ECON 2123 Problem Set 1 Solution
Instructor: Prof. Wenwen Zhang
TA: Mr. Ding Dong
Due at 15:00 on Monday, March 5th, 2018
Question 1: Suppose that a very simple economy produces three goods
and service: Pizzas, Haircuts, and Backpacks. Suppose the quantities
produced and their corresponding prices for 2002 and 2006 are showed
in the table below:
Please answer the following questions:
(a). What is nominal GDP in 2002 and in 2006?
(b). Taking 2002 as the base year, what is real GDP in 2002 and in 2006?
(c). Taking 2006 as the base year, what is real GDP in 2002 and in 2006?
Solution:
(a). Nominal GDP of 2002 = 100*10+50*15+200*40 = $9750;
Nominal GDP of 2006 = 120*12+45*20+210*45 = $11790.
(b). Real GDP of 2002 (base year 2002) = 100*10+50*15+200*40 = $9750;
Real GDP of 2006 (base year 2002) = 120*10+ 45*15+210*40= $10275.
(c). Real GDP of 2002 (base year 2006)= 100*12+ 50*20+ 200*45= $11200;
Real GDP for 2006 (base year 2006)= 120x12+ 45x20+ 210x45= $11790.
Question 2: During a given year, the following activities occur:
i. A silver mining company pays its workers $200,000 to mine 75 pounds
of silver. The silver is then sold to a jewelry manufacturer for $300,000.
ii. The jewelry manufacturer pays its workers $250,000 to make silver necklaces, which the manufacturer sells directly to consumers for
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$1,000,000.
Please answer the following questions:
(a). Using the production-of-final-goods approach, what is GDP in this
economy?
(b). What is the value added at each stage of production? Using the
value-added approach, what is GDP?
(c). What are the total wages and profits earned? Using the income
approach, what is GDP?
Solution:
(a). Only silver necklaces are final goods, thus GDP= value of silver necklaces =
$1,000,000.
(b). At stage one: No intermediate goods. Value added = value of silver = $300,000;
At stage two: Silver is intermediate goods. Value added = value of silver necklaces
- value of silver = $1,000,000 -$300,000 = $700,000.
The GDP (using approach of value-added) = $300,000+$700,000 =$1,000,000.
(c). At stage one: Wage for workers = $200,000; Income of silver company owner
= $300,000-$200,000 = $100,000. Total wage and income = $300,000;
At stage two: Wage for workers = $250,000; Income of jewelry manufacturer =
$1,000,000 - $300,000- $250,000 = $450,000. Total wage and income =$700,000.
The GDP (using approach of total income) = $300,000+$700,000 =$1,000,000.
Question 3. Suppose that the economy is characterized by the following
behavioral equations:
C = 160 + 0.6YD
I = 150
G = 150
T = 100
Solve for the following variables:
(a). Equilibrium GDP (Y)
(b). Disposable income (YD )
(c). Consumption spending (C)
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Solution:
(a). Aggregate Demand ≡ Z = C + I + G = 160 + 0.6(Y − T ) + 150 + 150.
At equilibrium, total production = aggregate demand: Y= Z; Or equivalently,Y =
160 + 0.6(Y − 100) + 150 + 150
Y = 1000
Thus, Equilibrium output is 1000.
(b). YD = Y − T = 1000 − 100 = 900.
(c). C = 160 + 0.6YD = 160 + 540 = 700.
Question 4. Balanced budget multiplier
Suppose that the economy starts with a balanced budget: G = T. If the
increase in G is equal to the increase in T, then the budget remains in
balance.
Please answer the following questions:
(a). Solve for equilibrium output.
(b). By how much does Y increase when G increases by one unit?
(c). By how much does Y decrease when T increases by one unit?
(d). How does the specific value of the propensity to consume, c1 , affect
your answer to part a? Explain.
Solution:
(a). Y = C + I + G
Y = c0 + c1 (Y − T ) + I¯ + G
Y = c0 + c1 Y − c1 T + I¯ + G
(1 − c1 )Y = c0 + I¯ − c1 T + G
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Y = (1−c
[c0 + I¯ − c1 T + G]
1)
With the assumption that G=T, above equilibrium condition can be written as:
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(1) Y = (1−c
[c0 + I¯ + (1 − c1 )G] (if you replace T with G); Or
1)
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(2) Y = (1−c
[c0 + I¯ + (1 − c1 )T ] (if you replace G with T).
1)
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¯ + G. Thus, a one-unit increase in
(b). From equation (1) in (a)., Y = (1−c
[c0 + I]
1)
G will lead to 1 unit increase in Y.
