How to calculate investment in a closed economy

102.

Consider a closed economy to which the Keynesian-cross analysis applies. Consumption is given by the equation C = 200 + 2/3(Y – T). Planned investment is 300, as are government spending and taxes.

a.

If Y is 1,500, what is planned spending? What is inventory accumulation or decumulation? Should equilibrium Y be higher or lower than 1,500?

b.

What is equilibrium Y? (Hint: Substitute the values of equations for planned consumption, investment, and government spending into the equation Y = C + I + G and then solve for Y.)

c.

What are equilibrium consumption, private saving, public saving, and national saving?

d.

How much does equilibrium income decrease when G is reduced to 200? What is the multiplier for government spending?

Answer :

a.

Planned spending is 1,600. Inventory decumulation is 100. Equilibrium Y should be higher than 1,500.

b.

Equilibrium Y is 1,800.

c.

Consumption is 1,200, private saving is 300, public saving is 0, and national saving is 300.

d.

Equilibrium Y decreases by 300. The multiplier is 3.

103.

Assume that the consumption function is given by C = 200 + 0.5(Y – T) and the investment function is I = 1,000 – 200r, where r is measured in percent, G equals 300, and T equals 200.

a.

What is the numerical formula for the IS curve? (Hint: Substitute for C, I, and G in the equation Y = C + I + G and then write an equation for Y as a function of r or r as a function of Y.) Express the equation two ways.

b.

What is the slope of the IS curve? (Hint: The slope of the IS curve is the coefficient of Y when the IS curve is written expressing r as a function of Y.)

c.

If r is one percent, what is I? What is Y? If r is 3 percent, what is I? What is Y? If r is 5 percent, what is I? What is Y?

d.

If G increases, does the IS curve shift upward and to the right or downward and to the left?

Answer :

a.

Y = 2,800 – 400r or r = 7 – 0.0025Y.

b.

The slope of the IS curve is –0.0025.

c.

If r is 1 percent, I is 800 and Y is 2,400. If r is 3 percent, I is 400 and Y is 1,600. If r is 5 percent, I is 0 and Y is 800.

d.

IS shifts upward and to the right.

104.

Assume that the equilibrium in the money market may be described as M/P = 0.5Y – 100r, and M/P equals 800.

a.

Write the LM curve two ways, expressing Y as a function of r and r as a function of Y. (Hint: Write the LM curve only relating Y and r; substitute out M/P.)

b.

What is the slope of the LM curve?

c.

If r is 1 percent, what is Y along the LM curve? If r is 3 percent, what is Y along the LM curve? If r is 5 percent, what is Y along the LM curve?

d.

If M/P increases, does the LM curve shift upward and to the left or downward and to the right?

e.

If M increases and P is constant, does the LM curve shift upward and to the left or downward and to the right?

f.

If P increases and M is constant, does the LM curve shift upward and to the left or downward and to the right?

Answer:

a.

Y = 1,600 + 200r, or r = –8 + 0.005Y.

b.

The slope of the LM curve is 0.005.

c.

If r is 1 percent, Y is 1,800. If r is 3 percent, Y is 2,200. If r is 5 percent, Y is 2,600.

d.

The LM curve shifts downward and to the right.

e.

The LM curve shifts downward and to the right.

f.

The LM curve shifts upward and to the left.

105.

a.

Suppose Congress decides to reduce the budget deficit by cutting government spending. Use the Keynesian-cross model to illustrate graphically the impact of a reduction in government purchases on the equilibrium level of income. Be sure to label: i. the axes; ii. the curves; iii. the initial equilibrium values; iv. the direction the curve shifts; and v. the terminal equilibrium values.

b.

Explain in words what happens to equilibrium income as a result of the cut in government spending and the time horizon appropriate for this analysis.

Answer:

a.

b.

The equilibrium level of income falls. This analysis is appropriate in the short run when prices and the interest rate are constant.

106.

a.

Suppose Congress passes legislation that significantly reduces taxes. Use the Keynesian-cross model to illustrate graphically the impact of a reduction in taxes on the equilibrium level of income. Be sure to label: i. the axes; ii. the curves; iii. the initial equilibrium values; iv. the direction the curve shifts; and v. the terminal equilibrium values.

b.

