1.4 Price change and Welfare Flashcards
From 1.1-1.3 what have we explored?
In 1.1 - 1.3 we explored how to find uncompensated demand, compensated
demand and the expenditure function
What will we do today?
examine the welfare effects of price changes
What are price indices?
A price index is a number whose movement reflects movement in the average level of prices
In the economy we know prices are changing at different weights so what do we want?
we want a weighted average of price changes, due to this votality of price. This will be a price index
What are the different price indicies in the uk?
CPI ( now the standard)
CPIH ( Consumer price index including owner occupiers housing costs)
RPI ( retail price index)
What is CPI?
Measures the change in the cost of a representative basket of goods and services bought by households
• Interpreted as a measure of how the cost of the standard of living is changing.
Official inflation target is 2%
Compares baskets quarterly, annually.
What is Consumer Prices Index including owner occupiers’ housing costs (CPIH)
Extends CPI to include a measure of the costs associated with owning, maintaining and living in one’s own home.
• OOH costs and Council Tax are significant expenses for many households
What is CPI an example of?
A base weighted index. ( It has a base year, were we draw comparisons from.
Define a base-weighted price index
A weighted average of prices or quantities, where the weights used are the quantities or the prices of the base period.
We are going to show the base weighted price index mathematically?
How do we show a representative consumer basket of n goods at date A and prices of the goods at date A.
Now show the mathematically representation of the prices when we look a year late and then show the base weighted price index?
Its essentiallty prices of same bundle at later date/prices of bundle at earlier date.
We are assuming the bundle is fixed, we are going focusing on prices.
What are some critiques of CPI?
1) The CPI does not take into account the real possibility that consumers would substitute among commodities because of changes in relative prices (cheaper product you buy more) . Substitution bias. Hence it overstates the inflation rate.
2) No representative consumer, there are different segments of consumer reflecting different basket of goods.
If income changes in line with the base weighted price index, then: A. Consumers are neither better off nor worse off B. Consumers cannot be worse off, but may be better off C. Consumers cannot be better off, but may be worse off D. Consumers will definitely be better off
B
If income changes in line with the base weighted price index, then: A. Consumers are neither better off nor worse off B. Consumers cannot be worse off, but may be better off C. Consumers cannot be better off, but may be worse off D. Consumers will definitely be better off
We are going to analyse why b is the answer. So suppose there are 2 goods, how does the CPI base weighted price index look like?
If income changes in line with the base weighted price index, then: A. Consumers are neither better off nor worse off B. Consumers cannot be worse off, but may be better off C. Consumers cannot be better off, but may be worse off D. Consumers will definitely be better off
We are going to analyse why b is the answer. Now show the prices and bundle consumers pick before changes in price and after price change and the utlitiy they get?
What does it mean if income changes at the same rate as the base weighted priced index
This means you can afford the original basket but wil lyou prefer the original basket?
It depends on what happens to prices individually( relative prices, subsistution effect) so the bundle is affordable but not optimal.
Now what is subsitution bias?
if consumers change their purchasing behavior in response to relative price changes. (• If relative prices p1/p2(increase in price of good 1 > increase in price of good 2) change and substitution is possible then the
consumer is better off!)
If income increases at the same rate as the base weighted price index
then the consumer cannot be worse off
To show why a consumer cannot be worse off if income changes at the same rate as the base weighted price index, draw the original budget line and graph and show optimal point?
1) Construct the budget line, with 2 goods?
PART 2) To show why a consumer cannot be worse off if income changes at the same rate as the base weighted price index,
Now suppose prices change but also income at the same rate so P1bX1a + P2bX2a =m. Lets imagine the price of good 1 rose higher than good 2 e.g. good 1 is fuel and it rose by 4% and good 2 rose by 2% but average so CPI went up by 3% , and income goes up by 3%. Show what happens to budget line. What what does it show about being worse off?
The budget line becomes steeper as prices of both goods have increased ( become steeper).
It still goes through bundle A because you can still afford (x1A,x2A). Thus cannot be worseoff.
Will the consumer pick bundle A, if he/she income rises at the same ratio as CPI (3%) increases, and he negotiates a 3% increase at work?
Draw where optimal consumption would be and explain what it shows about CPI?
