose the wage rate is is 1. Find the protmaximising choices of L and K. Calculate the protmaximising output level and the n1a1o'nn'sed prot. {There is no need to check the second order condition.) How does the prot in the long run compared to the prot in the short run {i.e., that in part {bl}? Why