Explain in words what happens to equilibrium income as a result of the tax cut and the time horizon appropriate for this analysis.

Answer:

a.

b.

The equilibrium level of income increases. This analysis is appropriate in the short run when prices and the interest rate are constant.

107.

a.

Use the Keynesian-cross model to illustrate graphically the impact of an increase in the interest rate on the equilibrium level of income. Be sure to label: i. the axes; ii. the curves; iii. the initial equilibrium values; iv. the direction the curve shifts; and v. the terminal equilibrium values.

b.

Explain in words what happens to equilibrium income as a result of the increase in the interest rate.

Answer:

a.

b.

The equilibrium level of income falls.

108.

a.

Graphically illustrate the impact of an open-market purchase by the Federal Reserve on the equilibrium interest rate using the theory of liquidity preference and the market for real money balances. Be sure to label: i. the axes; ii. the curves; iii. the initial equilibrium values; iv. the direction the curve shifts; and v. the terminal equilibrium values.

b.

Explain in words what happens to the equilibrium interest rate as a result of the open-market purchase.

Answer:

a.

b.

The equilibrium interest rate falls.

109.

a.

As an economy moves into a recession, income falls. Illustrate graphically the impact of a decrease in income on the equilibrium interest rate using the theory of liquidity preference and the market for real money balances. Be sure to label: i. the axes; ii. the curves; iii. the initial equilibrium values; iv. the direction the curve shifts; and v. the terminal equilibrium values.

b.

Explain in words what happens to the equilibrium interest rate as a result of the fall in income.

Answer:

a.

b.

The equilibrium interest rate falls.

110.

In explaining the 2003 bill to cut taxes, President Bush is quoted as saying, “When people have more money, they can spend it on goods and services.”

a.

In the IS–LM model, will a tax cut change the money supply in the economy? Does a change in the money supply shift the IS or the LM curve?

b.

In the IS–LM model, does a tax cut shift the IS or the LM curve?

c.

Based on your answers in a and b, how can you reconcile the president's statement with economics? Can you suggest how his statement could be modified to be consistent with the IS–LM model?

Answer:

a.

Tax cuts do not change the money supply, which is controlled by the central bank (Federal Reserve). Changes in the money supply shift the LM curve.

b.

Tax cuts shift the IS curve.

c.

The president used the word money as it is popularly understood, but his use was not according to its macroeconomic meaning. Rephrasing the statement to say “when people have more disposable income as a result of the tax cut, they can spend more on goods and services” would make the statement consistent with the economic model.

111.

Explain what force moves the market back to equilibrium if the market is initially in disequilibrium in:

a.

the market for goods and services;

b.

the market for real money balances.

Answer:

a.

In the market for goods and services if planned spending exceeds actual spending, for example, then inventories will become depleted, firms will increase production, hire more workers, and increase income and output until equilibrium is achieved.

b.

In the market for real money balances if the supply of real money balances exceeds the demand, for example, households will buy bonds, driving bond prices up and interest rates down. Interest rates will continue to decline until households are eventually willing to hold the amount of real money balances supplied.

112.

Two identical countries, Country A and Country B, can each be described by a Keynesian-cross model. The MPC is 0.9 in each country. Country A decides to increase spending by $2 billion, while Country B decides to cut taxes by $2 billion. In which country will the new equilibrium level of income be greater?

Answer: Income in Country A will increase more. The government-spending multiplier in Country A equals 10, so income in Country A will increase by $20 billion. The tax multiplier in Country B equals 9, so income in Country B will only increase by $18 billion.

113.

a.

The interest rate affects which variable in: (1) the market for goods and services and (2) the market for real money balances?

b.

The level of income affects which variable in: (1) the market for goods and services and (2) the market for real money balances?

Answer:

a.

The interest rate affects (1) investment in the market for goods and services, and (2) the demand for money in the market for real money balances.

b.

The level of income affects (1) consumption in the market for goods and services, and (2) the demand for money in the market for real money balances.

114.

Compare the predicted impact of an increase in the money supply in the liquidity preference model versus the impact predicted by the quantity theory and the Fisher effect. Can you reconcile this difference?

