University Economics Problem Set 6: Analyzing the Arcadian Economy

This assignment delves into macroeconomic principles through the analysis of two fictional economies, Arcadia and Borealis. The problem set explores key concepts such as marginal propensity to consume, consumption functions, aggregate expenditure, and income-expenditure equilibrium. It examines how changes in investment, government spending, and fiscal policy impact real GDP and aggregate demand and supply. The assignment also investigates the wealth effect, sticky nominal wages, and their effects on the aggregate demand and supply curves. Furthermore, it analyzes inflationary and recessionary gaps and the government's role in stabilizing the economy through fiscal policy tools like changes in government spending and taxation. The solution provides step-by-step calculations and explanations to illustrate the economic principles at play.

Page 1 of 12
Instructions:
1. All of your answers will be typed directly into this file. FOLLOW THE
INSTRUCTIONS IN EACH QUESTION REGARDING HOW TO RECORD
YOUR ANSWER.
2. For all typed answers, USE EITHER THE “ARIAL” OR “HELVETICA” FONT
(OR A SIMILAR FONT IF YOU DON’T HAVE THOSE)
3. For questions asking you to “explain your answer”, you must provide an explanation of
your answer to be eligible for full credit.
4. To prepare your file for submission, follow the directions in the description of the
assignment on Blackboard
5. Please name the file that you will submit to Blackboard as follows:
[Family Name]_[First Name]_PS6.pdf
So, for example, a submission from Joe Smith would be named: Smith_Joe_PS6.pdf
PROBLEM 1
In the country of Arcadia, the minimum amount of consumption spending that will occur in a
given year is $200 – that is, no matter what level of income households have, the aggregate
amount of consumption spending in the economy will be at least $200. In addition, for every
extra dollar of national income, consumption spending will increase by $0.60. (Note: For the
entirety of this problem, assume that the aggregate price level in Arcadia is fixed.)
a. What is the marginal propensity to consume in Arcadia? [TYPE YOUR ANSWER BELOW]
Answer
The term marginal propensity to consume means a metric through which one quantifies the
induced consumption. The term simply defines increase in personal consumption shall arise on
account of increase in disposable income of the individual. The formula for computation of
marginal propensity to consume is Delta of Expenditure/ Delta of Income. Thus in the current
case 0.6/1 which is 60%. The concept is based on Keynesian Macroeconomic theory.
b. Write out the consumption function for the Arcadian economy. [TYPE YOUR ANSWER
BELOW]
Answer
The consumption function of Arcadia shall be written as follows:
Consumption= 200+ 0.6* Change in National Income from given level or Delta of National
Income (subject to minimum of $ 200)

Page 2 of 12
In 2019 in Arcadia, planned investment expenditure was $200, there was no government
spending or taxation or government transfers and no exports or imports.
c. Write out the planned Aggregate Expenditure function for Arcadia. [TYPE YOUR
ANSWER BELOW]
Answer
Planned Aggregate Expenditure = Consumption + Investment + government + net exports.
Since, there was no government spending or taxation or government transfers and no exports or
imports, the function can be written as follow:
Planned Aggregate Expenditure for Arcadia in 2019= 200+ 0.6* Change in National Income
from given level or Delta of National Income (subject to minimum of $ 200)+200
Planned Aggregate Expenditure for Arcadia in 2019= 400+ 0.6* Change in National Income
from given level or Delta of National Income subject to minimum of $ 200
d. If real GDP (i.e. value of all production in the Arcadian economy) in 2019 were $800,
what would be the level of planned Aggregate Expenditure? Would production be exactly
equal to expenditure, or would suppliers have to reduce or increase inventories? If so, by
how much? [TYPE YOUR ANSWER BELOW]
Answer
Real GDP: $ 800
Planned Expenditure=$680 which is 400+ Real GDP * Marginal Propensity to consume. ( $ 200
as autonomous expenditure)
No production will not be equal to expenditure as production is $ 800 while expenditure is $ 880
Further, the inventory level shall decrease as production does not meet consumption and the
decrease shall be roughly $80.
e. What was the income-expenditure equilibrium level of real GDP in Arcadia in 2019?
Support your answer by filling in all of the blank cells in the table below.
Real GDP Disposable Consumption Planned Planned Unplanned

