econ 100 tutorial: week 16 [email protected] office: lums c85
TRANSCRIPT
Permanent Income Hypothesis
People will spend money at a level consistent with their expected long-term or lifetime income. When young, people generally borrow, when middle aged people pay off their loans and save for retirement, and when old, people spend what they saved.
Question 1(a)A woman thinks that her life-time earning will be as follows:Assuming that the interest rate is zero, calculate her annual permanent income.
Because the interest rate is zero, PI = sum of income each year = 35,000 + 35,000 + … + 15,000 + 15,000 = 5*35,000 + 5* 50,000 + … + 20*50,000 + 15*15,000 = 175,000 + 250,000 + 360,000 + 300,000 + 1,000,000 + 225,000 = 2,310,000
So the annual permanent income = 2,310,000/61 = $37,869
Age # yearsEarnings per
year ($)19-23 5 35,000
24-28 5 50,000
29-34 6 60,000
35-44 10 30,000
45-64 20 50,000
65-79 15 15,000
Question 1(b)Suppose at the age of 29 she wins $250,000 in the state lottery. What effect will this have on her annual permanent income?
Over the last 50 years of her life, her income is:PI = 60,000*6 + 30,000*10 + 50,000*20 + 15,000 * 15 + 250,000PI = 360,000 + 300,000 + 1,000,000 + 225,000 + 250,000 PI = 2,135,000Note: In Coskeran’s solutions he takes the permanent income in part (a) and subtracts from it the income she already earned up to age 29 and then adds on the lottery winnings.
Annual permanent income after age 29 is now 2,135,000/51 = $41,863
Age # yearsEarnings per
year ($)29-34 6 60,000
29 1 250,000
35-44 10 30,000
45-64 20 50,000
65-79 15 15,000
Permanent Income Hypothesis
In practice people don’t know exactly when they will die, so they will not consume 100% of their lifetime income. Instead they will consume a percentage of it, so they will have some left over if they outlive their life expectancy.
Question 1(b)Suppose at the age of 29 she wins $250,000 in the state lottery. In the previous slide, we calculated her Annual permanent income after age 29 as $41,863.Assuming she consumes 85% of her permanent income, what will be her marginal propensity to consume when she is 29?
Her consumption prior to age 29 was (37,869*0.85) = $32,188And at age 29, after re-assessing her annual PI, is (41,863*0.85) = $35,583
We want to find her Marginal Propensity to Consume (MPC)MPC = change in consumption/change in income.
Increase in income = 250,000MPC = (35,583 – 32,188)/250,000 = 0.01358
Question 1(c)As her career progresses, the woman realises that Her earning opportunities are greater than she had thought. From the age of 35 to 64 she now earns $65,000 a year. What is her new annual permanent income from the age of 35? In both cases, assumeshe still has her lottery winnings from (b).
Her new annual permanent income is Annual PI = (30*65,000 + 15*15,000)/45 Annual PI = (1,950,000 + 225,000)/45Annual PI = $48,333
So her annual consumption is $48,333 * .85 = $41,083 Prior to this re-assessment of her earnings, her consumption was $35,583, in part 1(b).
Age # yearsEarnings per
year ($)35-64 30 65,000
65-79 15 15,000
Age # yearsEarnings per
year ($)29-34 6 60,000
29 1 250,000
35-44 10 30,000
45-64 20 50,000
65-79 15 15,000
Question 1(c)As her career progresses, the woman realises that her earning opportunities are greater than she had thought. From the age of 35 to 64 she now earns $65,000 a year. We calculated that her new annual permanent income from the age of 35 is $48,333.What is her marginal propensity to consume at the age of 35?
MPC = Δ consumption ÷ Δ incomeSo, first, let’s calculate her annual consumption:Annual consumption is $48,333 * 0.85 = $41,083 Prior to this re-assessment of her earnings, her consumption was $35,583, in part 1(b). So the change in consumption is $41,083 - $35,583 = $5,500
Next, let’s calculate her change in income. In the year that the woman was 35, her change in income was 35,000.So, when she was 35, her MPC = 5,500/35,000 = 0.157 The effect on MPC is greater with long run change in permanent income than it is with the short-run change in permanent income.
Question 2In an attempt to boost consumer spending, a government decides to cut VAT for a year from 20% to 15%. The Opposition argue that it would be better to cut the standard rate of income tax permanently by one percentage point. According to the permanent income hypothesis and the life-cycle hypothesis, which of these policies is more likely to raise consumer spending?
Effect of cutting VAT for a year from 20% to 15%:
According to the PIH, the limited tax cut should have little impact on consumption. Households save a high proportion of the tax cut to allow for the return to higher VAT in the future. The life cycle hypothesis suggests a similar outcome as households fail to consume faced with the prospect of higher future tax. There might be a substitution effect, however, if households decide to bring forward consumption, particularly of consumer durables such as washing machines and TVs. Future consumption would fall to compensate for this rise, a possibility the government would need to bear in mind in its future fiscal policy.
Question 2In an attempt to boost consumer spending, a government decides to cut VAT for a year from 20% to 15%. The Opposition argue that it would be better to cut the standard rate of income tax permanently by one percentage point. According to the permanent income hypothesis and the life-cycle hypothesis, which of these policies is more likely to raise consumer spending?
