GDP and Multiplier

Question 2. Suppose beef and fruit are the only goods produced in Cattleland. Below are data concerning economic performance in Cattleland in 1998.

	Final Output thousand pounds	Price per pound
beef	210	$2.0
fruit	430	$0.3

a)      What is the nominal value of GDP in Cattleland in 1998? (1 point)

$549,000

b)      Suppose in 1998, compensation for employees in Cattleland is $345,000, rent is $80,000, interest is $35,000, personal consumption expenditure is $315,000, gross domestic investment is $120,000, government purchases is $75,000. How much should the profit be? What can we say about the international trade condition of Cattleland? Identify clearly any definitions and formulas you use. (4 points)

Factor payment approach: GDP = wages + interests + profit + rent

Profit = $89,000

Expenditure approach: GDP = C + I + G + (X-M), where C is personal consumption expenditure, I is actual gross domestic investment, G is government purchases, X is exports and M is imports.

 (X-M) = $39,000

 which means Cattleland exported more goods than imports in 1998. It was a net exporter.

c)       If GDP per capita is $ 4,300, what is the population of Cattleland? (1 point)

127.67 (rounded at 128)

d)     Suppose capital depreciation is $3,000, what is the NNP of Cattleland in 1998? (1 point)

NNP = GNP – depreciation

= GDP + net factor income – depreciation

= $546,000 - factor payments to the rest of the world + factor income received from the rest of the world

 

Part I

Question 1.  The following data gives a complete picture of the household, business, government and foreign sectors for country Zerbia for the year 1998.  (All figures are in billion dollars.)

            Consumption spending                                                                     100

            Government transfer payments                                                        10

            Government expenditures on goods and services                            50

            Imports                                                                                             20

            Exports                                                                                             10

            Capital Stock (end of 1997)                                                             200

            Capital Stock (end of 1998)                                                             208

            Depreciation rate                                                                              6%

            Interest Rate                                                                                     10%

            Total Taxes                                                                                       20

a. How many units of capital wore out during the course of 1998?  (1 point)

Answer: 12 billion 

b.  What was the total amount of investment that occurred in 1998 including expenditures on the replacement of worn out capital?  (1 point)

Answer: 20 billion

c.  What is the value of GDP for this economy in 1998?  (1 point)

Answer: 160 billion

d.  What is the value of savings for this economy?  (1 point)

Answer: 50 billion

e.  With a macro model that includes a foreign sector we can think of leakages as being equal to S + T + M and injections as being equal to I + G + X.  Are leakages equal to injections for this economy?  (1 point)

Part I

Problem #1. Lucky Campus is a closed economy. When disposable income is $0, consumption in Lucky Campus is $80 billion (all the numbers are in billion of dollars). Suppose the marginal propensity to consume is 0.75; investment is $400; government purchases of goods and services are $600; and taxes are a constant $500 and do not vary with income. At the expenditure equilibrium (i.e. where aggregate expenditure equals total output) calculate:

(a)    real GDP; (1) $2820

(b)   consumption; (1) $1820

(c)    saving; (1) $500

(d)   marginal propensity to save. (1) 0.25

Problem #2.  The closed economy of Lakeland can be represented by the following model (all numbers are in billion of dollars, all notation is standard, the definition of new variables are given by formulas):

C=85 + 0.5*DI

I=$85, G=$60

T= -40 + 0.25*Y

DI=Y-T

Equilibrium: Y=C+I+G

Calculate:

(a)    the equilibrium level of output for this economy; (1) $400

(b)   the amount the government collects in net tax revenue when the economy is in equilibrium; (1) $60

(c)     the government budget deficit or surplus when the economy is in equilibrium; (1) $0

Suppose government purchases increase by $10 billion.

(d)   What is the new equilibrium income? (1) $416

(e)    Draw a graph representing the first equilibrium as well as the second equilibrium. Be sure this graph includes the consumption function, investment function, government spending function as well as clear labels for equilibria and any changes that occur. (1)

See figure.

