A firm, using two inputs K and L to produce one product, whose production function is (=2522K/, responds to a quantity demanded of 300 units. the price of L is 6, while the price of K is 10. What is his optimal cost and how many units of L and K will he use? Please prove that the marginal production(MP) curve will across the average production(AP)curve at APs maximum(Provided that the production function is differentiable) A firm produces one product using two inputs(K and L), if the production function of the firm is linearly homogeneous function, please prove the Clark-Wicksteed -exhaustion theorem. Namely Q=K·MPk+L·MP A firm uses two inputs K and l to produce one product whose production function market is @=2K L. The market demand function for the product is P-20-Q while the labor market is complete with wage w=4. In some period his capital K is fixed at 4 units and the price of K, is 10. a) How many units of L should he b) The product price P? The production Q and his profit Please prove that the short-run marginal cost(SMC)equal to the short-run average cost(SAC)at SACs minimum (Provided that the total variable cost function is differentiable)A firm, using two inputs K and L to produce one product, whose production function is 2 / 5 3/ 5 Q = 25L K , responds to a quantity demanded of 300 units. the price of L is 6, while the price of K is 10. What is his optimal cost and how many units of L and K will he use? Please prove that the marginal production (MP) curve will across the average production (AP) curve at AP’s maximum. (Provided that the production function is differentiable) A firm produces one product using two inputs (K and L), if the production function of the firm is linearly homogeneous function, please prove the Clark-Wicksteed product-exhaustion theorem. Namely Q K MPK L MPL =  +  A firm uses two inputs K and L to produce one product whose production function market is 1/ 2 1/ 2 Q = 2K L . The market demand function for the product is P=20-Q, while the labor market is complete with wage w=4. In some period his capital K is fixed at 4 units and , the price of K, is 10. a) How many units of L should he use? b) The product price P? The production Q and his profit. Please prove that the short-run marginal cost (SMC) equal to the short-run average cost (SAC) at SAC’s minimum. (Provided that the total variable cost function is differentiable)