Topic 1 - Consumption Flashcards
What are the conjectures to the Keynesian Consumption theory?
0 < MPC < 1
APC falls as incomes rise (C/Y)
Income is the main determinant of consumption
What does the Keynesian consumption graph look like?
SEE IN NOTES
What actually happened when they tested the Keynesian view on consumption?
Research initially supported Keynesian consumption function (Conjecture 1 worked)
But none of the other conjectures worked
What were the problems behind the Keynesian view?
Based on consumption function economists predicted that C would grow slower than Y over time
So savings rate increase then due to increase income
But this prediction did not come true
So what did the research prove about the Keynesian view on consumption following the prediction?
As incomes grew, the APC did not fall, and C grew just as fast.
Simon Kuznets showed that C/Y was very stable in long time series data.
What does the Keynesian Consumption function look like?
SEE IN NOTES
What are the assumptions behind Irving Fisher’s Intertemporal choice model?
- Assumes consumer is forward-looking and chooses consumption for the present and future to maximise lifetime satisfaction.
- Consumer’s choices are subject to an inter-temporal budget constraint,(measure of the total resources available for present and future consumption)
- Consumers prefer to smooth consumption over lifetime
What is the basic model of the Inter-temporal Model?
- Two time periods: t=0(current) ,1 (future)
- Real Income: y0 (current), y1 (future)
- Real Consumption Expenditure: c0(current), c1 (future)
- Real savings: s0 (Can only save in current period we can only get return in future period)
- Real interest rate on bonds: r (the same for lending and borrowing)
- Real budget constraint at time 0: c0+s0=y
- Real budget constraint at time 1: c1=y1+(1+r)s0
How do we figure out the lifetime/ Inter temporal budget constraint?
- Budget Constraint at Time 0: C0 +SO = Y
- Budget Constraint at Time 1: c1=y1 + (1+r)S0
From Budget Constraint 1 we get:
S0= (C1-Y1)/(1+R) (VIA MAKING S0 THE SUBJECT)
Therefore Lifetime/Intertemporal budget constraint is:
c0+(c1-y1)/(1+r)=y
OR
c0+c1/(1+r)= y+y1/(1+r)=W
OUR DISCOUNT RATE IS: 1/(1+R)
What does the Inter-temporal Budget Constraint look like?
SEE IN NOTES
What are the assumptions for Indifference curve related the Inter temporal model?
- More is better
- Preference for diversity
- Consumption today and tomorrow are normal goods
What does the Indifference Curve look like?
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How do you calculate the slope of the indifference curve?
U= U(Ct,C(t+1))= U(Ct)+β x U(C(t+1))
(Formula for total derivative) Δ𝑈=𝜕𝑈/(𝜕𝐶_𝑡 ) Δ𝐶_𝑡+𝛽∗𝜕𝑈/(𝜕𝐶_{𝑡+1} ) Δ𝐶_{𝑡+1}
-Given that Δ𝑈=0 at each indifference curve we can show:
𝜕𝑈/(𝜕𝐶_𝑡)Δ𝐶𝑡=−𝛽∗𝜕𝑈/(𝜕𝐶_{𝑡+1} ) Δ𝐶_{𝑡+1}
(Δ𝐶_{𝑡+1} )/(Δ𝐶{𝑡} )=− (𝜕𝑈/(𝜕𝐶_𝑡))/(𝛽∗𝜕𝑈/(𝜕𝐶{𝑡+1}))=𝑀𝑅𝑆(𝐶𝑡,𝐶(𝑡+1) )
So slope is negative marginal utility of 𝐶(𝑡+1) over marginal utility 𝐶𝑡
/ = Over (Like fractions)
What does Optimal choice look like in the Inter Temporal Model?
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What happens at Optimal Choice in the Inter Temporal Model?
At optimal point the slope of the budget constraint is equal to the slope of the indifference curve, i.e. (1+r) = MRSc0,c1
In other words: a rate at which consumer is willing to give up future consumption in order to get a unit of current consumption is equal to the rate prevailing in the market.
