A competitive software rm has a production function f(1]31,172) = 2% where 12 is the number of computers and 3:1 is number of workers employed. Let the workers' wage be it; = 8, the computer price is w; = 32, and output price be p = 8. Suppose that in the short run the rm can only vary the amount of workers it employs but not the number of computers and that the latter is xed at 5:2 = 4 in the short run- (a) Derive the rm's short run conditional input demand for workers if the rm wants to produce y units of output. What is the rm's short run cost flmction for producing output y? (b) What are the rm's xed costs, average variable costs, average costs and marginal costs of producing output 3;? Sketch the AC, AVC and MC curves on a graph. (c) What is the rm's short run supply curve? What is the prot maximizing amount of output that the rm will produce in the short run? At this output level how much prots/ losses does the rm make? Suppose now that the rm is in the long run and can vary both its inputs of production. (d) What are the rm's long run c0nditional input demands for producing y units of output? What is its long run cost function? What is its long run supply curve? (Hint: You can use the condition for optimum TBS = :'; to solve the m's cost minimization problem) (e) Assuming that input and output prices remain at their given short run levels in the long run as well, how much would the rm produce in the long run