 

416

400

                                                          

Problem 3.The closed economy of Dairyland has the following characteristics (all numbers are in billion of dollars):

·         autonomous consumption when disposable income is $0 is $100;

·         marginal propensity to consume is 0.9;

·         investment expenditure is $460;

·         taxes are constant and equal to $400;

·         government purchases of goods and services is $400.

(a)     Calculate the slope of the aggregate expenditure curve for this economy. (1) 0.9

(b)     Find the equilibrium level of real GDP. (1) $6000

(c)    Suppose the government cuts its purchases of goods and services to $300. (1)

(i)What is the change in real GDP? -$1000

(ii)What is the government spending multiplier? 10

(d)   Suppose the government continues to purchase $400 worth of goods and services and instead cuts taxes to $300. (1)

(i)     What is the change in real GDP? $900

(ii)   What is the tax multiplier? -9

(e)    Now the government simultaneously decreases both its purchases of goods and services and taxes to $300. What is the change in real GDP? (1) -$100

The government of Dairyland is unhappy with the constant taxes and it decides to replace them with a new tax, which depends on the level of real GDP. The new tax is calculated as 10% of real GDP. Use this information to answer the following questions.

(f)    What is the equation for taxes now? T=0.10*Y

(g)   What is the new equilibrium level of real GDP? (Round to the nearest billion) $5053

(h)   Suppose the government decreases its expenditures to $300 billion.

(i)     What is the new equilibrium level of output? (Round to the nearest billion) $4526

(ii) What is the change in consumer expenditure? -$427

(iii) Why was the change in consumption different from the change in government spending? Consumption changes more than government spending does because of multiplier effect and high MPC.

I. Concepts:

Desequilibrium

Potential Output

Disposable Income

Marginal Propensity to Consume

Marginal Propensity to Save

Consumption Function

Equilibrium Level of GDP

Aggregate Expenditure

Expenditure Multiplier

Tax Expenditure Multiplier

Autonomous Consumption

Inventory Changes

Actual Investment

Planned Investment

Government Balanced Budget Amendment

Government Surplus

Government Deficit

Government Debt

II. True/False and explain

1.       1.      During recessions output decreases and is usually below potential GDP. 

2.       2.      The unemployment rate rises during recessions and falls during expansions.

3.       3.      Shifts in the labor supply and/or the labor demand curves are the best explanation for economic fluctuations.

4.       4.      One assumption of the long run Classical model is that the labor market is always in disequilibrium.

5.       5.      During a recession wages are above the equilibrium wage.

6.       6.      Disequilibrium in the labor market is the reason why booms cannot last for ever.

7.       7.      Economic fluctuations are caused by spending shocks.

8.       8.      When a shock causes a recession, firms (temporarily) operate at below-normal rates of utilization.

9.       9.      With the short-run macro model we are trying to explain changes in output with changes in total spending.

10.    10.  The consumption function is the same as the Consumption - Income line.

11.    11.  The slope of the consumption function, the marginal propensity to consume, is more than one.

12.    12.  If there is a decrease in autonomous taxes T, then there will be a change in the slope of the Consumption – Income line.

13.    13.  If there is a change in  autonomous consumption, then there will be a shift in the Consumption – Income line.

14.    14.  Government spending and Investment are independent of income in the short-run model if they are autonomous.

15.    15.  If aggregate expenditure is larger than GDP, then we expect GDP to decrease in the future.

16.    16.  If an economy is in short run equilibrium, this implies that the economy is producing at full employment.

17.    17.  If firms decide to invest more, then GDP will increase in exactly the same amount.

18.    18.  Compare two different economies, A and B.  If economy A’s marginal propensity to consume (MPC) is larger than  economy B’s MPC, then that means that economy A has a smaller expenditure multiplier than does economy B.

19.    19.  Compare two different economies, A and B.  If economy A’s MPC is larger than economy B’s MPC, then it must be the case that economy A’s tax expenditure multiplier is larger in absolute value than is economy B’s tax expenditure multiplier.

