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. Let ?? and ?? denote the incomes earned by a high- and low-skilled worker respectively. These incomes are defined as ?? = (1 + ?)? and as ?? = (1 + ?)? , where H and L are constants (H > L) and 0 ? ? ? 1 is the fraction of the population that decides to become high skilled. The gain from education and acquiring skill is thus (?? ? ??). However, education and acquiring skill carries a positive cost of C (a constant). Assume that all individuals simultaneously choose whether to become skilled or not.

a) Does there exist any complementarity in acquiring skill? Describe it.

b) Suppose that H ? L f and cost of acquiring skill versus f. Is the situation in which only a fraction of the population becomes high-skilled equilibrium? Give an algebraic expression for this fraction. In case it is an equilibrium, is it stable or unstable? Find the other equilibrium values of f and determine which one is stable.

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4- 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. Let I H and I L denote the incomes earned by a high and low-skilled worker respectively. These incomes are dened as 1H = (1 + f)H and as IL = (1 + f)L , whereHandL are constants (H > L) and 0 S f S 1 is the fraction of the population that decides to become high skilled. The gain from education and acquiring skill is thus (1H 1;). However, education and acquiring skill carries a positive cost of C (a constant). Assume that all individuals simultaneously choose whether to become skilled or not. a) Does there exist any complementarity in acquiring skill? Describe it. b) Suppose that H - L