How to Finance Government Spending
Consider a closed economy where consumption spending depends on output: , where is autonomous consumption and is disposable income (income after tax). The tax rate is flat at the level of 20% on all income without double taxation. The ShortRun Aggregate Supply (SRAS) is flat at . Investment is given by , where is the real interest rate expressed in percentage points (for example, means that interest rate is 1.12%, not 112%). The supply of loanable funds is given by . Initially, the equilibrium level of GDP , all demand for loanable funds comes from investment, the state budget is balanced. The government wants to reduce unemployment and increases by 10.
(a) (10 rp) Assume that the government just has this money at its disposal, so there is no need to borrow it or find elsewhere. How will the increase in affect GDP? If the increase in GDP does not equal to the increase in , explain the difference.
Ответ
Please note that since the economy is closed, there are no exports or imports. Moreover, loanable funds are not restricted to savings by consumers. That is, as given in the problem and .
Collected taxes are , budget is balanced, so as well. In the credit market, , so and .
In equilibrium, output must equal demand, that is,
Let's plug what we know to the output equation: . From this we get . So, the equilibrium condition is:
a) In this part, and . Plugging this into the equilibrium equation, we obtain:
So, , GDP goes up by 27.78. This is greater than because of the multiplier effect.
Alternative solution: use the government spending multiplier
(b) (10 rp) Now, assume that the government will finance its new spending through collected taxes, thus adjusting the tax rate. Find the new level of GDP in equilibrium. If it does not equal to the new level of GDP in (a), explain the difference.
Ответ
In this part, is unknown, and . Plugging this into the equilibrium equation, we obtain:
So, , GDP goes up by 10 compared to the initial state. This is less than in (a) because increase in taxes has a partially offseting effect on GDP.
(c) (10 rp) Assume that instead of raising taxes, the government will borrow 10 in the financial market, affecting the interest rate. How will this affect GDP when the goods market and the loanable funds market are the new equilibrium? If it does not equal the new level of GDP does not equal the new level of GDP in (a), explain the difference.
Ответ
The government enters the loanable funds market as a borrower aiming to borrow 10, so it is now , and . With this rate, ; also . Plugging this into the equation, we get:
So, , GDP goes up by 22.22 compared to the initial state. This is less than in (a) because by entering the loanable funds market, the government forces the interest rate higher, which reduces investment (this is called the crowding out effect).