Answer: The liquidity preference model predicts that an increase in the money supply will decrease interest rates. The quantity theory predicts that an increase in the money supply will increase inflation, which, via the Fisher effect, will increase the nominal interest rate. The liquidity preference model emphasizes the short-run effect when prices are fixed, while the quantity theory and Fisher effect are long-run effects when prices are flexible.

115.

The IS–LM model simultaneously determines equilibrium in two markets.

a.

Which two markets?

b.

What two variables adjust to bring equilibrium in the markets?

Answer:

a.

The IS–LM model simultaneously determines equilibrium in the goods market and the money market.

b.

The interest rate (r) and real output (Y) are the two variables that adjust to bring equilibrium in both markets.

116.

Explain why a decrease in planned investment, which is a change in the goods market, will upset the equilibrium in the money market.

Answer: A decrease in planned investment spending decreases planned spending, which will reduce the equilibrium level of income in the goods market. A decrease in income decreases the demand for real money balances in the money market, which will decrease the equilibrium level of the interest rate in the money market. Graphically, this is represented by a shift in the IS curve to the left and a movement down the LM curve.

117.

Explain why an increase in the money supply, which is a change in the money market, will upset the equilibrium in the goods market.

Answer: An increase in the money supply will decrease the equilibrium interest rate in the money market. A lower interest rate will increase investment spending in the goods market, which will increase the equilibrium level of income in the goods market. Graphically, this is represented by a shift in the LM curve to the right and a movement down the IS curve.

118.

During a recession, consumers may want to save more to provide themselves with a reserve to cushion possible job losses. Use the Keynesian model to describe the impact of an exogenous decrease in consumption (a decrease in C) on the equilibrium level of income in the economy. Will aggregate national saving increase?

Answer: A decrease in exogenous consumption reduces planned spending, which reduces the equilibrium level of income by a greater amount via the consumption spending multiplier, i.e., a decrease in consumption spending leads to a decrease in income, which leads to another decrease in consumption spending, and so on. At the new lower equilibrium level of income, both income and consumption spending will have decreased by the same amount, so that national saving (Y – C – G) will be unchanged.

119.

a.

Graphically illustrate how an increase in income affects the equilibrium levels of saving, investment, and the interest rate in the loanable funds model. Be sure to label: i. the axes; ii. the curves; iii. the initial equilibrium values; iv. the direction the curve shifts; and v. the terminal equilibrium values.

b.

Explain in words what happens to the equilibrium levels of saving, investment, and the interest rates as a result of the increase in income.

Answer:

a.

b.

The equilibrium levels of saving and investment increase. The interest rate falls.

Use the following to answer question 120:

120.

The above figure is a basic representation of the Keynesian cross. Just by looking at the graph, deduce the fundamental prerequisite condition for the Keynesian-cross model to hold true.

Answer: The slope of the planned expenditure line has to be less than 45° in order to intercept the actual expenditure curve. Given that the slope of the planned expenditure curve is the marginal propensity to consume (MPC) and that a 45° line has a slope = 1, this implies that the MPC has to be less than 1. This in turns means that not all of the income earned is spent on consumption, and people have an intention to save.

121.

How can the government expenditure multiplier be reinterpreted in terms of savings?

Answer: We know that Y / G = 1/(1MPC). Rearranging the equation, we have Y = G/(1MPC). MPC denotes how many people are willing to spend on consumption for every dollar earned. (1-MPC) denotes how many people save out of every dollar earned. Therefore, for every increase of government expenditure, the income rise is inversely related to the propensity to save; the lower the propensity to save the greater is the rise in total income.

Use the following to answer question 122:

122.

The above diagram shows how a rise in government expenditure (G) shifts the IS curve from IS1 to IS2. What are the levels of investments in Y1 and Y2?

Answer: The investment level remains same in both cases. The shift in the IS curve denotes that for the same levels of investment and consumption, the economy is now at a higher level of output Y because of a rise in government expenditure G.

123.

Of the following comments related to equilibrium level in an IS-LM model, which best denotes the logical causality, and why?

