1].- I LLULJLJLJiVJD Problem 1 A competitive tech rm has a production function f[;:1=wg) = 3? where 1:2 is the number of machines and 2:1 is number of workers employed. The workers1 wage is 101 2 15 the machine price is 1.92 = 16 and the output price is p = 16. Suppose that in the short run the rm can only vary the amount of workers it employs but not the number of machines and that the latter is xed at 2 = 4 in the short run. (a) Find the rms short run conditional factor demand for workers if the rm wants to produce '9 units of output. What is the rmls short run cost function for producing output '9? (b) What are the rm's xed costs? average variable costs, average costs and marginal costs of producing output y? Sketch the SRM'C, AVG and SRAC curves on a graph. (c) What is the rms short run supply curve? lWhat is the protmaximizing amount of output ySH that the rm will produce in the short run? At this output level how much prot or loss does the rm make? Suppose now that the rm is in the long run and can vary both its factors of production. ((1) lWhat are the rm's long run conditional factor demands for producing Q units of output"? lWhat is its long run cost function? 'What is its long run supply curve? (e) Use your results from parts (a) and (d) to nd and the shortrun and longrun average costs for any y. Show that SRAC[y) 2 LRAC(Q) for any '9. Explain why. (f) vae that the shortrun and longrun average costs are equal and tangent to each other- at the output level Q which solves R() = 4 where :r'Rw) is the longrun conditional demand for machines from part (d). Explain why this is the case (a graph may help). (g) Assuming that the input and output prices stay at their given values, how much would the rm produce in the long run"