Problem Set 3 l. The production function for Hobbes' Tiger Tails is q=ltltltl*min[L, 2K] where c1 is the number oftiger tails, L is the number of workers, and K is the number of transmogriliers. a. Draw the isoquants for this production function b. For a listed number oftransmogrifiers, say 3, draw the total product, average product oflabor, and marginal product oflabor curves. 2. Suppose the process of producing snowballs by Derkin's Snow Defense is described by the function g = lK'5{L 40F where q is the number of snowballs produced, K the number of computerized machine hours, and L the number of personhours oflabor. MPL= 5K'5(L 4}"5 MP]; = 5K"5[L 401'5 In addition to capital and labor, $ltl worth of raw materials is used in the production of each snowball, so that TC{q] = wL + rK. + lq a. By minimizing cost subject to the production function, derive the cost-minimizing demands for K and L as a function of output [q], wage rates {11'}, and rental rates on machines {r}. Use these results to derive the total cost function: that is, costs as a function of q, r, w, and the constant Ell] per unit materials cost. b. This process requires workers, who earn $5 per hour [I know, that's absurd, but the numbers work]. The rental rate on the machines used in the process is 5243' per hour. At these factor prices, what are total costs as a function of :3? Does this technology exhibit decreasing, constant, or increasing returns to scale? c. Derkins's Snow Defense plans to produce EDD snowballs per week. At the factor prices given above, how many workers should the firm hire {at 413 hours per week] and how many machines should it rent {at 4'3 machinehours per week)? What are the marginal and average costs at this level of production? 3. Suppose the clover market is perfectly competitive, and Seamus' Clovers is one ot'many identical rms in the market. The market demand for clovers is given by: Qd = Ell] 2? Currently, the market price for a clover is $ltll]. Seamus' Clovers has costs of production given by: TC = 400 t dq t q3 which means that the marginal cost is given by: MC = 4!) t 2:] and the average total cost is given by: ATE = (4mm) t 4t] 1 q a] In the short run, how many turkeys should Seamus produce in order to maximize prots? b} What are Seamus' profits in the short run? c) How many firms are currently in the market? d} What is the breakeven price, or the price at which Seamus earns normal prots? e) Assuming all of the rms are already at the ideal level ot'capital, how many firms enter into the clover market in the long run