Question

4. Dan needs to hire workers and use oven hours to cook and serve para. The production function is F(LK) 60VLVK, where Lis the hour of labor input and K is the hour of oven usage. Note that the marginal product of labor is 30VK/VL and the marginal product of capital is 30VL/VK. Suppose the cost of labor is given to be $10 per hour and the cost of capital is $10 per hour. In the long run, all inputs are adjustable. (a) (5 points) What are the two conditions the least costly input combination to produce 120 pizzas should satisfy? Write out the two equations (b) (5 points) What is the least costly input combination to produce 120 pizzas?

Answer 1

Production function : FCL, K) = 6057 Sk mp Couginder det MP (morginal product of capital) = 3 0 1 1 1 EZ A ay labo w =$40/hr ; r =$10/hr 0 a) The two conditions are : Pomp Pompe = w = w [ marginal Revenue = Margina 7 Product of labor cost it p 30 KK -40 ...O Pomprar [ Marginal Revenue of – marginal city cepital of capital J p 30 10 ...@ . . b ī z 40 finding lest costly input combination taking ratio of Q ¢ ® p 30 JK . - P(3u2 VE 10 Ķ =4 => [k=42]..6 substituting value g k in production function = 60 JL JUL -> Q=120 L ITQ7 Obhima

k=42= 4le) = a Sofka 47 of fimel capital So, (L,K") =( optimal in but . combinations for produring a output 20