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As chief economist for Western Motors, your job is to figure out where to locate a new plant.
Q 1. As chief economist for Western Motors, your job is to figure out where tolocate a new plant. The only inputs used in making automobiles are steel and labour,and the production function is A = SL. The marginal products of steel and labourare MPs = L4S and MPL = S4L . You can locate the plant in Calgary,where steel cost $7 per tonne and labour cost $7 per hour, or in Edmonton, wheresteel cost $8 per tonne and labour costs $6 per hour.a) (1 points) Will the plant exhibit constant, increasing or decreasing returns to scale inits production? Why?b) (3 points) Write the cost of production, C, as a function of A for each of the twolocations.c) (1 point) In which city should you locate the plant to minimize your cost per unit ofoutput?2. For better or worse, Western Motors has decided to build its new plant in Winnipeg.In the short run it must use 16 tonnes of steel. The production function and marginalproduct in question 1. above still apply. In Winnipeg steel costs $4 per tonne andlabour cost $4 per hour.a) (3 points) Write the short run cost of production, C, as a function of A.b) (1 point) How much will it cost to produce 48 automobiles (A=48)?c) (3 points) What are the average fixed (AFC) and average variablecost functions (AVC) and average cost(AC) functions? Write downtheir algebraic form and graph them.d) (2 points) Where will the marginal cost curve be in relation to theAVC? Explain why?3. J’s Hauling Service has a production function y = ML where M=truckhours andL=labour hours. The marginal products are MPL = M4L and MPM = L4M . Inthe short run it has a contract for 64 truck hours. Labour costs $16 per hour and truckscost $20 per hour (or $1280 for the 64 hour contract).a) (4 points) What are its short run and long run average cost functions (average cost asa function of output)?b) ( 2 points) Explain the general nature of the relationship between short run and longrunaverage cost curves.24. Doufffelberry Juice is a mild intoxicant. It is produced on farms where douffelberrysare grown. Baskets of Doufffelberries (B) are produced using grams of seeds (S) andhours of labour spent growing berries (L) , according to the production functionB = SL. The marginal product of L is MPL = S4L and the marginal product of Sis MPS = L4S . Once the baskets of berries have been produced, they are squeezedto make litres of juice. The production function for juice is J = Min B, H , where J islitres of juice and H hours of labour spent squeezing berries. Both kinds of labour cost$9 per hour and seeds cost $9 per grama) ( 1 points) How much B and H should be used to produce 10 litres of juice?b) ( 2 points) How much S and L should be used to produce 10 baskets of berries?c) (2 points) How much does it cost to produce 100 litres of juice?d) ( 2 points) Does the complete process exhibit constant, increasing or decreasingreturns to scale? Hint: If you double all inputs (S, L and H) what happens to theoutput J?5. When farmer Hogland applies N kilos of fertilizer per hectare, the marginal productof fertilizer is MPN=1 - N200 kilos of corn. The price at which the farmer can sell hiscorn is $4 per kilo, and the price at which he can buy fertilizer is $1.20 per kilo.a) (2 points) How many kilos of fertilizer should the farmer apply to maximize hisprofit?b) (2 points) If the price of corn drops to $2, how will Hogland change his fertilizerusage?c) (2 points) If the price of fertilizer drops to $0.40 per kilo, with the corn priceremaining at $2, how much fertilizer should he use?6. Dent operates an auto body shop. His long-run total cost of repairing y cars per week isc y = 3y2 + 75. His long-run marginal cost is MC = 6y. Dent operates in a perfectlycompetitive industry in which he is a price taker.a) (2 points) How many cars per week will he repair at price per car repaired of $48? What ishis profit?b) (2 points) How many cars per week will he repair at price per car repaired of $18? What ishis profit?c) (3points) What is Dent’s long-run supply curve? Graph and explain?Attachment Preview:Assignment _2.pdf Download AttachmentThis is an