Suppose w=5, r=20, and the production function is Q=53L0.5k0.5. For this production function MPL=26.5(K/L)0.5 and MPk=26.5(L/K)0.5. A. Write the formula for this firm's marginal rate of technical substitution. When this firm uses the same amount of labour as capital, MRTS = B. Suppose the firm wants to produce Qo=1007. Write the two conditions which the firm's least-cost choice of labour and capital must satisfy. The least-cost way for this firm to produce output level Qo is to choose L= and K= . In this case the firm's total cost will be $ C. Give the equation for this firm's total cost. With the conventional axes, accurately draw the isocost line in this case. The slope of this isocost line is and the vertical intercept is . Now sketch a representative isoquant for Qo passing through the firm's choice of labour and capital. D. Suppose the union doubles wages. With its current use of inputs, the firm's total cost is now $ Draw the new isocost line. It has slope and vertical intercept E. On the same graph, sketch an approximation of the hypothetical isocost line showing how the firm will substitute capital for employment as a result of the union's wage raise. Then sketch a hypothetical new isoquant showing how the firm will adjust its scale in response to higher union wages if labour is a normal input