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¯ + T . Thus, a one-unit increase in
(c). From equation (2) in (a)., Y = (1−c
[c0 + I]
1)
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T will lead to 1 unit increase in Y.
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[c0 + I¯ + (1 − c1 )G], it can be seen that, given autonomous
(d). From Y = (1−c
1)
spending level, a higher c1 leads to a higher equilibrium output, Y.
Question 5. Automatic stabilizers
In this chapter we have assumed that the fiscal policy variables G and
T are independent of the level of income. In the real world, however,
this is not the case. Taxes typically depend on the level of income and
so tend to be higher when income is higher. In this problem, we examine how this automatic response of taxes can help reduce the impact of
changes in autonomous spending on output.
Consider the following behavioral equations:
C = c0 + c1 Y D
T = t0 + t1 Y
YD = Y − T
G and I are both exogenous. Assume c1 and t1 are between 0 and 1.
Please answer the following questions:
(a). Solve for equilibrium output.
(b). What is the multiplier? Does the economy respond more to changes
in autonomous spending when t1 is larger? Explain.
(c). Why is fiscal policy in this case called an automatic stabilizer?
Solution:
(a).Y = C + I + G
Y = c0 + c1 (Y − T ) + I + G
Y = c0 + c1 (Y − t0 − t1 Y ) + I + G
Y = 1−c11+c1 t1 [c0 − c1 t0 + I + G]
(b). The multiplier is 1−c11+c1 t1 . When t1 is larger, the multiplier 1−c11+c1 t1 is smaller,
thus at any given level of autonomous spending [c0 − c1 t0 + I + G], the equilibrium
output will be smaller. Or equivalently speaking, given any positive change in autonomous spending, the increase in output tends to be lessen when t1 is larger, so
does YD and C. In other words, the economy responds less to changes in autonomous
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spending when t1 is larger.
(c). Compared with the multiplier in standard goods market model of chapter 3:
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, in this question the multiplier is 1−c11+c1 t1 . Because of the automatic effect of
1−c1
taxes on the economy, the economy responds less to changes in autonomous spend1
).
ing than in the case where taxes are independent of income (since 1−c11+c1 t1 < 1−c
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As output tends to vary less (to be more stable), fiscal policy is called an automatic
stabilizer.
Question 6. Suppose that a persons wealth is $50,000 and that her yearly
income is $60,000. Also suppose that her money demand function is given
by:
M d = $Y (0.35 − i)
Please answer the following questions:
(a). Derive the demand for bonds. Suppose the interest rate increases
by 10 percentage points. What is the effect on her demand for bonds?
(b). What are the effects of an increase in wealth on her demand for
money and her demand for bonds? Explain.
(c). What are the effects of an increase in income on her demand for
money and her demand for bonds? Explain.
Solution:
(a). B D = 50, 000 − 60, 000(0.35 − i)
If the interest rate increases by 10 percentage points, bond demand increases by
$6,000.
(b). An increase in wealth increases bond demand, but has no effect on money
demand. Because money demand depends on income (a proxy for transactions demand) rather than wealth.
(c). An increase in income increases money demand, but decreases bond demand.
Because at any given level of wealth, an increase in money demand implies a decrease in bond demand.
Question 7. The Money Multiplier (Modified )
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Assume the following:
i. The public holds no currency.
ii. The ratio of reserves to deposits is 0.1.
iii. The demand for money is given by:
M d = $Y (0.8 − 4i)
Initially, the monetary base is $100 billion, and nominal income is $5
trillion.
Please answer the following questions:
(a). What is the demand for central bank money?
(b). Find the equilibrium interest rate by setting the demand for central
bank money equal to the supply of central bank money.
(c). Given that overall money supply equals (1/reserve ratio)*monetary
base, is it equal to the overall demand for money at the interest rate you
found in part (b)?
(d). What is the impact on the interest rate if central bank money is
increased to $300 billion?
(e). If the overall money supply increases to $3,000 billion, what will be
the impact on i ? [Hint: Use what you discovered in part (c).]
Solution:
(a). All money is in checking accounts, so demand for central bank money equals
demand for reserves. Therefore, demand for central bank money = 0.1($Y)(.8 - 4i).
(b). b. $100B = 0.1($5,000B)(.8 - 4i)
i = 15%.
(c). Money multiplier = 1/reserve ratio = 1/.1=10.
M s = 10* $100B=$1,000B
M = M d at the interest derived in part (b).
(d). If H increases to $300B the interest rate falls to 5 %. (e). The interest rate
falls to 5%, since when H equals $300B, M = 10*$300B = $3,000B.
THIS IS THE END OF PROBLEM SET 1 Solution.
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