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ECON204: Intermediate Microeconomic analysis Assignment #3: Explaining Tastes;Production & Costs

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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;0;100;200;300;400;500;West Kelowna;Total Arrests;0;40;80;120;160;200;Central Kelowna;Total Arrest;0;45;80;105;120;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 firms 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;persons type with certainty.;1;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 years production target;Q for organic fertilizer (in millions of tonnes) is 20. The manager is asked to allocate the production;across the companys two plants. The average total cost and marginal cost curves for each plant are;described as follows;20;Plant A: ATC A;4, MC A 4;qA;q;5 qB;Plant B: ATC B;MC B B;qB;4;2;where ATC and MC are in dollars per million of tonne, and q A is the quantity produced (in millions of;tonnes) 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 total;cost? 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 is;units 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-run;total cost is equal to $70, how much capital and laobur it will employ to product how many units of;output? What is the long-run average cost?

 

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