Consider a 2-period economy in which Yt = AtKt. The households start with a quantity a1 > 0 of initial assets and maximize lifetime utility given a per-period utility function u(c) = ln (c). 1. Do households earn any labor income? Solve the household’s Euler Equa- tion. 2. Solve the firms’ problem. Is the production function constant returns to scale? Do firms make any profits? 3. Define an equilibrium for this economy. 4. Solve for the equilibrium
Consider a 2-period economy in which Yt = AtKt. The households start with a
quantity a1 > 0 of initial assets and maximize lifetime utility given a per-period
utility function u(c) = ln (c).
1. Do households earn any labor income? Solve the household’s Euler Equa-
tion.
2. Solve the firms’ problem. Is the production function constant returns to
scale? Do firms make any profits?
3. Define an equilibrium for this economy.
4. Solve for the equilibrium of this economy. Solving for the equilibrium
means finding the value of all equilibrium objects as a function of the
parameters of the model: A1, A2, α, β, δ, a1
5. Assume that A1 = Ab1 = 1 and A2 = 1. What is rb1 equal to?
6. Assume that A1 = As1 = 1 −∆ and A2 = 1. What is rs1 equal to?
7. What is the percentage difference between As1 and Ab1 ? That is, find the
value of x such that As1 = (1 + x) Ab1. What is the percentage difference
between rb1 and rs1 ? How do these two differences relate to each other and
what does this connection remind you of?
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