Answer Key 4

Answer Key 4 - PROBLEM SET 4 I. TRUE OR FALSE (No...

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PROBLEM SET 4 I. TRUE OR FALSE (No justification needed but again, you should think of one for the exam) 1. The production set of a firm is the set of all products the firm can produce. FALSE 2. If there are constant returns to scale, then doubling the amount of any input will exactly double the amount of output. FALSE 3. If the production function is f ( x , y ) = min{2 x + y , x + 2 y }, then there are constant returns to scale. TRUE 4. The production function f ( x , y ) = x 2/3 + y 2/3 has increasing returns to scale. FALSE 5. A firm’s production function is f ( x 1 , x 2 ) = x 1 + 2 x 2 . This means that x 2 is twice as expensive as x 1 . FALSE 6. A fixed factor is a factor of production that is used in fixed proportion to the level of output. FALSE 8. If the production function is f ( x 1 , x 2 ) = min{ x 1 , x 2 }, then the cost function is c ( w 1 , w 2 , y ) = min{ w 1 , w 2 } y . FALSE 9. The cost function c ( w 1 , w 2 , y ) expresses the cost per unit of output of producing y units of output if equal amounts of both factors are used. FALSE 10. A firm uses a single variable input x to produce outputs according to the production function f (x) = 300 x - 6 x 2 . This firm has fixed costs of $300. This firm’s short-run marginal cost curve lies below its short-run average variable cost curve for all positive values of x . FALSE 11. The average variable cost curve must always be U-shaped. FALSE 12. The marginal cost curve passes through the minimum point of the average fixed cost curve. FALSE II. MULTIPLE CHOICE 13. If a firm moves from one point on a production isoquant to another point on the same isoquant, which of the following will certainly not happen? a. A change in the level of output b. A change in the ratio in which the inputs are combined c. A change in the marginal products of the inputs d. A change in the rate of technical substitution e. A change in profitability 14. Which of the following production functions exhibit constant returns to scale? In each case y is output and K and L are inputs. (1) y = K 1/ 2 L 2 /3 . (2) y = 3 K 1/2 L 1/2 . (3) y = K 1/2 + L 1/2 . (4) y = 2 K + 3 L . a. 1, 2, and 4 b. 2, 3, and 4 c. 1, 3, and 4 d. 2 and 3 e. 2 and 4
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15. A firm uses only two inputs to produce its output. These inputs are perfect substitutes. This firm a. must have increasing returns to scale. b. must have constant returns to scale. c. could have increasing returns to scale, constant returns to scale, or decreasing returns to scale. d. must have decreasing returns to scale.
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Answer Key 4 - PROBLEM SET 4 I. TRUE OR FALSE (No...

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