ARME 608Final ExamFall 19951.Consider the production function y = x1x2+ x12x22. Is it homogeneous? Is it homothetic?2.For the following crop production function, derive the demand functions, supply function, and theprofit function:y = 5x1.5+ 2x2.53.Consider the following representation of a firm’s cost function:Cy r rr=++211 2213231212rwhere y is output and riis the price of the ith input. Is this a plausible cost function? Why or whynot?4.A farmer produces an output by the single input production process y1= f(x). Unfortunately, theproduction of y1has a negative impact on y2that the farmer also produces. Determine how muchinput x the farmer should use to maximize profits.5.Consider a profit-maximizing farm with the production function y = f(x1,x2) facing output price ρand factor prices r1and r2. Suppose the farm is taxed according to the total cost of factor 2 at rate t.
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