20.    20.  Changes in planned investment, government purchases, net exports, or autonomous consumption, lead to a multiplier effect on GDP.

III. Short Answer Problem.

1.             1.            Let’s think about an economy where

·         ·       C = a + b*Y_D

·         ·       Y_D = Y – T

·         ·       AE = C + I^P + G + (X – M)

And

a= 100; b=0.6; T= 100; I^P= 45, G= 80 and (X – M) = 35.

Then

1. What is the equilibrium level of output?
2. What is the marginal propensity to save?
3. What is the expenditure multiplier?
4. What is the equilibrium level of output if G= 100?
5. What is the tax  expenditure multiplier?
6. If  AE is 550, then what is the change in inventories?
7. In order to get a new equilibrium level of output at 650, what must the change in autonomous taxes be equal to?

2.             2.            Suppose we want to compare the effect of a tax cut in the economy given in the first problem to the effect of the same size tax cut on an economy with a MPC of 0.8.  If everything else about these two economies is the same (except for their MPCs), then which one will experiences a larger change in GDP as a consequence of the tax cut?  How much larger is the change in GDP?

Economics 102

Answers to Practice Questions 4

Spring 2001

Answer Key:

I. Refer to the textbook.

II. True/False and explain

1.       1.      T

2.       2.      T

3.       3.      F. shifts in both are to small over time to explain big changes.

4.       4.      F. It is always in Equilibrium as every market.

5.       5.      T

6.       6.      T

7.       7.      T

8.       8.      T

9.       9.      T

10.    10.  F. the consumption function is related to Yd and Consumption - Income line with Y.

11.    11.  F. is the fraction of an extra dollar spent in consumption. Then is between cero and one.

12.    12.  F. T just affect the ordinate. This is not an percent tax.

13.    13.  T

14.    14.  T

15.    15.  F. increase

16.    16.  F. equilibrium Y may be > or < than the full employment level of Y

17.    17.  F. that amount times the expenditure multiplier.

18.    18.  F. larger Exp multiplier = (1/(1-MPC)).

19.    19.  T

20.    20.  T.

II. Problems

1.

1. Y=500
2. MPC=0.6
3. Exp multiplier = 2.5
4. Y=550
5. Tax expenditure multiplier = -1.5
6. Change in inventory decrease 50
7. ?T= -100

2.       2.      ?GDP= - ?T* (MPC/(1-MPC))

First economy MPC=0.6 then ?GDP= - ?T*(0.6/0.4)= - 1.5*?T

Second economy MPC=0.8 then ?GDP= - ?T*(0.8/0.2)= - 4*?T

Homework 3

Econ 102

Due March 9,2006

Question 1:

Use the following relationships to fill in the table below:

        GDP = C + I + G + (X – M)

        KI = M – X

        I = Private Saving + Government Saving + (M-X)

        I = NS + KI

        Government Saving = T – TR – G

where

GDP = gross domestic product

C = Consumer spending

I = Investment spending

G = government spending

X = exports

M = imports

KI = capital inflow

NS = national saving

T = taxes

TR = transfers

	Year 1	Year 2	Year3	Year 4
GDP	890	7678
Consumption	720		7686	7689
Investment	98	1765	545
Gov Purchase		650		87
Gov Saving			54
Private Saving	32			758
National Saving				755
Transfer		885	456	543
Tax	150	1000	750
Export	10	76		66
Import		85	74	87
Capital Inflow	23		71

Question 2:

Suppose that the demand for labor in Fantasyland is given by the equation w = 1000 – 2L while the supply of labor in Fantasyland is given by the equation w = 100 + 2L where w is the wage per year and L is the number of labor units hired per year.

1. What is the equilibrium level of employment per year and the equilibrium wage rate in Fantasyland?
2. According to the Classical view, what will happen if the wage rate in Fantasyland is currently at $500?
3. If the aggregate production function is:

Output = 50 – (2500)/(50 + number of Workers)

What is the full employment output for this economy?