How can we see if someone is a borrower/lender in the Inter temporal Model?
See in notes
How can we use the Euler Equation as an analytical solution to the Inter temporal model?
Max utility s.t. budget constraint 𝑈=𝑈(𝐶𝑡)+𝛽∗𝑈(𝐶_(𝑡+1)) Max U s.t. Budget constraint: Lagrangian is: ℒ =𝑈(𝐶𝑡)+𝛽∗𝑈(𝐶(𝑡+1))+𝜆(𝑌𝑡+𝑌(𝑡+1)/(1+𝑟𝑡)−𝐶𝑡−𝐶(𝑡+1)/(1+𝑟𝑡 )) The first order conditions are: 𝑈′ (𝐶𝑡 )−𝜆=0⇒𝜆= 𝑈′ (𝐶𝑡 ) 𝛽∗𝑈′ (𝐶(𝑡+1) )−𝜆/(1+𝑟𝑡 )=0⇒𝜆=(1+𝑟𝑡)∗𝛽∗𝑈′(𝐶(𝑡+1))
The Euler equation:
𝑈’(𝐶𝑡 )=(1+𝑟𝑡 )∗𝛽∗𝑈′(𝐶(𝑡+1))
The Euler Equation can be presented as:
(𝑈′ (𝐶𝑡 ))/(𝛽∗𝑈′ (𝐶(𝑡+1) ) )=(1+𝑟𝑡 )
What does the Euler Equation determine?
determines the path of consumption, but not level. To find level you need to combine the Euler equation with the budget constraint.
How do you combine the Euler Equation with the Budget Constraint?
Lagrangian:
ℒ =𝑙𝑜𝑔(𝐶𝑡)+𝛽∗𝑙𝑜𝑔(𝐶(𝑡+1))+𝜆(𝑌𝑡+𝑌(𝑡+1)/(1+𝑟𝑡 )−𝐶𝑡−𝐶(𝑡+1)/(1+𝑟𝑡 ))
The first order conditions are:
1/𝐶𝑡 −𝜆=0⇒𝜆= 1/𝐶𝑡
𝛽∗1/𝐶(𝑡+1) −𝜆/(1+𝑟_𝑡 )=0⇒𝜆=(1+𝑟𝑡 )∗𝛽∗1/𝐶(𝑡+1)
Combining the two yields:
1/𝐶𝑡 =(1+𝑟𝑡 )∗𝛽∗1/𝐶(𝑡+1) ⇒𝑪(𝒕+𝟏) =(𝟏+𝒓𝒕)∗𝜷∗𝑪𝒕
2) Combining the budget constraint {𝐶𝑡+𝐶(𝑡+1)/((1+𝑟𝑡 ))=𝑌𝑡+𝑌(𝑡+1)/((1+𝑟𝑡 ) )} with the Euler equation yields
𝐶𝑡+((1+𝑟𝑡)∗𝛽∗𝐶𝑡)/((1+𝑟t))=𝑌𝑡+𝑌(𝑡+1)/((1+𝑟𝑡))⇒𝐶𝑡 (1+𝛽)=𝑌𝑡+𝑌(𝑡+1)/((1+𝑟𝑡 ) )
𝐶𝑡=1/(1+𝛽) [𝑌𝑡+𝑌(𝑡+1)/((1+𝑟𝑡 ) )]
What does the Inter temporal Budget Constraint look like when we consider an increase in interest rate to lenders and borrowers?
SEE IN NOTES
What can we note about the Increase in interest rate to a person’s budget constraint?
Future Consumption relatively cheaper (w1 to w2)
Current consumption more expensive so shifts left with future consumption increasing
(IN ACCORDANCE WITH NOTES)
What does the increase in Interest Rate to do a lender (implications)?
Implies:
- The intertemporal budget constraint becomes steeper
- Optimal allocation moves from point A to point B
Total Effect:
- C0 from CA0 to CB0
- C1 FROM CA1 to CB1
DIAGRAM SEE IN NOTES