Page 3 of 12
Income
(YD)
(C) Investment
(Ip)
Aggregate
Expenditure
(AEp)
Investment
(Iu)
700 700 620 200 820
800 800 680 200 880
900 900 740 200 940
1,000 1000 800 200 1000
1,100 1100 860 200 1060 40
1,200 1200 920 200 920 80
1,300 1300 980 200 980 120
1,400 1400 1040 200 1040 160
1,500 1500 1100 200 1300 200
1,600 1600 1160 200 1360 240
f. Suppose that planned investment increased to $400. Write out the new planned
Aggregate Expenditure function. [TYPE YOUR ANSWER BELOW]
Answer
Planned Aggregate Expenditure = Consumption + Investment + government + net exports.
Since, there was no government spending or taxation or government transfers and no exports or
imports, the function can be written as follow:
Planned Aggregate Expenditure for Arcadia in 2019= 400+ 0.6* Change in National Income
from given level or Delta of National Income subject to minimum of $ 200+200
Planned Aggregate Expenditure for Arcadia in 2019= 600+ 0.6* Change in National Income
from given level or Delta of National Income subject to minimum of $ 200
g. What is the value of the multiplier in Arcadia? (Note: you are being asked to provide a
numerical answer) [TYPE YOUR ANSWER BELOW]
Answer
Value of multipler is = (1+(1-MC))= (1/0.4)=2.5
h. What is the new income-expenditure equilibrium real GDP? (Note: in addition to
providing a numerical answer, you must show your work. You may use either a table or
algebra to arrive at your answer. If you want to use a table, you may use Table 1 on p. 7.
If you use the table, you do not need to fill in all of the blank cells. You may just fill in
enough cells to help you arrive at your answer.) [TYPE YOUR ANSWER BELOW (AND FILL

Page 4 of 12
IN TABLE 1 ON P. 7 IF YOU ARE USING THE TABLE TO SUPPORT YOUR ANSWER. IF YOU
ARE USING ALGEBRA TO ANSWER THE QUESTION YOU CAN JUST SHOW YOUR WORK
BELOW AND YOU DO NOT NEED TO ALSO FILL IN THE TABLE).]
Aggregate Plan Expenditure
Planned Aggregate Expenditure for Arcadia in 2019= 400+ 0.6* Change in National Income
from given level or Delta of National Income subject to minimum of $ 200+200
Thus Real Income= 600+ 0.6X
X=600+0.6X
X=1500
Thus, equilibrium shall be at $1500
PROBLEM 2
a. Explain how the “wealth effect” causes the Aggregate Demand curve to be downward
sloping. [TYPE YOUR ANSWER BELOW]
Answer
Wealth Effect causes the Aggregate demand curve to be downward sloping as with decrease in
price level with a given amount of money results in higher spending which increases the
aggregate demand. The result in increase in demand causes the curve to be sloping downward.
b. Explain how “sticky nominal wages” cause the Short-Run Aggregate Supply curve to be
upward sloping. [TYPE YOUR ANSWER BELOW]
Answer
The rational behind the curve to upward sloping is that nominal wages adjust slowly in the short
run. Suppose, price level falls and there is contract between labour and company which shall
result in pay to be same, there by increasing real pay. The same shall result in higher pay to
labourer which shall increase the cost and as on outcome, firm shall decrease the production and
labour. As an outcome, the curve shall be upward sloping.
c. The table below lists a number of economic events. For each event, indicate
i. whether it will shift the AD curve to the right (by entering “R”), to the left (by
entering “L”), or not at all (by leaving it blank);
ii. whether it will shift the Short-Run AS curve to the right (by entering “R”), to
the left (by entering “L”), or not at all (by leaving it blank)
iii. what will happen to equilibrium Real GDP as a result of the shifts (enter “+”
for an increase, “-” for a decrease or “?” if the result is ambiguous);

Page 5 of 12
iv. what will happen to the equilibrium Aggregate Price Level as a result of the
shifts (enter “+” for an increase, “-” for a decrease or “?” if the result is
ambiguous)

Page 6 of 12
The first entry is filled in for you. [FILL IN THE REMAINING ROWS, AS INSTRUCTED
ABOVE]
Events
AD
Shift
S-R AS
Shift
Change
in
Eq. GDP
Change in
Eq. Price
Level
An increase in consumer optimism causes a rise in
consumption R + +
A nationwide, prolonged internet outage severely
decreases worker productivity L - +
A sharp rise in the stock market increases consumer
wealth R + +
The price of oil sharply decreases AND businesses
decrease investment due to pessimism about the
future
L - +
A sharp rise in health insurance premiums requires
employers to increase their workers’ overall
compensation
L - +
d. Is the economy depicted in Figure 1 (on p. 6) experiencing an inflationary gap, a
recessionary gap, or neither? Explain your answer. [TYPE YOUR ANSWER BELOW]
Answer
inflationary gap as demand is higher than supply.
e. Assume that the government takes no action in response to the situation depicted in
Figure 1. How will the economy adjust over time so that short-run equilibrium real GDP
eventually equals potential real GDP? (Note: For full credit you must NOT ONLY
indicate which curves will shift and in which direction, BUT ALSO what will cause the
curves to shift.) [TYPE YOUR ANSWER BELOW]
Answer
GDP shall become 300 in the long run which shall cause a shrinkage of economy. The economy
shall adjust by supply curve by shifting left in the long run while the demand shall remain same.
PROBLEM 3
In the country of Borealis, the minimum amount of consumption spending that will occur is $300
– that is, no matter what level of income households have, the aggregate amount of consumption
spending in the economy will be at least $300. In addition, for every extra dollar of national
income, consumption spending will increase by $0.75.