unformatted preview. Please download the attached document for the original format.1 ECON 301 (01) Winter 2011Assignment #2, Total Points=40Worth 10% of Course Grade, Due March 22nd by 4:30 p.m.Instructor Dr. E.A. Wilman1. As chief economist for Western Motors, your job is to figure out where tolocate a new plant. The only inputs used in making automobiles are steel and labour,and the production function is A = SL . The marginal products of steel and labourS . You can locate the plant in Calgary,L and M P =are M Ps =L4L4Swhere steel cost $7 per tonne and labour cost $7 per hour, or in Edmonton, wheresteel cost $8 per tonne and labour costs $6 per hour.a) (1 points) Will the plant exhibit constant, increasing or decreasing returns to scale inits production? Why?b) (3 points) Write the cost of production, C, as a function of A for each of the twolocations.c) (1 point) In which city should you locate the plant to minimize your cost per unit ofoutput?2. For better or worse, Western Motors has decided to build its new plant in Winnipeg.In the short run it must use 16 tonnes of steel. The production function and marginalproduct in question 1. above still apply. In Winnipeg steel costs $4 per tonne andlabour cost $4 per hour.a) (3 points) Write the short run cost of production, C, as a function of A.b) (1 point) How much will it cost to produce 48 automobiles (A=48)?c) (3 points) What are the average fixed (AFC) and average variablecost functions (AVC) and average cost(AC) functions? Write downtheir algebraic form and graph them.d) (2 points) Where will the marginal cost curve be in relation to theAVC? Explain why?3. J’s Hauling Service has a production function y = ML where M=truckhours andM and M P =L . InL=labour hours. The marginal products are M PL =M4L4Mthe short run it has a contract for 64 truck hours. Labour costs $16 per hour and truckscost $20 per hour (or $1280 for the 64 hour contract).a) (4 points) What are its short run and long run average cost functions (average cost asa function of output)?b) ( 2 points) Explain the general nature of the relationship between short run and longrun average cost curves.2 4. Doufffelberry Juice is a mild intoxicant. It is produced on farms where douffelberrysare grown. Baskets of Doufffelberries (B) are produced using grams of seeds (S) andhours of labour spent growing berries (L) , according to the production functionS and the marginal product of SB = SL . The marginal product of L is M PL =4LL . Once the baskets of berries have been produced, they are squeezedis M PS =4Sto make litres of juice. The production function for juice is J = Min B, H , where J islitres of juice and H hours of labour spent squeezing berries. Both kinds of labour cost$9 per hour and seeds cost $9 per grama) ( 1 points) How much B and H should be used to produce 10 litres of juice?b) ( 2 points) How much S and L should be used to produce 10 baskets of berries?c) (2 points) How much does it cost to produce 100 litres of juice?d) ( 2 points) Does the complete process exhibit constant, increasing or decreasingreturns to scale? Hint: If you double all inputs (S, L and H) what happens to theoutput J?5. When farmer Hogland applies N kilos of fertilizer per hectare, the marginal productof fertilizer is MPN =1 - N kilos of corn. The price at which the farmer can sell his200corn is $4 per kilo, and the price at which he can buy fertilizer is $1.20 per kilo.a) (2 points) How many kilos of fertilizer should the farmer apply to maximize hisprofit?b) (2 points) If the price of corn drops to $2, how will Hogland change his fertilizerusage?c) (2 points) If the price of fertilizer drops to $0.40 per kilo, with the corn priceremaining at $2, how much fertilizer should he use?6. Dent operates an auto body shop. His long-run total cost of repairing y cars per week isc y = 3y 2 + 75. His long-run marginal cost is MC = 6 y. Dent operates in a perfectlycompetitive industry in which he is a price taker.a) (2 points) How many cars per week will he repair at price per car repaired of $48? What ishis profit?b) (2 points) How many cars per week will he repair at price per car repaired of $18? What ishis profit?c) (3points) What is Dent’s long-run supply curve? Graph and explain?
