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
Explain PIH evidence from tax rebates and fiscal stimulus
Johnson tax rebates. The average household spent 20-40% more in period after the cheque was received, rather than when the program was announced. Against PIH.
Shapiro. Survey on how households would spend after Bush stimulus.
Consistent with PIH as:
- Only 1/5 intended to spend the money
- Those who spend are mostly older consumers
Explain why there is evidence against PIH
- Consumption smoothing may not be possible
- Impatience
- Uncertainty about future income
Explain papers analysing/for/against q theory
Hayashi. Established conditions under which marginal and average q coincide, opening the door for testing. Before, X could be correlated with q, and the error term capture other determinants of I/K
Summers. Analyses q - the features of the tax code that affects investment. Finds that q is small. However, there is measurement error which causes the responsiveness of investment to q toward zero. Also the error terms are correlated with q induce biased estimators.
To solve measurement errors, Cummins uses tax reforms. Investment changed the most for firms facing the greatest change in tax reforms.
Fazzari tests whether investment depends on financial factors. Financial factors does affect investment.
Lamont uses the effect of an oil shock to test if cash-flow is correlated with q. Investment falls when oil prices fall. This shows firm cash-flow affects investment. Evidence against q-theory.
What is Frisch elasticity in the labour model?
∂ln Lt/∂ln Wt = <3
Show the 2-period household problem in the labour model
max u(C1) + βu(C2) s.t. c1 + c2/1+r = W1L1 + W2/1+r L2
What is the intertemporal substitution hypothesis in the labour model?
Real wage fluctuations drive cyclical fluctuations of labour supply
What is the effect of a productivity shock on labour supply? On consumption?
↑A2 ↑MPL2 ↑W2 ↑W2/W1
Substitution and income effect!
W1 does not change but:
↑W2 ↓L2 ↓MUL ↑C1
Explain the role of Frish elasticity in the intertemporal substitution hypothesis
RBC considers productivity shocks as the main driver of cyclical fluctuations. The optimal response to a change of relative wages is to change the number of hours working
Explain the empirics of labour supply across countries
Prescott offers many different explanations (…). He considers logarithmic utility and pays consumption, income and investment taxes. He says that taxes are the main reason of differences