Page 7 of 12
Planned investment spending in Borealis is $100, and Government spending on goods and
services is also $100. Taxes, transfers, exports and imports all equal zero.
a. Write out the planned Aggregate Expenditure function for Borealis. [TYPE YOUR
ANSWER BELOW]
Answer
Planned Aggregate Expenditure = Consumption + Investment + government + net exports
PAE=300+0.75*(GDP)+100+100= 500+0.75*GDP
b. Solve for the income-expenditure equilibrium level of real GDP. (Note: in addition to
providing a numerical answer, you must show your work. You may use either a table or
algebra to arrive at your answer. If you want to use a table, you may fill in Table 2 on p.
7. If you use the table, you do not need to fill in all of the blank cells. You may just fill in
enough cells to help you arrive at your answer.) [TYPE YOUR ANSWER BELOW (AND FILL
IN TABLE 2 ON P. 7 IF YOU ARE USING THE TABLE TO SUPPORT YOUR ANSWER. IF YOU
ARE USING ALGEBRA TO ANSWER THE QUESTION YOU CAN JUST SHOW YOUR WORK
BELOW AND YOU DO NOT NEED TO ALSO FILL IN THE TABLE).]
Answer
PAE=300+0.75*(GDP)+100+100= 500+0.75*GDP
GDP=PAE
GDP=500+0.75*GDP
GDP=2000
The economic advisers to the President of Borealis calculate that Borealis’ potential real GDP is
$3,000. The state of Aggregate Demand and Aggregate Supply in the economy is depicted in
Figure 2 on p. 6. The president informs her advisers that she would like to use expansionary
fiscal policy to push the economy closer to its potential.
c. What is the value of the multiplier in Borealis? [TYPE YOUR ANSWER BELOW]
Answer
Value of multipler is = (1+(1-MC))= (1/0.25)=4

Page 8 of 12
d. What are the three tools of fiscal policy the president could use to stimulate expenditure?
In your answer, be sure to indicate which of the three categories of aggregate expenditure
(i.e. C, I or G) each fiscal policy tool would primarily affect. [TYPE YOUR ANSWER
BELOW
Answer
The three tools of fiscal policy are
(a) Increased Government Expenditure: This shall result in increased G part of the Planned
Expenditure;
(b) Reduction in Taxes: This shall result in increasing Consumption portion of Planned
Expenditure;
(c) Direct Benefit Transfer: What are the three tools of fiscal policy the president could use to
stimulate expenditure.
e. Suppose the President decides to increase government spending on goods and services
from $100 to $350. If prices remain fixed, what would be the new income-expenditure
equilibrium real GDP? (Note: in addition to providing a numerical answer, you must
show your work. You may use either a table or algebra to arrive at your answer. If you
want to use a table, you may fill in Table 3 on p. 7. If you use the table, you do not need
to fill in all of the blank cells. You may just fill in enough cells to help you arrive at your
answer.) [TYPE YOUR ANSWER BELOW (AND FILL IN TABLE 3 ON P. 7 IF YOU ARE USING
THE TABLE TO SUPPORT YOUR ANSWER. IF YOU ARE USING ALGEBRA TO ANSWER THE
QUESTION YOU CAN JUST SHOW YOUR WORK BELOW AND YOU DO NOT NEED TO
ALSO FILL IN THE TABLE).]
Answer
PAE=300+0.75*(GDP)+100+350= 7500+0.75*GDP
GDP=PAE
GDP=700+0.75*GDP
GDP=3000
f. Will the increase in government spending on goods and services to $350 be enough to
close the recessionary gap? Explain your answer, being sure to mention the significance
of the upward-sloping short-run aggregate supply curve and the aggregate price level.
[TYPE YOUR ANSWER BELOW]

Page 9 of 12
Answer
Yes, as the Real GDP shall be $ 3000 which shall be equal to long run supply curve and
represents a full employment situation. Thus, the government spending will be game changer.

Page 10 of 12
Figure 1.
0
100
200
300
400
500
600
700
800
900
0 100 200 300 400 500 600 700 800
Aggregate Price Level
Real GDP
Short-Run
AS
AD
Long-Run
AS
Figure 2. Aggregate Demand and Aggregate Supply in Borealis
0
50
100
150
200
250
300
350
400
0 500 1,000 1,500 2,000 2,500 3,000 3,500 4,000
AGGREGATE PRICE LEVEL
REAL GDP
AD
Short-
Run
AS
Long-Run
AS

Page 11 of 12
Table 1. For (optional) use with Problem 1 part (h)
Real GDP
Disposable
Income
(YD)
Consumption
(C)
Planned
Investment
(Ip)
Planned
Aggregate
Expenditure
(AEp)
Unplanned
Investment
(Iu)
Table 2. For (optional) use with Problem 3 part (b)
Real
GDP
Disposable
Income
(YD)
Consumption
(C)
Planned
Investment
(Ip)
Government
Spending
(G)
Planned
Aggregate
Expenditure
(AEp)
Unplanned
Investment
(Iu)
Table 3. For (optional) use with Problem 3 part (e)
Real
GDP
Disposable
Income
(YD)
Consumption
(C)
Planned
Investment
(Ip)
Government
Spending
(G)
Planned
Aggregate
Expenditure
(AEp)
Unplanned
Investment
(Iu)

Page 12 of 12