This will show for individuals, CPI basket of goods are not constant, here substation effects causes you to buy the cheaper thing (x2). Thus as we saw last week to get same utility, your overall inflation is <3% but CPI overstate it to 3%.( due to subsitution effects because of changes in relative price, CPI is an overestimate, as the bundle of goods are fixed, but actually they change)
Are consumers always better off when there is an iincrease in income in line with an increase in CPI? ( remember relative prices change, 1 is the same as the other)
No is the answer, it depends whether or not there is a subsitution effect of not. so perfect complements there will be no change in allocation.
If PC if income rises higher than CPI or just rises, then they will be better off.
What happens if prices rise ( e.g. good 1 and 2 rise by 3% at the same rate as income so 3%?
The budget line stats the same, this is because it is homogeneous to degree 0
or
The BL intercepts are m/p1 and m/p2 so an increase in both as no change BlA = BLb ( consumers are no better off or worse off)
So in summary we line wages, income etc to inflation to get away from harmful effects of inflation ( CPI increases) but whats the problem of this use the example previously?
Subsitution bias can make people better off e.g. if you give a rise in income, to someone who experiences a relative price change with 3% overall( price changes different for the 2 goods,) they might substitute away and be better off. THUS THERE IS OVER COMPENSATION.
Suppose you wanted to compensate the person for inflation ( CPI increases), but not over compensate them ( make them as well off as before, but go on a higher indifference curve– so less money), how would we do this?
By using something called the expenditure function price index.
What is the expenditure function E(p1,p2,u) again?
is the minimum amount of money you have to spend to get utility u with prices p1 and p2.
How would the expenditure function price index work and show the mathematically representation of it?
So you keep utility constant and find the minimum expenditure of achieving that utility b4 and after the price change. e.g. if the minimum expenditure needed UA in august 2020 was 100, then the minimum expenditure needed to get UA in 2021 is £102, thats a 2% rise and thats exactly how much extra money you have to give to compensate them, keeping utlity constant.
How would we show the expenditure function price index on a diagram? Does the budget line go through bundle A?
1) The new budget line doesn’t go through bundle A, as we are not trying to compensate the individual through bundle A.
2) We have IC of an individual Ua, we know prices initially and we are trying to minimise the cost of achieving UA, so we get bundle A.
3) Relative prices change ( e.g. good 1 increases by 4% and good 2 2% so overall =3% cpi), now we find what is the minimum to achieve UA now. We find new bundle C.
4) The ratio of the y intercepts is the expenditure price index
What would it mean if income was to go up at the same rate as the expenditure function price index and compare with CPI?
Then people will be as well off as before and after inflation. But you wouldn’t be overcompensating or undercompensating them. If this happens with CPI the consumer is possibly better off.( subsitution bias)
Now put it all together the base weighted price index vs expenditure function price index. If price rises e.g. good 1 rises by 4% and good 2 rises by 2% so cpi average increase is 3% and you compensate them with CPI giving 3% increase in income but with Expenditure function price index you compensate using the exact amount of the proportion using the expenditure function show that on a graph?
1) August 2020 we are at bundle A, if we compensate people at original bundle, they subisutute and go to a higher IC with utility Ub
2) . If we the expenditure price index, the consumer is at bundle c ( less money
What are problems with the expenditure function price index ( BTW this is not a real thing)?
1) Requires knowledge of the expenditure function( we need to know preferences.)
2) The expenditure function is derived from a utility function ( what is a representative utility function of society.)
EXAM QUESTION Margaret’s consumption reflects the weights of the Consumer Price Index (CPI). If the inflation rate is 3% (as measured by the CPI) and Margaret’s income increases by 3%, can she ever be worse off? What determines if she will be better off?
You can draw a diagram
1) Margaret’s consumption is exactly the one used to compute the CPI so she is still able to afford her initial consumption bundle if she receives an income increase of 3%. As the original bundle she was consuming is still available to her, she can never be worse off.
She might be better off if not all items in the basket considered have a higher price (so relative price changes) and she can substitute to cheaper goods (substitution bias)
(c) Alex lives in London and has unusual tastes in consumer goods. His income increases by 3%, in line with the Consumer Price Index. Could he be worse off?
Alex can be worse off. He may not be consuming the same goods as those considered in the computation for the CPI. This means that while his income increases in line with the CPI, his previous bundle of consumption might have a much higher price now and he may not be able to afford it. If this is the case Alex will be worse off even though he now earns more. Because we don’t know anything about those prices we cannot determine whether he will be better off, equally well off or worse off.
