Chapter 19 Spending Allocation Model

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Chapter 19Spending Allocation Model

• Spending Shares
• Effect of Interest Rates on Spending Shares
• Determining the Equilibrium Interest Rate

The spending allocation model applies more to the
long run than to short-run economic fluctuation.
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Spending Shares

• Y C I G X
• Dividing each side by Y
• ? 1 (C/Y) (I/Y) (G/Y) (X/Y)
• where
• C/Y Consumption share
• I/Y Investment share
• G/Y Government purchase share
• X/Y Net export share

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Numerical Example of Spending Shares
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Figure 19.1History of Spending Shares in GDP
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Interest Rate and Spending Shares (I)

• The interest rate affects the three shares of
  spending consumption, investment, and next
  exports.
• When one of spending component increases
  (decreases) such as consumption, the real output
  must increase (decrease) by the same amount and
  its spending share will increase (decrease).
• Ex. Consumption decreases by 1,000 billion.

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Interest Rate and Spending Shares (I)

• Real interest rate rather than nominal interest
  rate
• The real interest rate in the long run is
  determined by balancing private demands for
  consumption, investment, and net exports with the
  available supply of goods and services in the
  economy.
• Response by consumers, firms, and foreigners to
  changes in interest rate takes a long time.

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Consumption and Saving

• A consumer must make a choice between consumption
  and saving out of his/her income.
• More a consumer saves today, more money available
  to consume in future.
• A choice between consumption and saving today is
  a choice between consumption today and
  consumption in future.

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Consumption and Interest Rate (I)

• A choice between consumption and saving today
  depends on the interest rage.

• Example. You can spend 100 today or save it at
  8 interest rate and spend it next year.
• Next year you will get 108 and can consume 108
  worth of goods and service.
• If you think spending 100 today worth more than
  spending 108 next year, you should consume 100
  today.
• If you think spending 100 today worth less than
  spending 108 next year, you should save 100
  today.

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Consumption and Interest Rate (II)

• A higher the interest rate,
• More goods and services a consumer can consume in
  future
• More saving a consumer makes today
• Less consumption a consumer makes today.
• The consumption is negatively related to the
  interest rate.
• The consumption share is negatively related to
  the interest rate.
• The consumption share function is downward
  sloping.

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Figure 19.2The Consumption Share and the
Interest Rate
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Investment and Interest Rate (I)

• Firms borrow the funds to purchase capital and
  pay back in future when it makes profits from its
  production.
• The higher the interest rate,
• the more they must pay back in future.
• The less they borrow today.
• The investment is negatively related to the
  interest rate.
• The investment share is negatively related to the
  interest rate.
• The investment share function is downward sloping.

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Investment and Interest Rate (II)

• The investment is more sensitive to interest
  rates than consumption.
• Future profits from the investment are not known.
• Higher interest rate makes an investment project
  riskier.
• The investment share function is less steep than
  the consumption share function.

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Figure 19.3The Investment Share and the Interest
Rate
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Net Export and Interest Rate (I)

• The interest rate affects the exchange rate, and
  in turn, affects the net exports.
• Exchange rate the price of one currency in terms
  of another.
• Net exports are negatively related to the
  interest rate.

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Net Export and Interest Rate (II)

• Interest rates in U.S. increase
• Foreigners want to save more funds in the U.S.
• Foreigners need to exchange their currencies to
  the U.S. dollar.
• The value of U.S. dollar increases relative to
  foreign currencies.
• The price of U.S. goods become more expensive
  relative to foreign goods.
• U.S. consumers buy cheaper foreign goods more.
• Net exports (Export Import) decrease in the
  U.S.

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Figure 19.4The Net Exports Share and the
Interest Rate
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Effect of Interest Rate on Spending Shares

• Non-government shares
• Sum of consumption share, investment share, and
  net exports share
• Interest rate increases
• Consumption share decreases
• Investment share decreases
• Net exports share decreases
• Non-government shares also decrease
• ?Non-government shares function is downward
  sloping.

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Figure 19.6Summing up Consumption, Investment,
and Net Exports Shares
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Government Purchases Share

• The government share does not depend on the
  interest rate.
• Once the government determines its share (by
  setting the government purchase), the
  non-government share is determined as one minus
  the government share.
• 1 (NG/Y) (G/Y)
• Where (NG/Y) (C/Y) (I/Y) (X/Y)

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Supply and Demand for Spending by the Private
Sector
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Determining Equilibrium Interest Rate

• Given the government share, the non-government
  share function determines the interest rate which
  makes the sum of all four shares equal to one.
• The equilibrium interest rate determines shares
  of consumption, investment, and net exports.

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Figure 19.7Determining the Equilibrium Interest
Rate and the Shares of Spending
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Changes in Interest Rate

• The interest rate will change when there is a
  change (shift) in the the supply of resources
  available for private sector or the demand for
  spending by private sector.
• Changes in government purchases share
• Shift of consumption share, investment share, or
  net export share

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A Shift in Government Purchases

• The share of government purchases share
  increases, then
• The share (supply) available for non-government
  uses increases.
• Interest rate decreases.
• Shares of consumption, investment, and net
  exports increase.
• Crowding out the decline in private investment
  due to an increase in government purchases.

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Figure 19.8The Effect of a Decrease in
Government Purchases
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A Shift in Consumption

• Consumers spend more (save less)
• The consumption share function shifts to the
  right.
• The non-government share function shifts to the
  right.
• The interest rate increases.
• The shares of investment and net exports decrease.

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Figure 19.9Effect of a Shift in Consumption
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National Saving Rate and Interest Rate

• High interest rate is a result of
• low national saving rate (by households and
  government) leads to a higher interest rate (S
  Y C G).
• Higher government purchases
• Higher consumption
• high non-government share
• Higher investment
• Higher net exports