ARME608 final EXAM 1999 - decomposed into percentage...

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ARME 608 Final Exam Fall 1999 1. Graphically show both short-run and long-run cost as a function of an input price. 2. For a profit-maximizing firm with the production function c b x ax y 2 1 = facing an output demand function d y p = , and facing constant prices, r 1 and r 2 , in the input market, derive the FOC for both inputs. 3. Show how linear programming models: a) product-product decisions b) factor-factor decisions c) factor-production decisions. 1. The following Cobb-Douglas production function was estimated in ln form. 3 2 1 ln 42 . 0 ln 18 . 0 ln 30 . 0 2 . 3 ln x x x y + + + = If the amount available to expend on all three inputs is $10,000 and input x 1 costs $6 per unit, how many units of x 1 should be purchased? 2. For the utility function , 1 , < = b ax u b where u is utility and x is wealth, compute Pratt’s risk aversion and determine whether this utility function exhibits increasing, constant, or decreasing aversion to risk. 3. In agriculture, output over time is a function of input use and time ). ), ( ( t t x f y = Assuming cost minimization, show how the percentage change in output over time can be
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Unformatted text preview: decomposed into percentage changes in input usage over time and technological change. Use your results to explain how you would measure technological change. 4. A profit maximizing farm would prefer the price of its output to remain fixed at some value, rather than to fluctuate around this value. Explain. 5. The long-run total cost for each agricultural firm that supplies output q is C = q 3- 4q 2 + 8q. Firms freely enter the industry if profits are positive and leave the industry if profits are negative. Derive the industrys long-run supply function. Assume that the corresponding industry demand function is Q = 1,800 - 100P. Determine equilibrium price, aggregate quantity produced, and the number of firms in the industry. Calculate the amount of consumer and producer surplus....
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