Lets look at consumer surplus first, do 2 things 1) show on an indifference map an increase in price of good 1 from p1a to p1b ( just showing the overall change 2) translate this on an uncompensated demand curve diagram? ASSUME BOTH GOODS ARE NORMAL GOODS. Explain both diagrams and what happens when you move long the demand curve. Where is the CS?
1) Indifference map: originally consumer optimises his ultiity given prices and income, but then price of good 1 increases so the budget line pivots inwards, meaning we cant afford same bundle. As both goods are normal we buy less of both goods overall, so we get lower levels of utlitiy.
2) Bundle B represents a higher price and lower quantity and different utlitiy level. in relation to A involves a higher quantity and a lower price, hence we can translate this to the demand curve.
3) As we move along the uncompensated demand curve the utlitiy is changing ( Bundle A has a higher utlity than B)
Consumer surplus is the blue area.
How would we show CV on a indifference map diagram? So lets say the price increases from p1A to P1B for good 1? what is the movement from A. to B the subsitution effect, there is a change in compensated demand.
1) Price increases from P1A to p1b, thus budget line pivots inwards, leading to point B,( lower utility)
2) The consumer then needs to get income added back to push them back to the original level of utility, so we draw a parallel line or increase income line till it is tangent to the original indifference curve, as we know we have compensated them. ( IT doesn’t go through A) the consumer will end up at B.
What are are the intercepts? and how does this give us an estimate of EV.
1) The intercept of the original budget line is the minimum expenditure needed to achieve utility uA ( expenditure function)/p2 as its quantities .
2) The intercept of new compensated budget line is the minimum expenditure needed to achieve uA at the new prices/p2 as its quantities.
The difference in the y axis is the compensated variation CV/p2
so E( p1b,p2b,ub)-E(p1a,p2a,ua)
Recall the shephards lemma and use the fact to find out what happens when we integrate?
1) If we partially differentiate the expenditure function with respect to price of good 1 we can get the the compensated demand for h1.
2) If we integrate the h1 function across 2 price limits p1A and p1B, you get the difference of the 2 y intercepts which is the compensating variation.
Now show compensated demand on a demand curve for good 1?
1) Bundle B represents a higher price and less quantity but same utility, so we illustrate that in respect to A, the key here is that the utlitiy is not changing here on the compensated demand curve.
How do you draw EV on an indifference diagram?
1) We are at bundle A with utility UA, the prices of good 1 rises, budget line pivots inwards, thus the consumer reoptimises at bundle B, and achieves utility UB.
2) Now we would have to show an income reduction that would have been as bad as a price increase.
3) so you do a parallel shift from the original budget line until you get tangent to the new indifference curve and you get bundle C.
4) B to C represents the change in compensated demand along the utility curve
What are the y intercepts
The higher intercept is the minimum expenditure needed to achieve UB at new prices
The lower intercept is the minimum expenditure needed to achieve THE same utility but at original prices.
The gab between these is EV/P2 so times by P2 and you get EV ( change in income that would be as bad as a price change.
Draw the EV on a demand diagram?
Remember its in relationship to that?
B and C not A
First of all draw CV AND EV on an indifference map and explain it again, assuming prices went up for good 1 and it is CB preferences.
1) Price increase for good 1, budget line pivots in and we get to a new bundle point C, which is a higher price and lower quantity bundle with a lower utility.
2) We want to compensate the consumer back to his original utility, but not make him better off or worse off, so draw a fake budget line up the original indifference curve to a new bundle B parallel to C.
3) Now with EV, we want to calculate the amount of money we have to take away that would be as bad as a tax. ( from the original budget line, draw a fake budget line downwards until its tangent to the new indifference curve to get bundle D, which is parallel to A.
Now how would we illustrate this on a demand curve for good 1 when the price increases for good 1 ( both goods are normal goods)
1) We can identify the original bundle A and quantity x1A on the RHS
2) Price goes up and consumer goes to bundle C, we can identify this on demand curve( C is higher price, less Qd) Now connect the uncompensated demand dots. Utility is changing on this line. near the 2 prices on the y axis we can put letters assigned E and F and we can find CS on demand curve ECAF. ( WE READ FROM TOP RIGHT TO LEFT DOWN)
3) With compensating variation on the indifference curve, it is a parallel shift upwards until it touches the original indifference curve, which is B, with a parallel shift from C to B, its just a horizontal movement in the demand curve diagram and but we only focus on were b is in relation C in terms of quantities, B is on the right ( higher quantity so we show that on demand diagram. Now B is on the same indifference curve as A so we can join that line together to get compensated demand. We can highlight the CV now on the demand curve it is EBAF
4) Also notice the uncompensated line is more elastic than the compensated,( there is a greater reduction in the uncompensated demand for x1 than there is the compensated demand).