4. If we define labor productivity for Fantasyland as output divided by the level of labor used in a year, what is the value of labor productivity for Fantasyland if it produces the full employment level of output?
5. What is the value of labor productivity when the economy employs the level of workers that corresponds to an annual wage of $500?
6. Sketch a diagram illustrating the relationship between the level of output in the economy and the level of employment in the economy.  Put output on the vertical axis and employment on the horizontal axis.  Draw in two lines that illustrate labor productivity when the annual wage is $500 and when the economy produces at the full employment level of output.

Question 3:

        Using a diagram of the labor market and a diagram of an aggregate production function, illustrate and verbally describe what happens for the following cases. Be sure to identify what happens to the level of employment, the wage rate, the level of production, and labor productivity.

a)             The supply of labor shifts to the right, holding everything else constant.

b)             There is an increase in physical capital holding everything else constant.

c)             There is a decrease in human capital holding everything else constant.

d)             The demand for labor shifts to the right, holding everything else constant.

Question 4:

You have the following information about the closed economy in Macroland for the year 2006:

Private Saving = $1000

Planned Investment = $300

Government Purchases = $900

Taxes = $200

Transfers = $0

1. What is the level of national saving for this economy?
2. What is the level of government saving for this economy?
3. Is there a budget deficit or surplus in this economy? Compute its value.
4. Compute the quantity of funds supplied and the quantity of fund demanded.  Does the loanable funds market clear in this economy?
5. Does Say’s Law (total output = total expenditure) hold in this economy?  Why or why not?

Question 5:

The country of Badgerland produces only one good: Bucky Badger Pie.  The following information is available:

Output: 300,000,000 units

Employment: 2.5 million people

a.       What is the productivity of labor in Badgerland?

b.       Suppose the capital stock in Badgerland decreases holding everything else constant.  What will happen to labor productivity assuming employment stays constant at 2.5 million people?

c.        Suppose with the decrease in capital stock that the level of output produced falls to 250,000,000 units.  Assuming employment is unchanged, what is the value of labor productivity now?

d.       Suppose capital stock was initially equal to 10 million units.  If the level of capital decreases to 7.5 million units, what will the change in capital per worker equal?

Answers to Homework 3

Econ 102

Due March 9,2006

Question 1:

Use the following relationships to fill in the table below:

        GDP = C + I + G + (X – M)

        KI = M – X

        I = Private Saving + Government Saving + (M-X)

        I = NS + KI

        Government Saving = T – TR – G

where

GDP = gross domestic product

C = Consumer spending

I = Investment spending

G = government spending

X = exports

M = imports

KI = capital inflow

NS = national saving

T = taxes

TR = transfers

	Year 1	Year 2	Year3	Year 4
GDP	890	7678	8400	8531
Consumption	720	5272	7686	7689
Investment	98	1765	545	776
Gov Purchase	95	650	240	87
Gov Saving	43	-535	54	-3
Private Saving	32	2291	420	758
National Saving	75	1756	474	755
Transfer	12	885	456	543
Tax	150	1000	750	627
Export	10	76	3	66
Import	33	85	74	87
Capital Inflow	23	9	71	21

Question 2:

Suppose that the demand for labor in Fantasyland is given by the equation w = 1000 – 2L while the supply of labor in Fantasyland is given by the equation w = 100 + 2L where w is the wage per year and L is the number of labor units hired per year.

