1. A firm produces output using the production function q = VKL (a) Find expressions for the short-run conditional demand for labour and the short-run total cost function of the firm (assuming capital is fixed at K in the short run). (b) Use your expression for the short-run cost function from (a) to derive the long-run conditional demands for capital and labour, along with the long-run total cost function. (e) Confirm your answers in part (b) by solving the long-run cost minimization problem using the method of Lagrange multipliers. (d) Suppose the firm wishes to produce 40 units of output. Further suppose that each input has a price of one. What are the cost-minimizing choices of labour and labour and the total cost of production? (e) Suppose that after the firm acquires capital, it decides that output should be 20. Show that STC > TC for the level of capital found previously. How do the costs incurred by the firm differ from those incurred if the firm could choose capital optimally. Calculate the difference in costs between the STC and the TC