## Closed Economy - Impact of Fiscal Policy on the Interest Rate

Because the interest rate is the cost of borrowing and the return to lending in the financial market, we can better understand the role of the interest rate in the economy by thinking about the financial markets. To do this we rearrange the national income accounts identity as:

Y – C – G = I

The term Y – C – G is the output that remains after the demands of consumers and the government have been satisfied. This can be referred to as national savings or simply savings (S). In this form the national income account identity shows that savings equals investment.

We can distinguish between savings in the private sector and savings in the public sector through the introduction of our tax identities.

This allows the previous identity to be rewritten as:

S = (Y – T – C) + (T – G) = I

The term (Y – T – C) is disposable income minus consumption, which is private savings. The term (T – G) is government revenue minus government spending, which is public savings. If government spending exceeds government revenue, the government runs a budget deficit, and public savings is negative. National savings is the sum of both private and public savings. This equation states that the flow into the financial markets (public and private savings) must equal the flows out of the financial markets (investment).

To see how the interest rate affects this system and brings the financial markets into equilibrium we substitute the consumption function and the investment function into the national income accounts identity.

S = (Y – T – [C (Y – T)]) + (T – G) = I(r)

S = Y – C(T – T) – G = I(r)

Next note that G and T are fixed by policy (as discussed previously) and Y is fixed by factors of production. The left hand side of this equation shows that national savings depends on income Y and fiscal policy G and T. For fixed values of Y, T and G, national savings is also fixed. The right hand side shows that investment depends on the interest rate.

The below is an interactive graph of savings and investment. For simplicity, we will use the previous assumption that saving is fixed (i.e. does not depend on the interest rate). This results in a vertical savings line as regardless of the interest rate there will be no change in the quantity saved. The investment function slopes downward as the higher the interest rate the fewer investment projects are profitable. The diagram resembles a supply and demand diagram. Indeed we can think of the good being demanded as loanable funds and the price being the interest rate. Savings is the supply of loanable funds. Investment is the demand for loanable funds.

The interest rate adjusts to bring savings and investment into balance. The vertical line represents savings – the supply of loanable funds. The downward sloping line represents investment – the demand for loanable funds. The interaction of these two curves determines the equilibrium interest rate. At the equilibrium interest rate, households’ desires to save balances firms’ desires to invest, and the quantity of loanable funds supplied equals the quantity demanded. We can now use this framework to consider what happens when various elements of the national income accounting framework change.

We will now use our model to show how fiscal policy affects the economy. When governments change their spending or levels of taxation, it effects the demand for the economy’s output of goods and services and alters national savings, investment and the equilibrium interest rate. Consider the impact of an increase in Government purchases by ΔG. The immediate impact is to increase the demand for goods and services by ΔG. But since total output is fixed, the increase in government purchases must be met by a decrease in some other category of demand. Because disposable income Y – T is unchanged, consumption C is unchanged. Therefore, the increase in government purchases must be offset by a fall in investment. To induce investment to fall, the interest rate must rise.

To grasp the impact of an increase in government expenditure we will consider the interactive graph below. Use the filter option to show the impact of an expansion in fiscal policy. Because an increase in government expenditure is not accompanied by an increase in taxes, the government finances additional spending through borrowing – that is reducing public savings. With private savings unaffected, the impact of a reduction in public savings is to reduce the overall levels of national savings. This causes a shift in the below graph. At the initial interest rate the demand for loanable funds exceeds the supply of loanable funds. This excess demand causes an increase in the “price” of loanable funds, which is the interest rate. This continues until a new equilibrium is reached.

The opposite occurs if we have a contractionary fiscal policy. Use the contraction option on the interactive graph to see what happens.

Y – C – G = I

The term Y – C – G is the output that remains after the demands of consumers and the government have been satisfied. This can be referred to as national savings or simply savings (S). In this form the national income account identity shows that savings equals investment.

We can distinguish between savings in the private sector and savings in the public sector through the introduction of our tax identities.

This allows the previous identity to be rewritten as:

S = (Y – T – C) + (T – G) = I

The term (Y – T – C) is disposable income minus consumption, which is private savings. The term (T – G) is government revenue minus government spending, which is public savings. If government spending exceeds government revenue, the government runs a budget deficit, and public savings is negative. National savings is the sum of both private and public savings. This equation states that the flow into the financial markets (public and private savings) must equal the flows out of the financial markets (investment).

