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ARME608 MID TERM EXAM 2000 - ∑-ρ = ∏ i i y c r,y where...

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~ ~ ARME 608 First Exam Fall 2000 1. Given the production function y = - a + bx - cx 2 , where y is output and x is input, graphically show what range of inputs would be used by a profit maximizing farmer. 2. You are interested in determining the amount of input to apply to a legume crop that also produces nitrogen for a wheat crop the following year. You have the legume production function and the relationship between legume output and nitrogen made available the following year to the wheat crop. Unfortunately, you do not have the wheat-nitrogen production function. How can you determine the quantity of input to use on the legume if the goal is to maximize profits? 3. The profit function can be written as:
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Unformatted text preview: ∑-ρ = ∏ * i i y c ( r,y * ) where i ρ is the price of output i , * i y is the supply function for output i , c is the cost function. Show that the first derivative of this profit function with respect to an output price will derive the supply function for that output. 4. Illustrate how linear programming can be used to model isoquants. 5. Can the following function be used as a profit function? ρ-ρ-ρ---ρ = ∏ 2 1 5 2 2 4 2 1 3 2 2 1 1 2 2 r r b r b r b r b r b a 6. Is the Cobb-Douglas production functionally separable such that some inputs can be aggregated into a composite input?...
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