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TrueorFalse(justifyyouranswer);1.;The cost function c(w1, w2, y) expresses the cost per unit of;output of producing y units of output if equal amounts of both factors;are used.;2.;A competitive, cost-minimizing firm has the production function;f(x, y) = x + 2y and uses positive amounts of both inputs. If the price;of x doubles and the price of y triples, then the cost of production;will more than double.;3.;The total cost function c(w1, w2, y) expresses the cost per unit;of output as a function of input prices and output.;4.;If the production function is f(x1, x2) = min{x1, x2}, then the;cost function is c(w1, w2, y) = min{w1, w2}y.;5.;The conditional factor demand function for factor 1 is a function;x1(w1, w2, y) that tells the ratio of price to output for an optimal;factor choice of the firm.;PROBLEM2;1.;A firms production function is q = 12x0.50y0.50, where x and y;are the amounts of factors x and y that the firm uses as inputs.;If the firm is minimizing unit costs and if the price of factor x;is 5 times the price of factor y, the ratio in which the firm will;use factors x and y is closest to;a.;b.;c.;d.;e.;x/y;x/y;x/y;x/y;x/y;=;=;=;=;=;0.20.;0.40.;1.;1.67.;5.;2.;Lars runs a cookie factory. His cookies are made with sugar;peanut oil, and soybean oil. The number of boxes of cookies that he;produces is f(su, po, so) = min{su, po + 2so}, where su is the number of;bags of sugar, po the number of canisters of peanut oil, and so the;number of canisters of soybean oil that he uses. The price of a bag of;sugar is \$5. The price of a canister of peanut oil is \$9. The price of a;canister of soybean oil is \$19. If Lars makes 254 boxes of cookies in;the cheapest way possible, how many canisters of soybean oil will he;use?;a.;127;b.;0;c.;84.67;d.;169.33;e.;42.33;3.;Roberta runs a dress factory. She produces 50 dresses per day;using labor and electricity. She uses a combination of labor and;electricity that produces 50 dresses per day in the cheapest possible;way. She can hire as much labor as she wants at a cost of 20 cents per;minute. She can use as much electricity as she wants at a cost of 10;cents per minute. Her production isoquants are smooth curves without;kinks and she uses positive amounts of both inputs.;a.;The marginal product of a kilowatt-hour of electricity;is twice the marginal product of a minute of labor.;b.;The marginal product of a minute of labor is twice the;marginal product of a kilowatt-hour of electricity.;c.;The marginal product of a minute of labor is equal to;the marginal product of a kilowatt-hour of electricity.;d.;There is not enough information to determine the ratio;of marginal products. Wed have to know the production;function to know this.;e.;The marginal product of a minute of labor plus the;marginal product of a kilowatt-hour of labor must equal 50/;(20 + 10).;4.;Als production function for deer is f(x1, x2) = (2x1 + x2)1/2;where x1 is the amount of plastic and x2 is the amount of wood used. If;the cost of plastic is \$6 per unit and the cost of wood is \$1 per unit;then the cost of producing 5 deer is;a.;\$25.;b.;\$65.;c.;\$75.;d.;\$5.;e.;\$15.;5.;If output is produced according to Q = 4LK, the price of K is;\$10, and the price of L is \$40, then the cost-minimizing combination of;K and L capable of producing 64 units of output is;a.;L = 16 and K = 1.;b.;L = 2 and K = 8.;c.;L = 2 and K = 2.;d.;L = 32 and K = 32.;e.;L = 1 and K = 16.;6.;If output is produced according to Q = 4L + 6K, the price of K is;\$12, and the price of L is \$20, then the cost-minimizing combination of;K and L capable of producing 96 units of output is;a.;L = 20 and K = 12.;b.;L = 0 and K = 16.;c.;L = 24 and K = 16.;d.;L = 12 and K = 8.;e.;L = 24 and K = 0.;PROBLEM 3;Give the definition of;Cost Function;Conditional factor demand functions;Average Cost Function;Problem4;The production function is f(L, M) = 4L1/2M1/2, where L is the number of;units of labor and M is the number of machines. The cost of labor is 40;per unit and the cost of using a machine is 10.;(a) Draw an isocost line for this firm, showing combinations of machine;and labor that cost \$400 and another isocost line showing combinations;that cost 200. What is the slope of these isocost lines?;(b) Suppose that the firm wants to produce its output in the cheapest;possible way. Find the number of machines it would use per worker.;(Hint: The firm will produce at a point where the slope of the isoquant;equals the slope of the isocost line.);(c) On the graph, sketch the production isoquant corresponding to an;output of 40. Calculate the amount of labor ______ and the number of;machines ______ that are used to produce 40 units in the cheapest;possible way, given the above factor prices. Calculate the cost of;producing 40 units at these factor prices: c(40,10,40)=____________.;(d) How many units of labor _______ and how many machines;would the firm use to produce y units in the cheapest possible way? How;much would this cost?_______ (This gives long-run cost function).;Does the cost increase linearly, more than linearly, less than linearly;in output? Can you explain why?(Hint: notice that there are constant;returns to scale.);(e) Suppose that in the short run M=4. What is the short run cost;function of producing y units of output? ___________.;Draw the long-run and short-run cost functions you found in part (d) and;(e). Which one is higher? Can you explain why?;(f) What if M=(1/2)y? Compare the long-run and short-run cost function;of producing y units of output. Are they the same? If yes, can you;explain why?

Paper#28789 | Written in 18-Jul-2015

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