Question

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A. Blanchard and Johnson (2015), p. 57, question 5 For both political and macro- economic reasons, governments are often reluctant to run budget deficits. Here, we exam- ine whether policy changes in G and T that maintain a balanced budget are neutral for the macro economy. Put another way, we examine whether it is possible to affect output through changes in G and T so that the government budget remains balanced. Start with this equation: (18 marks) Y = (co +I+G – CT) 1-C1 1. By how much does Y increase when G increases by one unit? (3 marks) 2. By how much does Y decrease when T inceases by one unit? (3 marks) 3. Why are your answers to (1) and (2) different? (3 marks) Suppose that the economy starts with a balanced budget: T = G. If the increase in G is equal to the increase in T, then the budget remains in balance. Let us now compute the balanced budget multiplier. 4. Suppose that both G and T increase by exactly one unit. Using your answers to parts (1) and (2), what is the change in equilibrium GDP? (6 marks) 5. How does the value of the marginal propensity to consume affect your answer? Why? (3 marks)

Answer 1

In the given equation, the equation in brackets is known as autonomous spending. c₀ is consumption at zero income. c₁ is known as propensity to consume, that is, the part of extra income that could be used for consumption.

a) For knowing the change in Y for 1 unit change in G, assume all other factors constant and take derivative of Y with respect to G. This gives:

ay ag=1/(1 - 1)

Thus, for 1 unit increase in G (govenment spending), Y increases by 1/(1-c₁) units.

b) Similar to part 1, if we take derivative of Y with respect to T, we get:

= -c₁/ (1- c₁)

OY/OT = 1/(1 - 1)X(-1)

The negative sign indicates that as T (tax) increases, Y should decrease. Thus, for 1 unit increase in T (taxes) Y decreases by c₁/ (1- c₁) units.

c) Explanation for the answers

Consider that G increases by one unit. Therefore, people in the country now have 1 unit more income at their disposal. They will use c₁ units and save (1-c₁) units. Now, the c₁ units witl enter the economy and lead to further consumption. The reason behind this expansionary effect of G(government spending) on Y is that the increase in public expenditure constitutes an increase in income, thereby triggering successive increases in consumption, which also constitutes increase in income.

If the government increases taxes by 1unit , this will mean that the people in the country have 1 unit less income at their disposal. But, the taxes paid depend upon income of the people. When the people have lesser income at their disposal, the economy will tend to contract due to lesser consumption and the incremental Taxes recieved by the government will not be equal to 1 unit but lesser than 1 unit. This is again dependant upon the propensity to consume (c₁) . If the people have 1 unit lesser income, they will not reduce their consumption by 1 unit, but by 1/ (1-c₁) units (which is greater than 1).  

Therefore, the effect of increase of Government expenditure and the effect of an increase in taxes is different on the economy.

4) If G increases by 1 unit, the economy increases by 1/(1-c₁) units.

If T increases by 1 unit, the economy decreases by c₁/(1-c₁) units.

Therefore, if both G and T increase by 1 unit, the amount of change in economy would be given as:

ChangeinY (AY)=1- - 1-4 = 1 1-ci 1-ci

Thus, if G and T both are increased by 1 unit, the GDP increases by 1 unit independant of the value of c₁. In other words, Balanced Budget Multiplier (BBM) is always unity independant of the marginal propensity to consume.

5) In this model, we assumed the uniform marginal propensity to consume (MPC) for all taxpayers and beneficiaries of government expenditure. However, let us consider that MPC of the taxpayers is different from those of the recipients of government expenditure. In this case, the increase 1 G by one unit will lead to a change in  Y by 1/(1-c₁) units, where c₁ is the MPC of recepients of government expenditure. The increase 1 T by one unit will lead to a decrease in  Y by c₂/(1-c₂) units, where c₂ is the MPC of taxpayers.

Thus, the total Change in Y is equal to 1/(1-c₁) -c₂/(1-c₂) units. In practice, c₁ is generally greater than c₂ , therefore the value of BBM is less than 1.