5) NOW with EV the reduction in income downwards from original BL to a new budget line which is tangent to the new indifference curve, allocates a new bundle D. D is parallel to A, so this is a horizontal to A on the demand curve. We only need to look at quantities and it is on the left to A. so we show on the demand diagram, it is before B tho in terms of quantities so make that clear on the diagram. As C and D are on the same indifference curve, we can highlight a compensated demand, which obvi is still less elastic than uncompensated demand curve. Now EV is ECDF.
We see that CV>CHANGE IN CV>EV FOR NORMAL GOODS
Explain why the uncompensated demand curve is more elastic than the compensated demand curve?
The uncompensated demand captures the subsitution and income effect, whereas the compensated demand curve captures the substation effect so the reduction in quantity is smaller here.
Show a rise in price for an inferior good( fall in income you consume more of the good) ( good 1) on a diagram and explain it using subsitution and income effect Good 2 is a normal good? What effect dominates?
1)Originally we are at bundle A, increase in price of good 1, means budget line pivots inwards, we don’t allocate bundle C yet.
2) To show SUB AND INCOME effect, we draw a dashed budget line parallel from new budget line up to original indifference curve then we indicate point B. the movement from A to B is the subsitution effect.
3) Now as good 1 is an inferior good, we are going to be on the right of B. also Good B is a normal good so consumption for good 2 falls too, which is less than what we were consuming at A.
4) so point C, will be inbetween A and B but beneath A.
Overall the subsitution effect > income effect if not point ( IC>SC) C would to the right of A( Giffen good )
First of all draw CV AND EV on an indifference map and explain it again, assuming prices went up for good 1 for an inferior good.
1) Originally at bundle A, prices rise, budget line pivots inwards and we go to bundle C as good 1 is an inferior good remember its in b4 A and below A , as good 2 is a normal good.
2) To compensate the consumer, we will give them income just enough so they are on the same utility as before to get bundle B.
3) For EV, we need to now reduce income from original BL till its tangent to new IC to get bundle D.
Now how would we illustrate this on a demand curve for good 1 when the price increases for good 1 and good 1 is an inferior good and good 2 a normal good.
1) We can identify bundle A on the right hand side of the diagram
2) Prices for good 1 increase, so budget line pivots inwards and we arrive at another bundle C, which is a uncompensated demand shift ( we explained this in the last flashcard why its there), C constitutes to a lower quantity and higher price, so we show this on the demand curve. We can connect C and A which gives the uncompensated demand. We can also Find Consumer surplus. If we Give E to price P1B and F to P1A. Consumer surplus is ECAF ( captures the compensated and uncompensated demand)
3) For CV, we want to add income to compensate them back to the original utility, so this is a parallel shift from original indifference curve from C upwards and we get bundle B. On the demand diagram B to C is a parallel shift, so its horizontal and B is on the left of C. As B and A are on the same indifference curve we can connect the compensated demand up which is more elastic than uncompensated demand. CV = EBAF
4) For EV, we want to reduce income which is as bad a price change, so have a fake budget line going down until its parallel to the NEW IC. We get to bundle D ( on the right of C). D is a parallel shift from A, so this is horizontal on the demand curve and D is on the right of A. As C and D are on the same iC we can join the 2 dots together to get compensated demand at utilty ub. EV = ECDF.
EV > CHANGE IN CS> CV
Why is the COMPENSATED DEMAND CURVES ELASTIC THAN THE UNCOMPENSATED DEMAND CURVE?
The uncompensated demand reduction in x1 is much smaller than the reduction in x1 from a negative subsitution effect from compensated demand.
