ECON 105A Deanza College Intermediate Macroeconomic Theory Questions
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ECON 105A Intermediate Macroeconomic Theory
Problem Set #2
Due: October 20th, 2021 (5 PM)
Instructions: Please provide complete answers to the following questions. You must submit the
solution file via your TAs ilearn webpage. Email submissions will not be accepted. Note that it
is plagiarism if your answers look remarkably similar to someone elses and you do not indicate
the group work. Plagiarism will be heavily penalized. Illegible answers can lose points, so write
your answers as CLEARLY as possible or type them up. Lastly, make sure to accompany
appropriate reasoning or calculation as part of your answer.
I. Consider first the goods market model with (exogenously given) constant investment.
Consumption is given by
?? = ??0 + ??1 (?? ? ??)
and ??, ??, and ?? are given.
a. Solve for equilibrium output. What is the equation for the multiplier?
Now let investment depend on both sales and the interest rate:
?? = ??0 + ??1 ?? ? ??2 ??
b. Lets assume that ??1 + ??1 < 1. Solve for equilibrium output. At a given interest rate, is
the effect of a change in autonomous spending bigger than what was in part (a)? Why?
Next, write the LM relation as
??/?? = ??1 ?? ? ??2 ??
c. Solve for equilibrium output. (Hint: Eliminate the interest rate from the IS and LM
relations.) Derive the multiplier (the effect of a change of one unit in autonomous
spending on output).
ECON 105A
1
This content is protected and may not be shared, uploaded or distributed. © Dongwon Lee 2021
II. Consider the following IS-LM model:
?? = 200 + 0.25????
?? = 150 + 0.25?? ? 1,000??
?? = 250
?? = 200
??
(??/??) = 2?? ? 8,000??
??/?? = 1,600
a. Derive the IS relation. (Hint: You want an equation with ?? on the left side and everything
else on the right.)
b. Derive the LM relation. (Hint: It will be convenient for later use to rewrite this equation
with ?? on the left side and everything else on the right.)
c. Solve for equilibrium real output. (Hint: Substitute the expression for the interest rate
given by the LM equation into the IS equation and solve for output.)
d. Solve for the equilibrium interest rate. (Hint: Substitute the value you obtained for ?? in
part (c) into either the IS or LM equation and solve for ??.)
e. Solve for the equilibrium values of ?? and ??, and verify the value you obtained for ?? by
adding ??, ??, and ??.
f. Now suppose that the money supply increases to ??/?? = 1,840. Solve for ??, ??, ??, and ??,
and describe in words the effects of an expansionary monetary policy.
g. Set ??/?? equal to its initial value of 1,600. Now suppose that government spending
increases to ?? = 400. Summarize the effects of an expansionary fiscal policy on ??, ??, and
??.
III. We revisit the paradox of saving here in the context of the IS-LM framework in which
investment depends on the interest rate and output.
a. Suppose households attempt to save more so that consumer confidence falls (lets capture
this change by a decrease in ??0 from the consumption function). Using an IS-LM diagram,
show the effect of the fall in consumer confidence on output and the interest rate.
b. How will the fall in consumer confidence affect consumption, investment, and private
saving? Will the attempt to save more necessarily lead to more saving? Will this attempt
necessarily lead to less saving?
c. What do you think about the chances of having the paradox of saving in the IS-LM model
compared to the goods market equilibrium model (i.e., the IS relation)? Discuss.
ECON 105A
2
This content is protected and may not be shared, uploaded or distributed. © Dongwon Lee 2021
IV. The government closure in the U.S. in 2013 has made some banks on Wall Street feel feared,
leading to the widespread concerns of bank runs. As a result, a majority of commercial banks
decided to keep more reserves. How would this change affect our economys output and interest
rate in the short run? Show the effect on the interest rate and output using an IS-LM model.
ECON 105A
3
This content is protected and may not be shared, uploaded or distributed. © Dongwon Lee 2021
ECON 105A Intermediate Macroeconomic Theory
Problem Set #2
Due: October 20th, 2021 (5 PM)
Instructions: Please provide complete answers to the following questions. You must submit the
solution file via your TAs ilearn webpage. Email submissions will not be accepted. Note that it
is plagiarism if your answers look remarkably similar to someone elses and you do not indicate
the group work. Plagiarism will be heavily penalized. Illegible answers can lose points, so write
your answers as CLEARLY as possible or type them up. Lastly, make sure to accompany
appropriate reasoning or calculation as part of your answer.
I. Consider first the goods market model with (exogenously given) constant investment.
Consumption is given by
?? = ??0 + ??1 (?? ? ??)
and ??, ??, and ?? are given.
a. Solve for equilibrium output. What is the equation for the multiplier?