Effect of cutting standard rate of income tax permanently by 1%:A cut in income tax would have a permanent, albeit small, effect that could cause households to raise spending based on their higher future expected disposable income. As shown in the answer to question 1, the MPC is likely to be higher from a permanent change in income than from a one-off, transitory, change in income. The reason is the distinction between temporary and permanent income. If people anticipate a rise in tax rebates or any other form of stimuli (this is true for companies as well, not just consumers) to be temporary, they will save this money instead of spend or invest it. But when they anticipate a permanent rise in income (like getting a new or better paid job) they are much more likely to spend or invest now as they anticipate a certain future stream of income. With a temporary cut or rebate, they know that next year this won't happen so they better put the money away for now.
Question 3(a)The economy can be described as follows: Y = C + I C = 0.8YP YP = 0.75Y + 0.25Y-1I = 350
What is the equilibrium income in the economy?In this question, we are focusing on the long-run equilibrium.
In the long run, we set Y to be equal in all years (that’s the PIH).So that allows us to say: Y = Y-1
Then YP = 0.75Y + 0.25Y-1 can be rewritten as:
YP = 0.75Y + 0.25Y YP = Y
So then we can re-write C as C = 0.8YAnd we can plug C an I into our equilibrium equation: Y = C + I
Y = 0.8Y + 350 0.2Y = 350 Y = 1,750
Question 3(b(I))The economy can be described as follows: Y = C + I C = 0.8YP YP = 0.75Y + 0.25Y-1I = 400
If investment rises to 400, what is the new equilibrium income?We’ll use the same steps as in part (a):
In the long run, Y = Y-1 (because of the PIH)
So, YP = 0.75Y + 0.25Y-1 = 0.75Y + 0.25Y = Y
If YP = Y, we can re-write C as C = 0.8Y Plugging into our equilibrium equation:
Y = 0.8Y + 400 0.2Y = 400 Y = 2,000
Question 3(b(II))The economy can be described as follows: Y = C + I C = 0.8YP YP = 0.75Y + 0.25Y-1I = 400
If investment rises to 400, what is the long run value of the multiplier?First we need to know the equation for the multiplier:Multiplier = Change in income / Change in investment Income changed from 1,750 to 2,000 and Investment changed from 350 to 400.
Multiplier = 250/50 Multiplier = 5
Question 3(b(III))The economy can be described as follows: Y = C + I C = 0.8YP YP = 0.75Y + 0.25Y-1I = 400
If investment rises to 400, what is the long run marginal propensity to consume?How can we find the MPC?MPC is the slope, i.e. the coefficient on Y, of our Aggregate Demand (AD) line.
In the long run, our AD line is Y= 400 + 0.8Y So, our Long-run MPC = 0.8
We found this in part (a)
Sometimes, we call it the Aggregate Expenditure (AE) line.
Question 3(b(IV))The economy can be described as follows:
Y = C + I C = 0.8YP YP = 0.75Y + 0.25Y-1I = 400If investment rises to 400, what is the short run marginal propensity to consume?We know that MPC = slope of the AD line. To find short-run MPC, we need to find the short-run AD equation.In the short run, we are only concerned with the current period Y. So, we’re going to treat Y-1 as a constant.
Y = 0.8YP + 400Y = 0.8(0.75Y + 0.25Y-1) + 400
Y = 0.6Y + 0.2Y-1 + 400
So our short-run MPC = 0.6 (that’s the coefficient on Y, or the slope of the short-run AD line).
This is our short run AD line. Note, Because we are treating Y-1as a constant, Y-1 does affect the intercept but it does not affect the slope.
Question 3(b(V))The economy can be described as follows:
Y = C + I C = 0.8YP YP = 0.75Y + 0.25Y-1 I = 400If investment rises to 400, what is the short run value of the multiplier?We know how to find the value of the multiplier.
Multiplier = 1 /(1 – MPC) So, the short-run multiplier = 1 / (1 – short-run MPC)In part (b(IV)) we found the short-run MPC = 0.6.So, Short-run multiplier = 1/(1 – (0.6) Short-run multiplier = 2.5The answers to ii) and v) show a general point that, according to this particular model, the multiplier is lower in the short-run than in the long-run.
Question 3(c)The economy can be described as follows:
Y = C + I C = 0.8YP YP = 0.75Y + 0.25Y-1I = 400If full-employment income in the economy were 2,500, what problems would a government face in trying to use fiscal policy to achieve full-employment?
As a review, lets think about how much short-term government spending would be necessary to overcome this deflationary gap.
In this case, equilibrium Y = 2000. So, the deflationary gap = 500.We already found the short-run multiplier is 2.5.We know ΔY/ ΔG = multiplier, so then ΔY/multiplier = ΔG.So our increase in G should be 500/2.5 = 200 in the short runSo to close the deflationary gap in the short run, we need an increase in government spending from 0 to 200.
Question 3(c)The economy can be described as follows:
Y = C + I C = 0.8YP YP = 0.75Y + 0.25Y-1 I = 400If full-employment income in the economy were 2,500, what problems would a government face in trying to use fiscal policy to achieve full-employment?
In this simple model, it is possible to figure out what level of G would result in Y=2500 in the long run. Can you do it? Do you get G = 100? So in the first year, G=200, but in subsequent years G falls to 100.
However, we could imagine the calculation getting even more difficult, if PI depended on more past years than just Y-1. Also, it may be politically difficult to reduce G and avoid an inflationary gap (a bubble in the economy).That is essentially what Coskeran’s answer is talking about in the next slide.
Next Week• Work through the Tutorial Worksheet• Go through any problems from David Peel’s lecture