*) A manufacturer produces wheels according to the production function: = 41/21/2 , where K is measured in units of capital, L in number of workers, and q in number of wheels per week. The prices of capital and labor are = 2 = 4. a) Draw the isoquant corresponding to a production of 100 wheels per week? b) Consider the following input combinations: K = 400 and L = 25, K = 100 and L = 100 and K = 25 and L = 400. Are these points on the previous isoquant? Justify your answer. Represent graphically. c) Depict now the isoquants that go through the points K = 100 and L = 100, and K =400 and L = 400. Are there constant returns to scale? Explain why. Consider now and depict capital fixed at K = 100 and the possible productions with L = 100 and L = 400. Can you show with this example diminishing marginal returns to labor? d) Find the total cost function (Cost as a function of quantity). e) Represent in a diagram the firm's cost minimizing choice of factors to produce a given quantity q. If =800, how much K and L are used? 5) (*) Craft Corp.'s production function is given by q = min(10K, 20L), where q is the quantity produced and K and L are the amounts of capital and labor input. Input prices are r = 3 and w = 2. a) Find Craft Corp's long-run cost function. b) Draw Craft Corp's Long isoquants and isocost and show the equilibrium when q = 1000. What is the total cost to produce q = 1000? What is the labor cost to produce q = 1000? What is the capital cost to produce q = 1000? c) Suppose in the short run K is fixed at 10. Find Craft Corp's short-run cost function .