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##### ECON204 Assignment 3 Production Costs

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ECON204 Assignment 3 Production Costs;ECON204: Intermediate Microeconomic analysis;Assignment #3: Explaining Tastes, Production & Costs;Part I: Short-Answer Questions (4 marks each);1. The Kelowna Police Department must decide how to allocate 500 police officers between West;Kelowna and Central Kelowna. The following table provides the estimates of total arrests;corresponding to different numbers of police officers allocated in each region. If police can be;deployed only in groups of 100 officers, how should the police department allocate its officers;between the two regions? Explain your answer.;Number of Police Officers;West Kelowna;Total Arrests;Central Kelowna;Total Arrest;0 0 0;100 40 45;200 80 80;300 120 105;400 160 120;500 200 125;2. A firm purchases capital and labour in competitive market at price of r = \$6/machine-hour and w =;\$4/labour-hour, respectively. With the firm?s current input mix, the marginal product of capital is;12kg/machine-hour and the marginal product of labour is 18kg/labour-hour. Is the firm minimizing;its costs? Explain your answer with the use of an appropriate diagram.;3. If you are travelling though a remote small town, you may notice that vending machines are uncommon. The local bowling alley has an attendant to sell chips and pop, as does the gas station.;In large urban centres, on the other hand, vending machines are much more common. Explain this using the notion of relative input prices and isoquants.;Part II: Problems;1. (10 marks) Consider a population consisting of two types, ?cooperators? and ?defectors.? Each individual interacts with a randomly chosen member of the population. When two cooperators;interact, each earns a payoff of 6. When two defectors interact, each gets a payoff of 4. When a cooperator and a defector interact, the former gets a payoff of 0 whereas the latter gets a payoff of 8.;a) Summarize the situation described above in the game matrix where two individuals, X and Y, decide whether to cooperate or to defect. What is a Nash equilibrium (equilibria) for this game?;b) Let c be the population share of Cooperators. What will be the equilibrium population share of each type? Illustrate your answers in a diagram with population share of cooperators on the horizontal axis and expected payoffs on the vertical axis.;Suppose that goggles are available, at the cost of 1 per pair, which enables the wearer to identify each person?s type with certainty.;c) What will be the equilibrium population share of Cooperators in this case? Draw a new diagram;and explain your answers.;2. (5 marks) The manager of Green Chemical Co. has been informed that this year?s production target;Q for organic fertilizer (in millions of tonnes) is 20. The manager is asked to allocate the production;across the company?s two plants. The average total cost and marginal cost curves for each plant are;described as follows;Plant A: 4 20??;A;A;q;ATC, MCA? 4;Plant B;4;5 B;B;B;q;q;ATC??, 2;B;B;q MC?;where ATC and MC are in dollars per million of tonne, and A q is the quantity produced (in millions of;tonnes) by Plant A and B q is the quantity produced (in millions of tonnes) by Plant B.;a) Graph the marginal cost curve for each plant.;b) How should the manager allocate the production between the two plants so as to minimize total;cost? What is the resulting total cost?

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