a) (12 points) If the price of labor is w = 36, and the price of capital is r = 64, how much labor and capital should the firm hire in order to minimize the cost of production if the firm wants to produce output Q = 36? Equation of Isocost is: rK+wL=C; slope: -w/r; production function: Q=L^(1/2)*K^(1/2) In order to minimize cost: slope of isoquant=slope of isocost: -K/L = -w/r; K/L=36/64= 9/16; K=9/16*L; Q=L(^1/2)*K^(1/2) 36=L^(.5)*((9/16)*(L)) ^(.5) 1296=(9L^(2)/16) 20,736=9L^(2) So, L^(2)=2304 K=(9/16)*48 L=48 K=27