7. What is the equilibrium level of employment per year and the equilibrium wage rate in Fantasyland?  The equilibrium level of employment per year is 225 and the equilibrium wage rate is $550.  To find these answers set demand equal to supply and solve for L.  Once you have found L then you can use either the demand or the supply equation to find the value of w.
8. According to the Classical view what will happen if the wage rate in Fantasyland is currently at $500? According to the Classical view all markets clear, including the labor market. Thus, if the wage rate is currently $500 the labor market is in disequilibrium since at this wage there is an excess demand for labor.  The market will return to equilibrium due to wage adjustment: the wage will increase until supply equals demand and this will occur at a wage of $550.
9. If the aggregate production function is:

Output = 50 – (2500)/(50 + number of Workers)

What is the full employment output for this economy? From part (a) we know the equilibrium level of employment is 225 units (the Classical view assumes this will correspond to the full employment level for the economy).  Placing this number in the above equation results in Output = 50 – (2500)/(50 + 225) = (50 - 9.09) units of output = 40.91 units of output.

10. If we define labor productivity for Fantasyland as output divided by the level of labor used in a year, what is the value of labor productivity for Fantasyland if it produces the full employment level of output? Labor productivity for this economy equals (40.91 units of output)/(225 units of labor) or .18 units of output per unit of labor.
11. What is the value of labor productivity when the economy employs the level of workers that corresponds to an annual wage of $500? First you need to identify the level of employment that will occur when the annual wage is $500.  At w = $500, there will be 250 units of labor demanded and 200 units of labor supplied.  Thus, 200 units of labor will be the amount of labor that can be hired when the annual wage is $500.  Using this number and the formula in part (c) gives a value for output: the economy will produce 40 units of labor. Then calculate the labor productivity as 40/200 or .2 units of output per unit of labor.  Labor productivity increases since the economy is employing fewer units of labor for a given amount of capital: each unit of labor is more productive since each unit is now working with a larger capital to labor ratio.
12. Sketch a diagram illustrating the relationship between the level of output in the economy and the level of employment in the economy.  Put output on the vertical axis and employment on the horizontal axis.  Draw in two lines that illustrate labor productivity when the annual wage is $500 and when the economy produces at the full employment level of output. This should be a sketch showing an aggregate production function with two points identified in the drawing: the first point (point A) corresponds to a level of employment equal to 225 units of labor and a level of output corresponding to 40.91 units.  The second point (point B) corresponds to a level of employment equal to 200 units of labor and a level of output corresponding to 40 units.  The drawing should have two rays drawn from the origin: ray A intersects point A while ray B intersects point B.  Ray A is less steep than ray B: labor productivity is higher at point B than at point A.

Question 3:

        Using a diagram of the labor market and a diagram of an aggregate production function, illustrate and verbally describe what happens for the following cases. Be sure to identify what happens to the level of employment, the wage rate, the level of production, and labor productivity.

e)             The supply of labor shifts to the right, holding everything else constant. When the supply of labor shifts to the right this results in a higher level of employment, a lower wage rate, a higher level of production and a decrease in labor productivity.

f)              There is an increase in physical capital holding everything else constant. An increase in physical capital causes the aggregate production function to shift upwards so that for a given level of employment (and therefore no change in the wage rate) the level of output produced increases and labor productivity also increases.

g)             There is a decrease in human capital holding everything else constant. A decrease in human capital causes the aggregate production function to shift downwards so that for a given level of employment (and therefore no change in the wage rate) the level of output produced decreases and labor productivity also decreases.

h)             The demand for labor shifts to the right, holding everything else constant. When the demand for labor shifts to the right this results in a higher level of employment, a higher wage rate, a higher level of production and a decrease in labor productivity.

Question 4:

You have the following information about the closed economy in Macroland for the year 2006:

