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Homework answers / question archive / 1
1. can you think of any good real-world examples of 'game theory' type interactions? (It does not have to be in just the realm of economics.)
2.A monopolist can produce at a constant average (and marginal) cost of TC(Q)= 5Q, such that AC = MC = 5. The firm faces a market demand curve given by Q = 53 - P, where Q is produced quantity and P is the market price per unit.
Suppose this firm generates a pollutant that is industry-specific (or a local pollutant) and proportional to output (δ is the emission coefficient) and the firm does not have any further abatement technologies. Thus regulation refers to this single firm only and does not affect other industries. A real situation represented by such a model is a chemical or pharmaceutical firm specializing in the production of a certain output and generating either a specific or a local pollutant.
b. Suppose δ = 2 such that each unit of the product leads to 2 unit of emission, i.e. Q = 2e. Suppose the firm is subject to an emission tax, t(e)= 8 e. Write down the firm’s total cost function when taxes are included. Calculate the profit-maximising quantity for the monopolist.
c. What is the effect on quantity? In terms of welfare, what market imperfections do the policymaker need to balance?
1.The Prisoner's Dilemma is the most well-known example of game theory. Consider the example of two criminals arrested for a crime. Prosecutors have no hard evidence to convict them. However, to gain a confession, officials remove the prisoners from their solitary cells and question each one in separate chambers. Neither prisoner has the means to communicate with each other. Officials present four deals, often displayed as a 2 x 2 box.
The most favorable strategy is to not confess. However, neither is aware of the other's strategy and without certainty that one will not confess, both will likely confess and receive a five-year prison sentence. The Nash equilibrium suggests that in a prisoner's dilemma, both players will make the move that is best for them individually but worse for them collectively.
2.
Revenue = P*Q => R = (53-Q)*Q = 53Q - Q^2
Cost = 5Q
Profit = revenue - cost = 53Q - Q^2 - 5Q = 48Q - Q^2
For profit to be maximum, dP/dQ = 0
=> 48 - 2Q = 0 => Q = 24
Substituting value of Q in demand function, P = 53 - 24 = 29
Learners Index =( P - MC)/P = (29-5)/29 = 24/29 = 0.82
(b) Q = 2e ; Tax = 8e = 4Q
New cost function = 5Q + 4Q = 9Q
This tax would act as an additional tax for the company
Therefore, new profit function is
P = Revenue - cost
= 48Q - Q^2 - 4Q = 44Q - Q^2
Again for profit to be maximum, dP/dQ = 0
=> 44 - 2Q = 0 => Q = 2
(c) The impact on quantity is a reduction in 2 units being produced since the tax because of the polllutant has increased the firms cost structure. The firm needs to balance the negative externality (i.e the pollutant) by reducing the production quantity.
