1. The production function of a rm is given by q = ALQKPG, where q denotes output produced, A denotes the technology of production, and K and L denote capital and labour used per period. Further, the wage and rental rates are denoted by 'w and 7', respectively. For this CobbDouglas production function, the marginal product of labour is M PL = aALC\"1K'G, and the marginal product of capital is M PK = ALQK'G'l. Suppose or = = g, and that in the short run the rm's capital is xed at the level Kg. In this problem, '11), r, A and K0 are parameters (think of them as given constants or numbers). Using this information, answer the following questions for a costrninirnizing rm. Show your work. (i) In the short run, how many units of L will this rm use in order to produce q units of output? (ii) Derive the short run total cost function of this rm (i.e. express short run total cost as a function of q). (iii) In the long run, how many units of L and K will this rm use in order to produce q units of output? (iv) Derive the long run total cost function of this rm (i.e. express long run total cost as a function of (1).? [Note: Your answers to the above questions should be in terms of w, r, A, K0, q]