PROBLEM SET 6 ____ 1. A firm has the production function f(x, y) x1.20y2. This firm has a. constant returns to scale. b. decreasing returns to scale and increasing marginal product for factor xc. increasing returns to scale and decreasing marginal product for factor xd. decreasing returns to scale and diminishing marginal product for factor xe. None of the above. . . . ____ 2. A firm uses 3 factors of production. Its production function is f(x, y, z) minx3/y, y2, (z4x4)/y2. If the amount of each input is multiplied by 6, its output will be multiplied by z . ____ 3. Suppose that the production function is f(x1, x2) (xa1xa2)b, where a and b are positive constants. For what values of a and b is there a diminishing technical rate of substitution? 1 1 b 1 ____ 4. In Problem 2, the production function is given by f(x) 4x1/2. If the price of the commodity produced is $100 per unit and the cost of the input is $15 per unit, how much profit will the firm make if it maximize profits? ____ 5. In Problem 11, the production function is f(x1, x2) x1/21x1/22. If the price of factor 1 is $10 and the price of factor 2 is $20, in what proportions should the firm use factors 1 and 2 if it wants to maximize profits? a. We can’t tell without knowing the price of output. b. x12x2c. x10.50x2d. x1x2e. x120x2 . . . . ____ 6. A competitive firm produces output using three fixed factors and one variable factor. The firm’s short-run production function is q305x2x2, where xis the amount of variable factor used. The price of the output is $2 per unit and the price of the variable factor is $10 per unit. In the short run, how many units of xshould the firm use?
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- Spring '19
- Economics, $2, $3, B., c.