To see how the interest rate affects this system and brings the financial markets into equilibrium we substitute the consumption function and the investment function into the national income accounts identity.

S = (Y – T – [C (Y – T)]) + (T – G) = I(r)

S = Y – C(T – T) – G = I(r)

Next note that G and T are fixed by policy (as discussed previously) and Y is fixed by factors of production. The left hand side of this equation shows that national savings depends on income Y and fiscal policy G and T. For fixed values of Y, T and G, national savings is also fixed. The right hand side shows that investment depends on the interest rate.

The below is an interactive graph of savings and investment. For simplicity, we will use the previous assumption that saving is fixed (i.e. does not depend on the interest rate). This results in a vertical savings line as regardless of the interest rate there will be no change in the quantity saved. The investment function slopes downward as the higher the interest rate the fewer investment projects are profitable. The diagram resembles a supply and demand diagram. Indeed we can think of the good being demanded as loanable funds and the price being the interest rate. Savings is the supply of loanable funds. Investment is the demand for loanable funds.

The interest rate adjusts to bring savings and investment into balance. The vertical line represents savings – the supply of loanable funds. The downward sloping line represents investment – the demand for loanable funds. The interaction of these two curves determines the equilibrium interest rate. At the equilibrium interest rate, households’ desires to save balances firms’ desires to invest, and the quantity of loanable funds supplied equals the quantity demanded. We can now use this framework to consider what happens when various elements of the national income accounting framework change.

We will now use our model to show how fiscal policy affects the economy. When governments change their spending or levels of taxation, it effects the demand for the economy’s output of goods and services and alters national savings, investment and the equilibrium interest rate. Consider the impact of an increase in Government purchases by ΔG. The immediate impact is to increase the demand for goods and services by ΔG. But since total output is fixed, the increase in government purchases must be met by a decrease in some other category of demand. Because disposable income Y – T is unchanged, consumption C is unchanged. Therefore, the increase in government purchases must be offset by a fall in investment. To induce investment to fall, the interest rate must rise.

To grasp the impact of an increase in government expenditure we will consider the interactive graph below. Use the filter option to show the impact of an expansion in fiscal policy. Because an increase in government expenditure is not accompanied by an increase in taxes, the government finances additional spending through borrowing – that is reducing public savings. With private savings unaffected, the impact of a reduction in public savings is to reduce the overall levels of national savings. This causes a shift in the below graph. At the initial interest rate the demand for loanable funds exceeds the supply of loanable funds. This excess demand causes an increase in the “price” of loanable funds, which is the interest rate. This continues until a new equilibrium is reached.

The opposite occurs if we have a contractionary fiscal policy. Use the contraction option on the interactive graph to see what happens.

## Closed Economy - Impact of a Change in Investment Function on the Interest Rate

We have discussed how fiscal policy can impact on the interest rate and investment. We can also use our model to examine the other side of the market – the demand for investment. One reason investment demand might change is do to technological innovation. Suppose a new invention such as the computer is introduced. Before a business or household can take advantage of the new innovation, it must buy the investment good. Thus technological innovation can lead to increases in investment demand.

The below interactive graph shows the effects of an increase in investment demand on the interest rate. An increase in investment demand shifts the investment function to the right. This causes an immediate increase in the demand form funds. However, as funds are fixed (i.e. savings are fixed), demand exceeds supply. As a result of this the “price” of funds (i.e. the interest rate) increases. However, note that when savings are fixed, while the interest rate is higher, an increase in the investment function does not cause an increase in total investment.

The below interactive graph shows the effects of an increase in investment demand on the interest rate. An increase in investment demand shifts the investment function to the right. This causes an immediate increase in the demand form funds. However, as funds are fixed (i.e. savings are fixed), demand exceeds supply. As a result of this the “price” of funds (i.e. the interest rate) increases. However, note that when savings are fixed, while the interest rate is higher, an increase in the investment function does not cause an increase in total investment.

This strange result of unchanged investment given an initial increase in investment demand is a result of our assumption that the savings rate is fixed. If we allow the savings rate to vary, it becomes dependent on the interest rate. More people save more at higher interest rates as the return is greater. This generates an upward sloping from left to right savings curve (similar to a supply curve). With an upward sloping savings curve, an increase in investment demand would rise the equilibrium interest rate and the equilribium quantity of investment. This is shown in the below figure.

## Video Summary

A video tutorial discussing the above is available below.