1. (28 points) This question will look at the options a rm 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 : f(K,L) : (5\\E+10\\/E)2 and the other technology being: 80 40 : [CL :62.r ' L. I\" q g(&, ) OXHHD{(29> (g) 1} 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 if : 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 09(9). \\Vhich production method has a lower cost