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?
SEE IN NOTES
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?
SEE IN NOTES
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
What does the increase in Interest rate do to a lender that has their income increased (implications)?
Total effect:
=>C0: from CA0 to CB0
=>C1: from CA1 to CB1
Substitution effect:
=>C0: from CA0 to CC0
=>C1: from CA1 to CC1
Wealth effect:
=>C0: from CC0 to CB0
=>C1: from CC1 to CB1
What does the increase in interest rate do to a borrower (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
What does the increase in interest rate do to a borrower who’s income has increased (implications)?
Total effect:
=>C0: from CA0 to CB0
=>C1: from CA1 to CB1
Substitution effect:
=>C0: from CA0 to CC0
=>C1: from CA1 to CC1
Wealth effect:
=>C0: from CC0 to CB0
=>C1: from CC1 to CB1
SEE DIAGRAM IN NOTES
SLIDE 30 FOR BETTER VIEW OF DIAGRAM
What can we overall assume when there is a increase in the interest rate for borrowers and lenders?
Lenders:
c0 => SE (-); WE (+) => SE + WE = ?
c1 => SE (+); WE (+) => SE + WE > 0
Borrowers:
c0 => SE (-); WE (-) => SE + WE < 0
c1 => SE (+); WE (-) => SE + WE = ?
What is the Life-cycle hypothesis?
Modigliani (1950’s)
Based on Fisher’s work in that there is consumption smoothing
The LCH says that income varies systematically over the phases of the consumer’s “life cycle,” and saving allows the consumer to achieve smooth consumption.
(Saving and Spending habits over a lifetime)
What are the assumptions behind the LCH?
- zero real interest rate (for simplicity)
- consumption-smoothing is optimal
What is the basic model for the LCH?
- W= Initial Wealth
- Y= Annual Income until retirement (assumed constant)
- R= No. of years until retirement
- T= Lifetime in years
What are the more detailed models for the LCH?
Lifetime Resources:
W+RY
To achieve smooth consumption, consumer divides resources equally over time:
- C= (W+RY)/T
or
- C= aW +bY (LCH Consumption Function)
Where:
- a= (1/T) is marginal propensity to consume out of wealth
- b= (R/T) is marginal propensity to consume out of income
How can the LCH solve the consumption puzzle?
The APC implied by the life-cycle consumption function is: C/Y = a(W/Y ) + b
- Across households, wealth does not vary as much as income, so high income households should have a lower APC than low income households.
- Over time, aggregate wealth and income grow together, causing APC to remain stable.
What does the LCH graph look like?
SEE IN NOTES
What are the SR policy implications of the LCH hypothesis?
1) The Monetary Mechanism – wealth in the consumption function
2) Transitory Income Taxes-
Change in Income taxes
What are the criticisms behind the LCH hypothesis?
saving behavior of the elderly: (Consume less than predicted in the hypothesis)
1)Uncertainty
Medical care,car breakdown etc.
2)Bequest motive
Want to leave some money to pass on
What is the Permanent Income Hypothesis (PIH)?
Friedman (1957)
People alter their levels of consumption and saving in accordance with expected long term average income (permanent income)
People then use saving and borrowing to smooth consumption in response to a transitory change in income
Friedman believed Keynes looked at the wrong type of income and that we should focus on permanent income
What is the basic model of PIH Hypothesis?
Y= YP +YT
Where:
Y= Current Income
YP= Permanent Income
(Average income which people expect to persist into the future)
YT= Transitory Income
(Temporary deviations from average income)
What is the PIH Consumption Function?
C= aYp
Where a is the fraction of permanent income that people consumer per year
How can the PIH solve the consumption function?
The PIH implies
APC = C/Y = aY P/Y
- To the extent that high income households have on average a higher transitory income than low income households, the APC will be lower in high income households.
- Over the long run, income variation is due mainly if not solely to variation in permanent income, which implies a stable APC.
How can we identify if permanent or transitory changes impact consumption more?