Now let investment depend on both sales and the interest rate:
?? = ??0 + ??1 ?? ? ??2 ??
b. Lets assume that ??1 + ??1 < 1. Solve for equilibrium output. At a given interest rate, is
the effect of a change in autonomous spending bigger than what was in part (a)? Why?
Next, write the LM relation as
??/?? = ??1 ?? ? ??2 ??
c. Solve for equilibrium output. (Hint: Eliminate the interest rate from the IS and LM
relations.) Derive the multiplier (the effect of a change of one unit in autonomous
spending on output).
ECON 105A
1
This content is protected and may not be shared, uploaded or distributed. © Dongwon Lee 2021
II. Consider the following IS-LM model:
?? = 200 + 0.25????
?? = 150 + 0.25?? ? 1,000??
?? = 250
?? = 200
??
(??/??) = 2?? ? 8,000??
??/?? = 1,600
a. Derive the IS relation. (Hint: You want an equation with ?? on the left side and everything
else on the right.)
b. Derive the LM relation. (Hint: It will be convenient for later use to rewrite this equation
with ?? on the left side and everything else on the right.)
c. Solve for equilibrium real output. (Hint: Substitute the expression for the interest rate
given by the LM equation into the IS equation and solve for output.)
d. Solve for the equilibrium interest rate. (Hint: Substitute the value you obtained for ?? in
part (c) into either the IS or LM equation and solve for ??.)
e. Solve for the equilibrium values of ?? and ??, and verify the value you obtained for ?? by
adding ??, ??, and ??.
f. Now suppose that the money supply increases to ??/?? = 1,840. Solve for ??, ??, ??, and ??,
and describe in words the effects of an expansionary monetary policy.
g. Set ??/?? equal to its initial value of 1,600. Now suppose that government spending
increases to ?? = 400. Summarize the effects of an expansionary fiscal policy on ??, ??, and
??.
III. We revisit the paradox of saving here in the context of the IS-LM framework in which
investment depends on the interest rate and output.
a. Suppose households attempt to save more so that consumer confidence falls (lets capture
this change by a decrease in ??0 from the consumption function). Using an IS-LM diagram,
show the effect of the fall in consumer confidence on output and the interest rate.
b. How will the fall in consumer confidence affect consumption, investment, and private
saving? Will the attempt to save more necessarily lead to more saving? Will this attempt
necessarily lead to less saving?
c. What do you think about the chances of having the paradox of saving in the IS-LM model
compared to the goods market equilibrium model (i.e., the IS relation)? Discuss.
ECON 105A
2
This content is protected and may not be shared, uploaded or distributed. © Dongwon Lee 2021
IV. The government closure in the U.S. in 2013 has made some banks on Wall Street feel feared,
leading to the widespread concerns of bank runs. As a result, a majority of commercial banks
decided to keep more reserves. How would this change affect our economys output and interest
rate in the short run? Show the effect on the interest rate and output using an IS-LM model.
ECON 105A
3
Answer to A:
Equilibrium output with constant investment follows from goods market
equilibrium condition,
Y= Z with Y= 1/(1-?1)-[cO-cl*T+l+G).
Hence, The Multiplier is 1/(1-?1).
Question B.
Now let investment depend on both sales and the interest rate:
I = bo + b2Y - Bzi
b. Let's assume that C1 + b < 1. Solve for equilibrium output. At a given interest rate, is
the effect of a change in autonomous spending bigger than what was in part (a)? Why?
Using the goods market equilibrium condition Y= Z to solve for goods
market equilibrium.
Note: " where Z now also depends on i through investment"
=> Y for a given value of the interest rate i:
=> Y=2=C+I+G
=> Y= cO+ cl* (Y-1)+bO+b1* Y-b2*i+G
=> (1-c1-b1*Y= [cO+b0-c1*T+G-b2*i]
Y=1/1(1-c1-b1*[cO+b+c1*T+G-b2*i]
This equilibrium defines the IS Curve
The multilier is larger than in (a) because investment now also depends
on Y ie l has induced component change in autonomous expenditure
now not onlyget magnified by induced changes in consumption but
investment also.
Question C.
Next, write the LM relation as
M/P = d.Y – dzi
c. Solve for equilibrium output. (Hint: Eliminate the interest rate from the IS and LM
relations.) Derive the multiplier (the effect of a change of one unit in autonomous
spending on output)
Answer to C:
M/P= d1Y – d2i, i= (diY-M/P)/d2
Substitute i(d1Y-M/P)/d2 into
=> Y- cO+c1Y-c1T+b0 +bly-b2i+G
=> Y= [1/(1-c1-b1+b2d1/d2)[CO-c1T+60+(b2M/P)/d2+G]
Hence, the multiplier is 1/(1-c1-b1+b2d1/d2)
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Explanation & Answer:
1 Page
Tags:
economics
investment
Equilibrium
LM curve
goods market model
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