MACRO-Question 1 [10 markConsider a two-period eco

Question 1 [10 mark Consider a two-period economy with a household and government. The household behaves according to its intertemporal budget constraint, but faces a borrowing constraint that prevents period-1 consumption from exceeding period-1 disposable income, which can be written as follows,

C_{1}+\frac{C_{2}}{1+r}=\left(Y_{1}-T_{1}\right)+\frac{\left(Y_{2}-T_{2}\right)}{1+r} \quad \text { where } C_{1} \leq\left(Y_{1}-T_{1}\right)

The government also obeys its intertemporal budget constraint,

G_{1}+\frac{G_{2}}{1+r}=T_{1}+\frac{T_{2}}{1+r}

Here

C

is consumption,

T

is taxation,

G

is government expenditure, and

r

is the real interest rate. Subscripts denote periods 1 and 2. You may assume that household and government face the same real interest rate,

r

. Further, suppose that the household has a preference for consumption today, such that its borrowing constraint is binding, forcing it to consume its period-1 income today and period-2 income tomorrow. That is to say, initially

C_{1}=\left(Y_{1}-T_{1}\right)

and

C_{2}=

\left(Y_{2}-T_{2}\right)

. This situation is shown in the following diagram.

A

Key Concept

Intertemporal Budget Constraint

Explanation

The intertemporal budget constraint for the household shows the trade-off between consumption today and consumption tomorrow, given the household's income and taxes in both periods, adjusted for the real interest rate. The borrowing constraint indicates that the household cannot consume more than its disposable income in period 1, which leads to the binding constraint where

C_{1} = (Y_{1} - T_{1})

. This reflects the household's preference for present consumption over future consumption when faced with borrowing restrictions.

Now consider a situation where the government tries to stimulate the economy via a tax cut in period 1. The government maintains expenditure in each period at

G_{1}

and

G_{2}

, but it cuts taxes to

T_{1}{ }^{\prime}

in period 1 and consequently increases taxes to

T_{2}{ }^{\prime}

in period 2, to still obey its intertemporal budget constraint. Is the fiscal policy via the tax cut effective at stimulating period-1 consumption? Draw a diagram and provide clear explanation about how this example relates to Ricardian Equivalence.

Answer

The fiscal policy via the tax cut is not effective at stimulating period-1 consumption due to the Ricardian Equivalence theorem.

Solution

a

Initial Conditions: The household's initial consumption in period 1 is equal to its disposable income,

C_1 = (Y_1 - T_1)

, and in period 2,

C_2 = (Y_2 - T_2)

b

Government Policy Change: The government reduces taxes in period 1 to

T_1'

and increases taxes in period 2 to

T_2'

while keeping government expenditure constant in both periods

c

Household's Intertemporal Budget Constraint: The household's intertemporal budget constraint remains the same,

C_1 + \frac{C_2}{1+r} = (Y_1 - T_1') + \frac{(Y_2 - T_2')}{1+r}

, since the present value of taxes paid is unchanged

d

Ricardian Equivalence: According to Ricardian Equivalence, the household understands that a tax cut now will result in higher future taxes and thus does not change its consumption in period 1

e

Diagram Explanation: A diagram would show the budget constraint before and after the tax change, with the initial and new budget lines overlapping, indicating no change in period-1 consumption

Key Concept

Ricardian Equivalence

Explanation

Ricardian Equivalence suggests that consumers are forward-looking and understand that a tax cut today will be offset by higher taxes in the future, leading them to save the tax cut to pay for future tax increases, thus not altering their consumption.

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