ECON 448: Week 6-
1. New Growth Theories: Human Capital and Endogenous Technical Progress
1. Consider a hypothetical economy in which each worker has to decide whether to acquire education and become a high-skilled worker or remain low-skilled. Education carries a cost of C. Assume that interest-free education loans are available to everybody. Let IH and IL denote the incomes earned by a high and low- skilled worker respectively. These incomes are defined as IH = (1 + θ)H and IL = (1+θ)L, where H and L are constants (H > L) and θ is the fraction of the population that decides to become high skilled. This formulation captures the idea that a person's productivity is positively linked not only to his own skills, but also to that of his fellow workers. Assume that all individuals simultaneously choose whether or not to become skilled.
a. Explain why this is like a coordination problem. What is the complementarity?
b. Show that if H - L < C < 2(H - L), there are three possible equilibria: one in which everybody acquires skills, one in which nobody does, and a third in which only a fraction of the population becomes high-skilled. Give an algebraic expression for this fraction in the last case, and argue intuitively that this equilibrium is "unstable" and is likely to give way to one of the two extreme cases.
c. Change the preceding example slightly. Suppose the return to low-skilled occupations is now given by IL = (1 + λθ)L, where λ is some constant. The return to high-skilled jobs is the same as before. Show that if the value of λ is sufficiently high, there is only one possible equilibrium.
d. Explain why multiple equilibria arise in the first case but not in the second.
2. You are introducing a new vacuum cleaner design in a tropical society which works well under humid conditions. The vacuum cleaner is produced under increasing returns, so that the unit cost of production declines with the price. Discuss how the following factors affect your likelihood of success: (a) the proportion of the population who already use vacuum cleaners, (b) the per capita income of the society, (c) the market for loans, and (d) the flow of information. If vacuum cleaners are produced under decreasing return to scales, which of these factors continue to be important?
2. Introductory Game Theory
1. Game theory is the very useful framework to think about optimal decision making and resulted equilibrium(/a) when there are complementaries in payoffs. A game is defined by three elements: players, strategies and payoffs.
Example: Battle of Sexes (BoS) Game
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2
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Opera
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Football
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1
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Opera
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2,1
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0,0
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Football
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0,0
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1,2
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2. Nash Equilibrium: A strategy profile is a Nash equilibrium if no individual can do better by choosing an alternative strategy, assuming that all other players are choosing the strategy described in the strategy profile. There is always at least one Nash equilibrium in a finite game. There can be (infinitely) many Nash equilibria.
3. What can player 1 do to make it happen his desired outcome?