COMM 295 Assignment 1

# A find the marginal product of k mp k and marginal

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a) Find the marginal product of K (MP K ) and marginal product of L (MP L ). Does this production function exhibit the property of diminishing marginal product for each possible value of K and L? Explain. (4 pts) b) Find the expression for the average product of labor (AP L ). Graph both AP L and MP L in one diagram (with L on x-axis) while assuming K = 2. (4 pts) c) Does this production function exhibit increasing, decreasing, or constant returns to scale? (3 pts). (As with all questions, you must show your working, which in this case should be an algebraic proof.) d) Calculate the marginal rate of technical substitution (MRTS) for this firm when it is employing 40 units of K and 32 units of L. Show this MRTS on a graph that contains a single isoquant containing the point K = 40 and L = 32. Please place L on the horizontal axis and K on the vertical axis. The isoquant does not need to be to scale. (4 pts)

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5 e) Suppose there is technological progress that allows the firm to produce 10% more output with the same inputs. Show in a diagram what happens to the isoquants. (5 pts) Question 5: Cost A local entrepreneur from B.C. recently purchased a hand-bag producing factory for the price of \$75,000. The owner also spent \$25,000 in renovating the factory. If the entrepreneur decides not to produce output, the best alternative use of the factory is to lease it or rent it to another potential entrepreneur for \$15,000 per year. The cost of production is constant at \$10/bag and the prevailing market price is \$15. The annual fixed cost of operating the factory is \$5,000. a) Derive the formula for average total cost (AC) of producing the bags, Q, per year. Explain why you omitted, if you did, some of the costs described above from your AC calculation. (4 pts). b) Draw MC and AC functions in a diagram. What can you say about the relationship between these two functions? (4 pts) c) How many bags must be sold per year in order to avoid negative profits (losses) and therefore be able to stay in the business? (4 pts) d) Just prior to purchasing the factory, the owner discovers that it is possible to import bags from the U.S. at a cost (including transportation) of \$12 per bag. If the entrepreneur does not purchase and renovate the factory, the money that would have been spent can be invested at an interest rate of 10%. The selling price remains fixed at \$15. For what range of values for Q would the owner choose to not purchase the factory and instead import from the U.S. for resale in B.C.? (4 pts) e) How would your answer to (d) change if the owner discovered the import opportunity after the factory is purchased but before the renovation? (4 pts)
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