Private Saving = $1000

Planned Investment = $300

Government Purchases = $900

Taxes = $200

Transfers = $0

6. What is the level of national saving for this economy? The level of national saving in the economy is equal to the sum of private saving plus government saving.  In addition, the level of investment in the economy is equal to national saving or the sum of private saving plus government saving.  Thus, 300 = 1000 plus government saving.  Government saving equals -700 and so national saving is equal to $300 (which is the same as the level of investment).
7. What is the level of government saving for this economy? See the answer given in part (a).
8. Is there a budget deficit or surplus in this economy? Compute its value. The budget deficit equals government spending minus taxes or, in this case 900 – 200.  The government is spending more than it is collecting in taxes and thus, it is running a budget deficit of $700.
9. Compute the quantity of funds supplied and the quantity of fund demanded.  Does the loanable funds market clear in this economy? The quantity of funds supplied equals savings or $1000 and the quantity of funds demanded equals planned investment plus the budget deficit or $300 + $700 or $1000.
10. Does Say’s Law (total output = total expenditure) hold in this economy?  Why or why not? Yes, Say’s law holds in this economy given that total leakages = total injections.  Total leakages are equal to the sum of private saving plus taxes or $1200 while total injections are equal to the sum of investment plus government purchases or $1200.

Question 5:

The country of Badgerland produces only one good: Bucky Badger Pie.  The following information is available:

Output: 300,000,000 units

Employment: 2.5 million people

e.        What is the productivity of labor in Badgerland? To find labor productivity in Badgerland divide output by employment or 300,000,000 units of output/2.5 million people.  Thus, labor productivity equals 120 units of output per unit of labor.

f.        Suppose the capital stock in Badgerland decreases holding everything else constant.  What will happen to labor productivity assuming employment stays constant at 2.5 million people? Labor productivity will decrease since labor will now have less capital to work with and this will result in labor producing a smaller level of output than they initially produced.

g.        Suppose with the decrease in capital stock that the level of output produced falls to 250,000,000 units.  Assuming employment is unchanged, what is the value of labor productivity now? The value of labor productivity is now equal to 100 units of output per unit of labor.

h.       Suppose capital stock was initially equal to 10 million units.  If the level of capital decreases to 7.5 million units, what will the change in capital per worker equal? If the capital stock is initially 10 million units then the initial capital to worker ratio is (10 million units of capital)/(2.5 million people) or 4 units of capital per worker.  When the capital stock decreases to 7.5 million units then the capital to worker ratio is (7.5 million units of capital)/(2.5 million people) or 3 units of capital per worker.

Economics 102

Spring 2006

Homework #4

Problem 1

Suppose there are only two countries, Macronia and Micronia and that these two countries trade with each other. Use the Classical Model and the following information to answer this problem.

Hint:  You will find it helpful to be very organized in your work on this problem: I would suggest that you make two columns on your page and in the left-hand column compute the calculations for Macronia (please label the top of the column with the country’s name) and in the right-hand column compute the calculations for Micronia (label the top of the column with Micronia’s name).  This will help you keep track of all the various details involved in this problem.

Use this Classical Model:

Y = C + S_P + T – TR

Y = C + I + G + (X – M)

KI = M – X

S_G = T – TR – G

NS = S_P   + S_G  = Y – C – G

I = Y – C – G + KI

Leakages = Injections in Equilibrium or S_P  + T – TR + M = I + G + X

Note: in the table below i_R is the real interest rate and in the problem it is expressed as a decimal: e.g. if the real interest rate is 10%, then i_R  enters the mathematical expression as .1.

Country	GDP	C	G	T – TR	SP	I
Macronia	$6,000	4,700	700	200	1000+2000 iR	400-4000 iR
Micronia	4,000	2,800	600	200	800+4000 iR	1100-2000 iR

a. Calculate the equilibrium real interest rate for both Macronia and Micronia.

b. Calculate the value of net exports for Macronia and Micronia.  What do you notice about the relationship between the level of net exports for Macronia and Micronia?

c. Calculate the supply of loanable funds and the demand for loanable funds in the two countries. Does the market for loanable funds clear in each country?

d. Calculate NS + KI for each country and compare this sum with the value of investment for each country.

Problem 2

The private saving and investment spending of Macronia, which is a closed economy, can be described by linear equations (e.g.,  i_R= mI + b or I = (1/m)i_R - (1/m)b). Use the information in the following table and the Classical Model in problem (1) to answer this series of questions.  Assume the private saving and investment functions are stable and linear from year to year (e.g., once you have an equation that describes private saving, this equation will hold true for 2003, 2004, and 2005).

