Quantitative Question: Let the production technology of a particular competitive rm be described by a CobbDouglas production function of the following form Q : AK1/3L2/3 where K is the amount of capital hired, L is the amount of labour hired, and A is just a positive real number denoting the level of technology used by the rm. Let capital be xed in the short run. Finally, let the price of the output of the rm be P and the cost the rm is willing to incur for production is C. (a) Write down the prot function of this rm, and solve for the rm's short run choice for L, in terms of the xed short run choice for capital F, the rents 7\" (price of capital) and wages w, price P and A. (b) Show based on your previous answer that as the wages fall, the equilibrium level of labour hired in the short run rises. Explain your answer with the aid of a diagram. (0) Solve for the long run choice of both types of factor of production. (d) How would your answer to the above change if the production function is of the linear or Leontieff form. In other words, if Q = 2K+3L Q = min{2K,3L}