1. (28 points) This question will look at the options a firm has for production in the short run and in the long run as well as the cost of producing in a perfectly competitive market. Suppose the rm has two options for producing with the rst technology being: q : mg L) : (5x/Z+ Mix/FY and the other technology being: q : 9(K, L) : 62.5 x min { (g) L, (%) K} The market for labour and capital are both perfectly competitive with the market wage rate of $62.50 and the rental rate of capital at $250. The market price of the good being produced is P : $1. The rm will start with K : 36 that can be used in the production process for either technology. (a) (5 points) Based on the information about, what is the optimal choice of labour L* for each production process in the short run (i.e. when K : 36)? (Note: this means you should get L} and L3.) (b) (5 points) Find the short run cost function for each production method: Cq) and Cg(q). Which production method has a lower cost? (c) (3 points) Given your answers above, would a producer operate in this market in the short run or temporarily shutdown? What production method would they use? (d) (8 points) Given the same q found in part (a) and used for part (c), what would be the long run choice of capital and labour for each production method (Le. {L}, K?) and [L3, K5)? (Note: you should have found q : 10, 000, which is now the constraint: (j : 10,000. Also, one of the production functions is likely to produce an answer that is veryj very simple.) (e) (7 points) What is the long run cost function for both production methods? Which production method has a lower long run cost? Does either rm produce in the long run or do they exit the market? Explain