Year	iR	I	SP
2003	.02	$1,030	$1240
2004	.04	$1,010	$1480

a. Derive the equations for private saving and investment spending in Macronia (you will find it easier to write these equations as I = f(i_R) and S = f(i_R)).

b. In 2005,  C = $10,000, G = $800, T = $300, and TR = $100. Find the equilibrium interest rate, the level of private saving in 2005, and the level of investment in 2005.

c. Calculate the level of GDP in Macronia for 2005.

d. Calculate the value of leakages and injections in 2005 in Macronia.

e. An economist suggests that the government of Macronia should spend $130 more (i.e., G = $930). Holding everything else constant, what is the new equilibrium interest rate, the new level of private saving, and the new level of investment? Does this policy increase total output? Why or why not?

Problem 3

In the Classical model, the supply of money and the demand for money are equal. Let kdenote the percentage of income that people desire to hold as money, which is assumed to remain constant. In 2004 the money supply was $5,000 and the nominal GDP was $10,000. The inflation rate from 2004 to 2005 was 10%. In 2005 the money supply was $6,600.

a. Calculate the value of  k.

b. Calculate the nominal and real GDP in 2005 (using 2004 as the base year).

c. What is the growth rate of real GDP from 2004 to 2005?

d. Suppose that the money supply in 2005 is $13,200 (and not $6,600). Given this level of the money supply, what is the inflation rate, the level of nominal GDP and the level of real GDP in 2005? (Hint: you know the level of real GDP for 2005 since we are using a Classical Model.)

e. Suppose the government wants the inflation rate from 2004 to 2005 to be 5%.  What level of money should the government supply in 2005 to achieve this goal?

Problem 4

Use the following Keynesian Model of a closed economy to answer problem (4):

Y = C + S + T where T is net taxes (we will not worry about transfers in this problem)

AE = C + I + G

Y = AE in equilibrium

C = a + b (Y – T)

The aggregate consumption function of Macroland (a closed economy) is linear in the aggregate current disposable income, that is, C = a + b × (Y-T). We may divide the investment into planned and unplanned investments. And the total investment is I = I_{Planned +} I_Unplanned. The planned aggregate spending AE_Planned is the sum of C, G, and I_Planned.

Year	Y	T	Y-T	C	G	IPlanned	AEPlanned	IUnplanned
2002	$8,000	500		4150	1,000		5850
2003		500		4650	1,000	700		2,650
2004	10,000	1,000			4,000	800

a. Calculate the missing values in the above table.

b. What are the values of aggregate autonomous consumer spending and the marginal propensity to consume in Macroland?

c. In 2005, T= 1300, G=5,000, and I = 100. What is the equilibrium GDP for 2005 using the Short Run Keynesian Model?

Economics 102

Spring 2006

Answer Key for Homework #4

1.

a. To calculate the value of the equilibrium real interest rate you need to utilize the information you have and the model’s equations.  Start by considering the equation Y = C + S_P + T – TR.  For Macronia, you are given a value for Y, C, and (T – TR).  That allows you to solve for private saving and get 1100.  The table tells you that S_P= 1000 + 2000i_R: when private saving equals 1100, then the real interest rate must equal .05 or 5%. Performing a similar calculation for Micronia reveals that the equilibrium real interest rate in Micronia is also 5%.

b.  To calculate net exports again consult the model’s equations and the information you are given.  Using the formula Y = C + I + G + (X – M) note that you know Y, C, and G but do not know I or (X – M).  But, you do know the equilibrium real interest rate so, for example, in Macronia you can calculate I by noting that I = 400 – 4000i_R and plugging in a value of .05 into this equation.  Thus, I for Macronia equals 200. Now, you can solve for the level of net exports for Macronia and you will get (X – M) = 400.  Performing the same calculations using Micronia’s data you will find that investment in Micronia equals 1000 while net exports equal -400.  Note that net exports in Macronia (400) equals net importas (M- X) in Micronia. 

