# addprob2 - Econ 11 Additional Problems 1 Toyotas technology...

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Econ 11 - Additional Problems 1. Toyota’s technology for producing cars is given by the production function F ( K,L )= min { K, L } ,whe re K denotes the amount of capital inputs, and L denotes the amount of labor inputs necessary for producing cars. ( i ) For a given rental rate of capital v and a wage rate w , f nd Toyota’s input demands of K and L necessary to produce a quantity Q of cars. Also, f nd Toyota’s cost function. ( ii ) Suppose Toyota takes the price of its cars as given. If w =10 and v =10 , f nd Toyota’s long-run supply function of cars (as a function of its price P ) in the long-run, when Toyota can adjust both K and L . ( iii ) The demand for Toyota cars is given by Q =200 5 P . A twhatpr icewou ldthe market clear in the long run, if Toyota took the market price as given? In general, how would the market-clearing price depend on Toyota’s input prices? ( iv ) E f ectively, Toyota is the only supplier of Toyota cars, and therefore will price its cars as a monopolist, taking into account the e f ecto fthepr iceondemand .Whatquant ity will Toyota choose to produce in the long run? ( v ) In the short run, K is f xed at 40 , and input prices are f xat w =10 and v =10 .A sa function of P , what is the short-run optimal supply of cars, as a well as the market-clearing price for Toyotas? 2. Volkswagen has two plants in which it produces its cars: It can either produce cars in Germany, in a high-productivity, capital-intensive plant, or in Mexico in a lower pro- ductivity, labor-intensive plant. The production function for cars in the German plant is Q =2 K 2 / 3 L 1 / 3 , while the production function for cars in the Mexican plant is Q = K 1 / 3 L 2 / 3 . ( i ) I fthewagerateinGermany(Mex ico)is w G ( w M ), and the rental rate of capital is v (the same in both countries), what is the cost function for cars in Germany (Mexico)? ( ii ) In the long run, how will the production of cars depend on the price of cars, P ,the rental rate of capital v

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addprob2 - Econ 11 Additional Problems 1 Toyotas technology...

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