Economics 111 - Principles of Economics - Accelerated Treatment - Problem Set 6
Q1. Explain if the following statements are true or false:
a) Assume that there are only two people in a society, person A and person B. Person A is willing to pay $70 to have one unit (the first unit) of a public good produced, and person B is willing to pay $80 to have the first unit of public good produced and $70 to have the second unit produced. Given this information we know that a point on the joint (aggregate) market demand curve for this public good would be a price of $70 and quantity of demand of 3 units.
b) If there are external costs of production and firms do not account for these costs at the equilibrium level of output, price equals marginal cost (P=MC) and the price is smaller than marginal social cost (MSC). Use a graph.
Q2 Consider the following payoff matrix for an oligopoly consisting of two firms, Company A and Company B:
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Company B chooses:
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Low price
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High price
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Company A chooses:
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Low price
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Company A: $10 million
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Company A: $30 million
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Company B: $10 million
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Company B: $20 million
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High price
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Company A: $20 million
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Company A: $15 million
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Company A: $30 million
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Company A: $15 million
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a) Does Company A have a dominant strategy? Does it have a maxmin strategy? Explain briefly.
b) Does Company B have a dominant strategy? Does it have a maxmin strategy? Explain briefly.
c) Is there a collusion equilibrium in this game? If no, why not? If yes, explain how this collusion would work and determine the monetary gains from collusion.
Q3. Use the information in the payoff matrix below to answer the following two questions:
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B
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Left
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Right
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A
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Up
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1, 7
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4, 6
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Down
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9, 3
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X, Y
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a) For what value of x is “Down” a dominant strategy for A?
b) For what value of y is “Left” a dominant strategy for B?
Q4. The following is the payoff matrix for firm A and firm B when they produce “Low Quantity” or “High Quantity”. (For example, if Firm A executes strategy “Low Q” and Firm B executes strategy “Low Q”, then Firm A’s profits will be 4 million dollars and Firm B’s profits will be 3 million dollars.)
a) What is the maxmin strategy for firm A?
b) What is the maxmin strategy for firm B?
c) Is there a Nash equilibrium in this game? If yes, which one is it? If no, why not?
Q5. In a perfectly competitive market for air fresheners the demand is given by: P = 20 – 5Q and the marginal cost MC = 10. The production of air fresheners is creating positive spillover effects to other local businesses and residents that are not currently internalized by this industry. The marginal social benefit curve is MSB = 30 – 5Q.
a) What is the quantity of air fresheners the market alone will produce?
b) How much higher or lower is the socially optimal level of air freshener production?
c) Graph the market demand, marginal social benefit and marginal cost curve
d) Show on the graph and explain how high of a tax or subsidy needs to be implemented by the government for the efficient level of output for air fresheners to be produced.