c. If we define the supply of loanable funds as equaling private savings plus capital inflows (KI) then this means that the supply of loanable funds in Macronia equals 1100 + -400 for a total supply of loanable funds of 700.  The demand for loanable funds in Macronia is comprised of the demand by businesses for funds (I) and the demand by government for funds (-S_G): thus, the demand for loanable funds in Macronia is 200 + 500 or 700.  the demand for loanable funds equals the supply of loanable funds in Macronia.  Following the same logic for Micronia, the supply of loanable funds equals 1400 while the demand for loanable funds equals 1400.  Thus, the loanable funds market in both economies is in equilibrium.

d. National saving and capital inflows in Macronia equal 200 while investment also equals 200.  National saving and capital inflows in Micronia equal 1000 while investment equals 1000. Thus, the sum of NS + KI equals I in both countries.

2.

a. To find these equations sketch a coordinate graph with the real interest rate on the vertical axis and loanable funds on the horizontal axis.  Then you can plot the points you know: for instance, investment spending equals 1010 when the real interest rate is .02 (or 2%) and investment spending equals 1030 when the real interest rate is .04.  Then you can use your basic slope intercept form to solve for the equation.  You need to repeat this process using the information you have about private saving and the real interest rate.  The equations are I = 1050 – 1000 i_Rand Sp = 1000 + 12000 i_R.

b. One way to solve this question is to think about the fact that leakages equal injections in equilibrium.  Thus, S_P  + T – TR  = I + G.  We can substitute into this equation and get 1000 + 12000i_R + 200 = 800 + 1050 – 1000 i_R.  Solving this equation we find the equilibrium real interest rate equals .05 or 5%.  Plugging this value back into our equations for investment spending and private saving allows us to calculate investment as 1000 and private saving as 1600.  Alternatively, market clearing in the loanable funds market implies 1000 + 12000 i_R = 1050 – 1000 i_R+ 600 since private saving equals investment spending plus the negative budget balance. Thus i_R = .05. Then Sp = $1600 and I = $1000.

c.   Y = C + G + I = 10,000 + 800 + 1000 = $11,800.

d. The leakages = Sp + (T-TR) =1800 and injections = G + I = 1800.

e.  Market clearing implies 1000 + 12000 i_R = 1050 – 1000 i_R+ 730. Thus i_R is equal to .06.  Then Sp = $1720 and I = $990. Since consumption and investment are reduced by a total of $130, the level of  total output is unaffected by this increase in government spending (there is complete crowding out). In the Classical Model, fiscal policy does not affect the level of real GDP.

3.

a. M^s = M^d or 5000 = k × 10000 implies k = .5.

b. Since in equilibrium 6,600 = .5 × nominal GDP, the nominal GDP is $13,200. Since the price level increase 10%, the real GDP for 2005  = 13,200 / 1.1 = $12,000.

c. The growth rate of real GDP from 2004 to 2005 = (12,000 – 10,000) / 10,000 × 100 = 20%.

d. M^s = k P Y implies P = 13,200 / (.5 × 12,000) = 2.2. Thus the inflation rate is 120%. The nominal GDP is PY = M^s / k = $26,400 and the real GDP is $12,000.

e. M^s = k P Y = .5 × 1.05 × 12,000 = $6,300.

4.

a. From data of 2002 and 2003, we obtain C = 400 + .5 (Y-T).

Year	Y	T	Y-T	C	G	IPlanned	AEPlanned	IUnplanned
2002	$8,000	500	7,500	4,150	1,000	700	5,850	2,150
2003	9,000	500	8,500	4,650	1,000	700	6,350	2,650
2004	10,000	1,000	9,000	4,900	4,000	800	9,700	300

b. The aggregate autonomous consumer spending is $400 and the MPC = .5.

c. Y = C + G + I or Y = 400 + .5 (Y-1300) + 5000 + 100. Solving this equation for Y, we find Y = 9700.