Question 1. (5 points) Suppose the production of airframes is characterized by a CBS production function: 2 Q = (Li + K%) 1. Show that the marginal products of this production function are M PL 2 (L% + 11%) L_% and MPK = (13+ K%) K%. (1 point) 2. Find the conditional input demand functions of labor and capital (the cost-minimizing com- binations of labor and capital) for any given wage w, rental rate of capital 7' and quantity Q. That is, nd L*(Q,w,r) and K*(Q,w,r) (1 point) 3. Show that the total cost function TC(Q) as a function of w, 'r and Q is equal to TC(Q) = Q (1,113\") and nd the marginal cost TC' (Q) (1 point) 4. Suppose that the price of labor is $10 per unit and the price of capital,is $1 per unit. Find the cost-minimizing combination of labor and capital for an airframe manufacturer that wants to produce 121,000 airframes. (1 point) 5. Obtain the wage elasticity of the conditional labor demand and the rental rate (of capital) elasticity of the conditional capital demand at the above input prices and quantity (at w = $10, 7" = $1 and Q = 121,000. (1 point)