Macroeconomics Revision Flashcards
Explain the consumer’s problem with utility function and uncertainty about the future
The consumer’s problem is to maximize utility subject to an intertemporal budget constraint. You solve it with a Lagrangian, and take FOCs
Show the equation of lifetime utility. Also show a 2 period utility model
W = Σβt U(Ct)
U(C1) + βU(C2)
Define the Random Walk Theory of consumption
Hall (1978) says that consumption is a random walk - changes in consumption are unpredictable, it just responds to information.
Uses a consumption Euler equation with β(1+r)=1 and a quadratic utility.
Simplify Σ1/(1+r)k
1+r/r
Show the intertemporal budget constraint (for both infinity and 2 period with uncertainty)
Consumption
ΣCt/(1+r)k = At + ΣEtYt+k/(1+r)k
C1 + C2/1+r = Y1 + Y2/1+r
Explain the regularity (Inada) conditions of standard utility functions
- lim c→0 U’(C) = ∞
- lim c→∞ U’(C) = 0
- U’(C) > 0
- U’‘(C) < 0
Show and explain the Euler equation
U’(C1) = β(1+r)U’(C2)
βU’(C2)/U’(C1) = 1/(1+r)
U’(C1) = individual’s MRS between consumption in the two periods
1/(1+r) = price of future consumption in terms of present consumption
Explain the effects of increasing r on consumption path
- Substitution effect. Increases the price of consumption in the first period. A consumer will decrease Ct and increase Ct+1
- Wealth effect. Decreased PDV of future earnings. Decreases consumption in both periods
- Income effect. Increases income from assets for savers, or debt payments for borrowers.
Show the intertemporal budget constraint in the OLG model with interest. Also show the two flow budget constraints from which it is derived. Finally, combine this with the utility function of this model for the maximisation problem
Wt = Cy,t + (Co,t+1)/(1+r)
Wt = Cy,t + St
Wt+1 = (1+r)St
L = U(Cy) + βU(Co) + λ(Wt - Cy - Co/(1+rt)
Explain the firm’s objective and constraint in investment. Show the equation
A firm will maximise present discounted value of its life-time profits by choosing an optimal path of capital stock and investment s.t. a constraint on capital dynamics.
max Σ(1/1+r)^s-t (AKα - Is - C(I,K)) +q Kt+1-Kt - Is +(delta)K)
Where C(I,K) = investment adjustment cost (as given in the question hopefully!)
Explain the two types of the OLG model
Fully funded. Young make constributions which is paid back to them when old. Lifetime wealth stays the same, so intertemporal budget constraint is the same.
Pay-as-you-go. Government collects constributions from the young and distributes to the current old. This dominates a fully funded system with a large population growth
Define the transversality condition. Why is it necessary for efficient investment?
Individuals will not die with savings/assets
The transversality condition rules out suboptimal solutions that violate profit maximisation
Explain the maximisation problem and constraint in the labour supply model. Show the equation. How do optimal households behave?
Individuals maximise utility of consumption and leisure, which is equal to total time endowment net of time worked.
max U(Ct, Lt) = U(Ct) - V(Lt) s.t. Ct + At = wtLt
Optimal households behave according to Wt = MUL/MUc
Explain the firm maximisation problem mathematically in OLG model
max AKαL1-α - wL - rK
Explain empirical evidence for/against PIH
Hall regressed consumption growth. He advocated for PIH, after failing to reject for consumption and income. Difficult to interpret though.
Campbell and Mankiw found that there are two types of consumers: ones that live hand to mouth and ones that are rational PIH consumers, where lambda=0.5. This means that changes in income is correlated with innovations to permanent income.
However, these tests using micro data is challenging:
- Small sample size
- Strong assumptions necessary for aggregation
- Strong assumptions on preferences