Answer: Option (c) is correct. IS-LM analysis assumes prices to be fixed. Given that money supply is autonomously determined by the central bank, the supply of real balances is fixed. This helps determine the equilibrium level of the interest rate in the money market in the short run, thereby determining the level of investment in the economy. As government expenditure is parametric and consumption is a function of total income, the equilibrium level of investment helps determine the equilibrium level of output Y in the economy.

A. The goods and services market as denoted by IS curve gives an equilibrium level of Y, which when posited in the LM curve gives the equilibrium level of r.

B. The goods and services market as denoted by the IS curve gives an interest rate as a function of Y which helps solve for equilibrium in the money market.

C. The equilibrium rate of interest as determined by the demand for real balances for a given level of money supply in the money market helps determine the equilibrium level of investment that finally helps reach an equilibrium level of income.

124.

A falling investment function yields a falling IS curve, but a falling demand for real money balance curve yields a rising LM curve. Why?

Answer: Both the IS and the LM curves plot relationships between output level Y and interest rate r in the goods and services market and money market respectively. Both are logically derived from the investment function and real money demand curve, respectively, and are not functions of these demand schedules.

In the goods and services market, a higher rate of interest would lower the investment level and thereby reduce total output Y, and hence the IS curve is falling. In the money market, a higher level of interest rate denotes higher demand for real balances, which can only happen under higher levels of income (given prices are assumed constant) and is hence an upward rising curve.

125.

The demand for money (even if we take into account real balances, it is demand for money deflated by price levels) helps determine the equilibrium level of the interest rate, even though holding money does not earn any interest income. How is this possible?

Answer: Money is just one form of financial asset that we hold. At every point of time, individuals calculate a tradeoff between holding their assets in the most liquid form and potential income revenue they could earn from other asset forms. This is why the LM curve is called the liquidity preference and money supply curve, as the demand for real balance reflects the demand for liquidity. Because of this constant tradeoff, the demand for liquid money is intrinsically linked to the interest rate, and the equilibrium level of money demand is ultimately linked to the equilibrium level of interest rate in the economy.

126.

Assume that planned expenditure consists of consumption, investment, and government expenditures only. Further, assume that consumption C= c(Y – tY), where tY denotes taxes as a function of income. Calculate the equilibrium level of Y and the government expenditure multiplier.

Answer: For equilibrium, Actual Expenditure + Planned Expenditure

or Y = c (Y - tY) + I + G

or Y = cY –ctY + I + G

or Y +ctY –cY = I + G

or (1 + ct – c)Y = I + G

or Y = (I + G)/ (1 + ct – c)

The government expenditure multiplier will be = 1/ (1 + ct – c)

127.

Assume that a government raises its own expenditures and funds those expenditures by printing more money, thereby raising the money supply in the economy. How will this affect the IS-LM curve and the equilibrium level of income and the interest rate

Answer: The rise in government expenditures will shift the IS curve to the right.

[insert figure here]

In the money market, the demand for real balances will rise, raising interest rates, but a rise in money supply will shift the supply of real balances to the right thereby reducing interest rates. Consequently, the LM curve will become flatter and more horizontal.

Under equilibrium, the higher level of output Y will be attained at a lower level of interest rate r, as compared to the level of r it would reach under the old LM curve if the money supply were not raised.

128.

Assume that a government decides to maintain a constant interest rate in the money market and adjusts the money supply accordingly. What would be the impact of such a policy on the LM curve and IS curve?

Answer: If the government policy decided to maintain the constant interest rate, the money supply curve would be a horizontal line and not a vertical line. Moreover, as the interest rate is fixed for all levels of output, the LM curve too would be a flat horizontal line.

There would be no change in the IS curve. The IS curve plots the relationship between interest rate and output level in the goods and services market. The relationship between interest rate and investment does not change, and hence the IS curve retains its characteristic shape.

129.

Assume an economy where the consumption function is defined as C= CC + cY, and the investment function is defined as I= ir, where Y is total income and r is the interest rate. What does the slope of the IS curve depend on?

Answer: IS plots the equilibrium levels of interest rate and output in the goods and services market. Here, c denotes the marginal propensity of consumption, which relates consumption to levels of output and is not related to interest rates. The slope of the IS curve depends on i as it is the only factor in the expenditure side that relates to interest rates.