Investment and Saving

In a simple macroeconomics model,  with no government spending, and no international sector,
we have:  Y = C + S, where S = personal saving, Y = Real GDP and C - real consumption spending.
   Real GDP measures as a flow of earning is either consumed or saved.

    In equilibrium, all earnings are spent.  We have only two types of spending:  C and I = investment..

     Therefore, in equilibrium, Y = C+I  or Real GDP is spent on consumption and investment.

     Subsituting for how earnings are allocated, we get

             C + S = C + I

      or   I = S.

     Therefore, in a simple model, we can express macroeconomic equilibrium as I = S,

        or planned investment spending equals planned personal savings.
 

Assumptions about Investment spending:

    Investment decisions are influenced by the expected rate of profit, and the real interest rate.
       The Expected Profit Rate is determined by figuring the expected revenue from the investment minus the costs of
         making the investment.  Three major influences on the expected profit rate:

           Phase of the business cycle
           Advances in technology
           Taxes

       The real rate of interest:   the real rate of interest is the nominal rate minus the rate of inflation.  It measures the real return to an investment, or the
         real cost of borrowing.      When the real rate of interest is above the expected rate of profit, the investment is not worth doing.
        When the real rate is below the expected rate of profit, then it is worth doing. Therefore, investment spending varies inversely with the real rate of interest.
 

  Assumptions about Savings:

     Households decide how to allocate their disposable income between savings and investment. Therefore, household or personal savings depends on
      The real interest rate
      Disposable Income
      The purchasing power or real value of net assets
      Expected future disposable income.

   The real rate of interest:  The real rate of interest is the opportunity cost. of consumption.
      The higher the real rate of interest, the higher the opportunity cost of consumption.
   Disposable income:  aggregate income left for spending or saving.
   Purchasing power of net assets:  wealth influences savings.  The more wealth, the less savings out of current income.
   Expected future income:  the lower expected future income, the higher is savings.

We can graph savings and investment like a supply and demand graph. Investment is the demand component, and savings is the supply componenet.

The intersection of S(r) and I(r) determines the equilibrium real rate of interest.

Then,  if interest rates are flexible, then the interest rate should adjust so that the amount of saving and the amount
of investment spending in the economy are always equal to each other; where I(r) and S(r) cross in the diagram, at point E..
 


But, suppose investment spending changes because individual attitudes toward the future change, so that investment spending will be higher at every interest rate, like the curve I'(r) in the diagram.

Then, the equilibrium interest rate will rise, until savings and investment are again equal.  [point F in the diagram]

If this happens, investment spending and the level of savings both rise, until they are again equal.  We still have savings and investment equal to each other, so that the level of economic activity will not change, but the distribution of economic activities is different.  At point F, we have more investment spending, more saving, and less consumption spending.

Summary:  a shift in I(r) or S(r) will cause a redistribution in output between spending and saving, but there will be no change in the level of output.

A shift to the right by the I(r) curve will lead to more investment and less consumption, which should lead to faster economic growth.  The immediate effects are transitional, not permanent.
 

A More Complicated Model

    We can create a more complicated model by adding a government sector.

      In this case, we have:

       Aggregate Expenditure = C+I+G       There are three spending sectors in this economy; planned consumption spending, planned investment spending
                                                                     and planned government spending.

      Real GDP= DI + Tx                    Where DI = disposable income, or income available for expenditure by consumers after taxes.
                                                                     Tx = net taxes;   [sum of taxes and tranfsers]

                                                              Therefore, DI = C+S  where S = personal savings.

       In equilibrium,   Spending = Real GDP

                C + I + G = C + S + Tx

       or      I + G = S + Tx

       or        I = S + [Tx-G]              [Tx-G] = government budget balance.

        If the government is running a budget deficit, as shown below, the total supply of
savings in the economy is restricted.

 Crowding out:  government budet deficits decrease the level of private investment over what it would have been without the deficit.

Barro-Ricardo effect:   When Govt runs a deficit, it issues bonds to pay for the goods and services it is buying. Also, it must pay interest on the bonds.
So, it must collect taxes in the future to pay for the principal and interest.

Taxpayers, being rational and looking ahead, understand that their future taxes will be higher, due to the deficit and the need to finance it.
So, their expected future income has decreased, and they cut consumption spending and increase savings to deal with this. According to the Barro-Ricardo effect, taxpayers will cut their consumption spending by the same amount as the deficit. I

If this is so, then private savings adjust to compensate for the govt. deficit. In this case, there is no crowding out at all.