Ct=f(Yt, Yt+1, rt)
(Impact of small change in each variable)
ΔCt=(∂Ct/∂Yt) ΔYt+(∂C/∂Yt+1) ΔYt+1 +(∂C/∂rt) Δrt
Assume ΔYt= ΔYt+1 and Δrt=0 then:
A temporary change:
ΔCt/ ΔYt =∂Ct/∂Yt
A permanent change:
ΔCt/ ΔYt =∂Ct/∂Yt+∂C/∂Yt+1
Implication: Consumption responds more to permanent change in income
What are the similarities and differences in the PIH and LCH?
Both:
- People try to achieve smooth consumption in the face of changing current income.
- Both can explain the consumption puzzle.
LCH: current income changes systematically as people move through their life cycle.
PIH: current income is subject to random, transitory fluctuations.
What are the assumptions of the Random Walk Hypothesis?
Due to Robert Hall (1978)
- based on Fisher’s model & PIH, in which forward-looking consumers base consumption on expected future income
- rational expectations, that people use all available information to forecast future variables like income.
What is the Random Walk hypothesis?
Consumption should follow a random walk (Changes in consumption should be unpredictable)
A change in income or wealth that was anticipated has already been factored into expected permanent income, so it will not change consumption
Therefore, only unanticipated changes in income or wealth that alter expected permanent income will change consumption.
What is some of the views of economists that consumption shifts based on anticipated changes in Income
-Income increases: Wicox (1989), Shapiro and Slemrod (1995, 2003, 2009), Johnson, Parker, and Souleles (2006)
-Income decreases: retirement Banks, Blundell and Tanner (1998):
Considerable evidence that consumption appears to respond to anticipated income increases, consumption much less responsive to anticipated income decreases
Focus on the role of borrowing constraints
What are the opposing views that say unanticipated changes in income shift consumption?
Wolpin (1982), Paxton (1993), Blundell, Pistaferri, Preston (2008)
“consumption reaction to permanent shocks is much higher than that to transitory shocks. There is also evidence, at least in the United States, that consumers do not revise their consumption fully in response to permanent shocks.”
Focus on the role of precautionary savings
What impacts do constraints on borrowing have?
Example: If a consumer learns that her future income will increase, she can spread the extra consumption over both periods by borrowing in the current period.
However, if consumer faces borrowing constraints (“liquidity constraints”), then may not increase current consumption and her consumption may behave as in the Keynesian theory even though she is rational & forward-looking
What does the Budget Constraint look like (REGULAR, BINDING AND NON-BINDING)?
SEE ON NOTES
When is the Budget Constraint not binding?
If the consumer’s optimal C0 is less than Y0
What happens when the budget constraint is binding?
Optimal choice is at D
Since the consumer cannot borrow, best he can do is point E
What does the graph look like for borrowing constraints when income has increased?
SEE ON NOTES
How do we calculate expected future income?
E(Yt+1) = P x Yg(t+1) + (1-P) Yb(t+1)
Where:
Good state:
Income: Yg t+1
Probability: P
Bad State:
Income: Yb t+1
Probability: (1-P)
How do you calculate the marginal utility of expected consumption? (Not considering precautionary savings)
Firstly we assume the log utility (Ut= log (Ct)= 1/Ct)
Therefore we calculate it based on Ct calculated by the expected future income
e. g. Ut=Log (Ct)= 1/Ct
e. g Log (3)= 1/3= 0.3333
SEE NOTES FOR MORE DETAILS
What are the implications of uncertainty for consumers?
Because of uncertainty we are now looking looking at expected utility rather than utility of expected income
-Now need to calculate expected marginal utility instead of marginal utility of expected consumption
How do you calculate expected marginal utility?
E(U’ (Ct+1)) = P x 1/Cb (t+1) + Px 1/Cg +1
e.g:
E(U’ (Ct+1)) = 0.5 x 1/2 +0.5 x 1/4 = 3/8 = 0.375
SEE NOTES FOR MORE DETAILS
What did Carrol and Samwich (1998) state about precautionary savings?
Indicate 40-45% of savings is due to precautionary savings
What is the Psychology of Instant Gratification?
That consumers are not as rational utility maximisers as previously thought. And are more likely to maximise utility immediately
Laibson’s theory and we must consider psychology of consumers
