ECON 2103A - Microeconomics Assignment 1: Analysis of Consumption

This microeconomics assignment explores several key concepts in consumption theory and macroeconomics. The assignment begins with an analysis of Keynes' consumption puzzle, followed by explanations of how Modigliani's and Friedman's theories address this puzzle. It then delves into the Fisher model, examining intertemporal budget constraints, the impact of interest rate changes on consumption, and graphical representations of these changes. The assignment also covers the maximization problem in the context of the Fisher model, including the interpretation of the marginal rate of substitution. Furthermore, it explores the relationship between the marginal productivity of capital, real costs, and steady-state conditions. Finally, the assignment investigates the money multiplier, reserve deposit ratio, and currency deposit ratio, discussing their impact on the money supply and the effects of economic shocks.

MiCRO-ECONOMICS

Micro-Economics
Contents
Answer 1................................................................................................................................................2
Answer 2................................................................................................................................................3
Answer 3................................................................................................................................................6
Answer 4................................................................................................................................................8
Answer 5..............................................................................................................................................10
Answer 6..............................................................................................................................................12
References...........................................................................................................................................14
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Micro-Economics
Answer 1.
a) Following are the three things depicted by Keyne’s consumption puzzle:
1. MPC(Marginal Propensity to Consume) comes somewhere between 0 and 1
2. Amount of consumption comes down with the increase in income
3. Consumptions’ main cause is income and not the rate of interest (Breido and Tregub, n.d.).
The puzzle over consumption of Keynes’ theory arises because it was only based om short-run.
As per long run consumption, average propensity to consume remains same with the increase in
income.
b) The life period of a person or individual is divided in two parts and this is how Modigliani’s
consumption theory could resolve the puzzle. He explained wealth as well as income grows
together in long run which results in propensity to consume remains constant (Deaton, n.d.).
c) Friedman could solve the puzzle using permanent income hypothesis. As per him, the
average propensity to consumption relies upon the ratio of permanent income to temporary
income (Baker,2006). He also says that during fall in current income, the average propensity
of consumption goes up temporarily however when current income rises, the average
propensity of consumption decreases. According to Friedman, it would have been better to
use the theory of permanent income hypothesis for resolving the problem of average
propensity to consume (Chao and Hsiang, n.d.).
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Micro-Economics
Answer 2.
a) Let consumption in Period 1=C1
Let consumption in Period 2= C2
Let income earned in Period 1= I1
Let income earned in Period 2= I2
Interest rate=r
Therefore, Period 2 consumption is equal to earned income in Period 2 plus savings and
interest amount earned on savings in Period 1.
(C2=I2+(1+r)(I1-C1)=>C1+C2/(1+r)=I1+I2/(1+r)
Hence, Budget Constraint: C1+C2/(1+r)=200+100/(1+r)
b) Here, C1=150 and C2=160
Substituting above values in budget constraint for finding the value of r.
Therefore, 150+160/(1+r)=200+100/(1+r)
60/(1+r)= 50=>1+r=1.2
Hence, r=0.2
ORIGINAL BUDGET CONSTRAINT
C1+ C2/1.2= 200+100/1.2
1.2C1+ C2=240+100
1.2C1+C2=340 (BC1)
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Micro-Economics
Graph 1: Original and New Budget Constraint
c) Interest earned on savings would come down if the interest rate would change to 10%. This
is the reason why consumer would prefer to consume more during Period 1 and try to save
less during Period 2.
NEW BUDGET CONSTRAINT
C1+ C2/1.1= 200+100/1.1
1.1C1+ C2=320 (BC2)
Therefore, the budget constraint actually tilts and is depicted as BC2 in graph 1. In C2 it tilts
inward and it tilts outward in C1.
d) In case, rate of interest(r) increases to 30% then Sara can earn more interest in Period 2 by
saving money to consume. Hence, in Period 1 Sara will consume less and save money and in
Period 2 he will consume more.
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240
320
BC2
BC1
C2
C1

Micro-Economics
NEW BUDGET CONSTRAINT In Period 2
C1+C2/1+0.03= 200+100/1.3
1.3C1+C2= 260+100
1.3 C1+C2=360 (BC3)
Graph 2: Original and New Budget Constraint
Again the budget constraint has tilt and this it has tilted inwards in C1 and tilts outwards in C2.
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360
240
BC1
BC3
C2
C1277
283

