Question

1. In deriving government spending multiplier we assumed that government spending is exogenously fixed. However, it is also possible that government spending (G) increases with domestic income (Y). This is represented in the following equation. where G and g are parameters of the fiscal rule. The if GDP rises by $1, G rise by Sg x 1. marginal government spending rate: Government's choice variable here is G. Derive the government spending multiplier under this setup, i.e. derive ΔΥ/ΔG.

Answer 1

Usually we used the government expenditure as exogeneously given. But here we are asked to find out the new government expenditure multiplier when the G is not fixed rather it increases with Domestic Income(Y) i.e.

........(1) where and g are parameters of fiscal rule.

Now, we also know that the Consumption Function is

where c is marginal propensity to consume.

And, Investment is exogeneously given as .

Let's assume the economy is closed. Hence NX=Net Import-Export is 0.

Now, The total expenditure of the economy is

E = C+I+G

or, .........(2)

Now, at equilibrum, the total expenditure must equal the GDP of the economy. Hence

Y = E

or,

or,

or, .............(3)

Hence, this is the new equilibrum income for the economy.

Now, we will derive the government spending multiplier from equation (3). We will differentiate the both sides of equation (3) with respect to

Hence,

Hence, the new government spending multiplier is 1/(1-c-g).

Hope the solution is clear to you my friend.