# AK4 - Problem set 4 Answers I True of false 1 FALSE An...

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Answers I. True of false 1. FALSE. An element in the production set is a pair ( x;y ) where 0 y f ( x ) . For each input level, the second coordinate of the pair is the set of all possible production levels for that input level . It is not possible to determine if a point is an element of the production set without specifying the input level. 2. FALSE. If there are constant returns to scale, the output is doubled if all inputs are doubled at the same time. 3. TRUE f ( tx;ty ) = min f 2 tx + ty;tx + 2 ty g = min f t (2 x + y ) ;t ( x + 2 y ) g = t min f 2 x + y;x + 2 y g = tf ( x;y ) 4. FALSE. f ( tx;ty ) = ( tx ) 2 3 + ( ty ) 2 3 = t 2 3 x 2 3 + t 2 3 y 2 3 = t 2 3 ( x 2 3 + y 2 3 ) = t 2 3 f ( x;y ) < tf ( x;y ) 5. FALSE. For this production function, x 2 is twice as productive as x 1 . To know which one is more expensive, the input prices are needed. That information is not provided here. the output level increases. 7. FALSE. If the production function is f ( x 1 ;x 2 ) = min f x 1 ;x 2 g , the con- ditional input demands are x 1 = x 2 = y . Therefore the cost function is c ( w 1 ;w 2 ;y ) = w 1 y + w 2 y = ( w 1 + w 2 ) y 8. FALSE. The cost function c ( w 1 ;w 2 ;y ) expresses the total cost of produc- ing y units of output when the input prices are w 1 and w 2 and the cost minimizing combination of inputs given these prices is used. 1

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AK4 - Problem set 4 Answers I True of false 1 FALSE An...

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