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##### ECON 204 Assignment #3 - Explaining Tastes;Production & Costs

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Question;Part I: Short-Answer Questions (4 marks each)1.The Kelowna Police Department must decide how to allocate 500 police officers between WestKelowna and Central Kelowna. The following table provides the estimates of total arrestscorresponding to different numbers of police officers allocated in each region. If police can bedeployed only in groups of 100 officers, how should the police department allocate its officersbetween the two regions? Explain your answer.Number of Police Officers0100200300400500West KelownaTotal Arrests04080120160200Central KelownaTotal Arrest045801051201252.A firm purchases capital and labour in competitive market at price of r = \$6/machine-hour and w =\$4/labour-hour, respectively. With the firms current input mix, the marginal product of capital is12kg/machine-hour and the marginal product of labour is 18kg/labour-hour. Is the firm minimizingits 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 areuncommon. 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 thisusing the notion of relative input prices and isoquants.Part II: Problems1. (10 marks) Consider a population consisting of two types, cooperators and defectors. Eachindividual interacts with a randomly chosen member of the population. When two cooperatorsinteract, each earns a payoff of 6. When two defectors interact, each gets a payoff of 4. When acooperator 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 ofeach type? Illustrate your answers in a diagram with population share of cooperators on thehorizontal 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 eachpersons type with certainty.1c) What will be the equilibrium population share of Cooperators in this case? Draw a new diagramand explain your answers.2. (5 marks) The manager of Green Chemical Co. has been informed that this years production targetQ for organic fertilizer (in millions of tonnes) is 20. The manager is asked to allocate the productionacross the companys two plants. The average total cost and marginal cost curves for each plant aredescribed as follows:20Plant A: ATC A4, MC A 4qAq5 qBPlant B: ATC B, MC B BqB42where ATC and MC are in dollars per million of tonne, and q A is the quantity produced (in millions oftonnes) by Plant A and q B 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 totalcost? What is the resulting total cost?3. Adapted from #8 in Problems, FPA (5th ed. p. 330, 4th ed. p. 302).(5 marks) A firm has a production function Q = F(K,L) with constant returns to scale, where K isunits of capital and L is units of labour. Input prices are r = \$2 per unit of K and w = \$1 per unit of L.When it produces 5 units of output, it uses 2 units of capital and 3 units of labour. When its long-runtotal cost is equal to \$70, how much capital and laobur it will employ to product how many units ofoutput? What is the long-run average cost?

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