Micro-Economics
Answer 3.
a) Maximisation Problem:
Max U= 1-e c1 + β(1-e c2) wrt C1, C2
S.t. C1+ C2/1+r= y1+y2
b) Conditions of Equilibrium
(∂U/∂C1)=1/1(1+r)
Now, -e C1 / β(-e c2)= e C1 / β e =1+r
MRS= β(1+r)
By using logarithm, we are getting,
C1- ln β-C2=ln(1+r)
Now, using above in budget, we are getting:
-C2/(1+R)+y1+y2=C2+ ln[β(+r)]
-C2+(1+r)(y1+y2)=(1+r)C2+(1+r) ln[β(1+r)]
{[1+r][y1+y2-ln(β+ βr)]}/(2+r)= C2
C1=y1+y2- [y1+y2-ln(β+ βr)/(2+r)]
c) By using:
(∂U/∂C1)=1/1(1+r)
We are getting,
(∂U/∂C1)=U’ (C1)/ β U’(C2)= 1+r
U’(C1)= β(1+r) U’(C2)
=MRS U’(C2)
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Micro-Economics
d) Now,
R=0.1
Β=0.9
MRS= β(1+r)=0.9(1.1)=0.9
Interpretation: For inversing C1 by 1unit , we need to sacrifice 0.9 units of C2.
Answer 4.
a) The above equation represents that marginal productivity of capital (MPK) depends upon
the real price of capital, real rate of interest and depreciation. The left hand side of the
equation gives the profit or benefit from buying a single unit of capital and right hand side of
equation implies the cost of one additional unit of capital.
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Micro-Economics
b) For Production:
Real cost of capital(K)= Benefit of
R/p= MPK
For Rental company:
Benefit=Rent=R/p
Cost:
1. Interest cost= iPk where, i= nominal rate of interest, PK=Price of Capital
2. Change in PK of = -∆PK
3. Depreciation= 𝛿
Hence, Cost=P 𝛿 iPk- -∆PK + 𝛿PK
=PK[i- ∆PK/PK+ 𝛿]
=PK[i-x+ 𝛿]
=PK [r+ 𝛿]
now, real cost= PK(r+ 𝛿)/P
So, π= R/P- PK/P (r+ 𝛿)
= MPK- PK/P(r+ 𝛿)
Now at steady state:
MPK=Pk/P(r+ 𝛿)
c) Y= K ½ L ½
L=100
PK=P=1
R=0.1
𝛿=0.1
MPK=∂Y/∂K= ½(L/k)1/2 =1/2* 10/√k
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Micro-Economics
Real cost: Pk/P(r+ 𝛿)= 1/1[0.1+0.1]=0.2
Now steady state:
1/2* 10/√k=0.2
√k=5/0.2=5/2*10= 25
K*= 625
d) At the time of price increase the real cost of capital will decrease keeping all other things
constant. Therefore, producer will employ have to employ more capital.
e) In case, P=2
Real cost of capital= ½(0.2)=0.1
Then equating with MPK we arrive at:
K*=2500
Answer 5.
a)
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Micro-Economics
Graph 3: Downward Sloping Investment Function
In the economy, when interest rate falls the cost of borrowing also falls. This promotes the
businessmen to invest and therefore when there is fall in interest rate, investment in the
economy goes up.
b) When there is increase in labor, marginal product of capital in the economy also increases
and ultimately increase investment in the economy.
Now,
I=IK[MPK-(PK/P)(r+)]
Under interest and investment space, rise in MPK will make the curve shift to right and that
is how investment increases.
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Investment
(I)
Interest
Rate
Interest
Rate

Micro-Economics
Graph 3: Effect of increase in Labour on the Investment
Answer 6.
a) Money Multiplier term
1. Reserve Deposit Ratio: It refers to the ratio held by the bank in their reserve. Business
policies, bank regulating laws, banks etc. determine this ratio (Agarwal, 2019).
Rr= R/D
2. Currency Deposit Ratio: It refers to the ratio held by the people as a fraction of their demand
deposits’ (D) holdings (Dontigney, 2016).
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Investment
(I)