Economist for Western Motors

Q 1. As chief economist for Western Motors, your job is to figure out where to locate 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 labour are 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, where steel cost $8 per tonne and labour costs $6 per hour. a) (1 points) Will the plant exhibit constant, increasing or decreasing returns to scale in its production? Why? b) (3 points) Write the cost of production, C, as a function of A for each of the two locations. c) (1 point) In which city should you locate the plant to minimize your cost per unit of output?

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 marginal product in question 1. above still apply. In Winnipeg steel costs $4 per tonne and labour 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 variable cost functions (AVC) and average cost(AC) functions? Write down their algebraic form and graph them.d) (2 points) Where will the marginal cost curve be in relation to the AVC? Explain why?

3. J’s Hauling Service has a production function y = ML where M=truck hours andL=labour hours. The marginal products are MPL = M4L and MPM = L4M . In the short run it has a contract for 64 truck hours. Labour costs $16 per hour and trucks cost $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 long run average cost curves. 2

4. Doufffelberry Juice is a mild intoxicant. It is produced on farms where douffelberrys are grown. Baskets of Doufffelberries (B) are produced using grams of seeds (S) and hours of labour spent growing berries (L) , according to the production function B = 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 squeezed to 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 decreasing returns 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 his corn 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 price remaining 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 perfectly competitive 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 is his profit? b) (2 points) How many cars per week will he repair at price per car repaired of $18? What is his profit?c) (3points) What is Dent’s long-run supply curve? Graph and explain?

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