Draw a diagram when good 1 is a giffen good and good 2 is a normal good and the price of good 1 increases? ( remember income effect > substitution effect. ( EXPLAIN THIS )
The key thing is that the substitution effect on demand for good 1 (consume less of good 1 because it is relatively more expensive) is outweighed by the income effect in the opposite direction (consume more of good 1 because you feel poorer). This means that the total effect involves an increase in consumption of good 1 and the uncompensated demand curve for good 1 slopes upwards ( for an inferior good it doesn’t outweigh, so still slopes downwards)
First of all draw CV AND EV on an indifference map and explain it again, assuming prices went up for good 1 for a giffen good?
1) Originally at bundle A, prices rise, budget line pivots inwards and we go to bundle C as good 1 is a giffen good, c is on the on the right of A below A.
2) We need to compensate the consumer for this price rise, so therefore, we add income up to where the fake budget line tangent to the original indifference curve to get bundle b.
3) With EV, we need to reduce income, which is equivalent to the price change, so we reduce income, until it is tangent to the new indifference curve and we get point D, which is further to the righf than C.
Now how would we illustrate this on a demand curve for good 1 when the price increases for good 1 and good 1 is a giffen good and good 2 a normal good. find out what bigger EV CV and what would it be if the price fell.
ADD TO THE DIAGRAM E AND F
1) Original bundle A and quantity, we can identify this on the RHS. As prices rise for good 1, the budget line pivots inwards and we arrive at another bundle C( parallel to B), we can show this on demand curve, C ( REMEMBER GIFFEN GOOD, so there is an increase in quantity hence price must be higher) We can join And C together to get uncompensated demand that slopes upwards. The CS is ECAF.
2) Now we want to compensate consumers, so we add income from new budget to the original indifference curve, to get bundle B. B is parallel to C and is on the left of C, so on the demand curve it is horizontal but to the left of . As B and A are on the same IC we can join them up to get compensated demand at UA. The CV = EBAF.
3) For EV we want to take away income which is( so parallel shift from original budget line (A) ) down to when its tangent to new IC) so get to bundle D. D is parallel to A, so its horizontal on the demand curve but its on the right of A, and the quantity is higher than C. As D and C are on the same IC we can join the dots to get compensated demand for that UB. EV = ECDF.
So EV> CHANGE IN CS> CV it would be the other way round if prices decreased.
When we have quasi linear preferences and income is enough ( so we have interior solution Show EV, CV and CS on a diagram ( explain in your head)
CV = EV = CHANGE IN CONSUMER SURPLUS, AS THERE IS NO INCOME EFFECT. ( WHEN THE INCOME ELASTICITY OF THE UNCOMPENSATED DEMAND =0, THE INCOME EFFECT OF PRICE CHANGE = 0.
REMEMEBER THERE IS AN INCOME EFFECT ( IF WE ARE AT THE CORNER SOLUTION)
Explain intuitively why CV = EV when there is no income effect.
What do we use when income effects are small and large
Show the effect of an excise tax on good 1 that raises price from P1A to PLA + t where t is the tax, assuming both goods are normal goods. Then compute EV.
What is the budget constraint btw for bundle b and gradient of the new budget line?
EV ( how much income reduction would be equivalent to this tax decrease, you take the original budget line and shift it down until it touches the indifference curve of lower utility is, and we get bundle C.
(p1A + T)x1b + p2x2B = m
Now how do we show the revenue raised from tax?
We draw a line going bundle B with same gradient as original budget line through the new bundle.
The higher intercept going through bundle A tells us the income needed to purchase bundle A.
The line going through bundle b tells us the income i would have needed at the original prices to purchase the new bundle ( as you can see less money is needed) the money went to the government. so revenue is r/p2 ( remember we want q)
What can we say about the revenue raised by the government in comparison to EV( what is EV)?
The revenue gained is less than EV ( the revenue raised isn’t enough to cover the loss of the consumer( EV is a financial measure telling us the cost of the consumer in monetary terms
The gap between EV- R/p2 = excess burden of tax EB/p2
What is the best way for the government to raise revenue? AND WHAT ARE DRAW BACKS OF IT
Lump sum tax ( not on the product, just takeaway income, meaning no subsitution effect.)
With lump sum taxes the loss to the consumer measured by the
equivalent variation is equal to the tax revenue, i.e. there is no
deadweight loss to taxation.
With taxes that are not lump sum there is a deadweight loss unless
the two goods are perfect complements.
But for the tax to be lump sum it would have to unaffected by any
decisions the consumer makes, which in practice means that it would
be the same for each consumer. This is politically infeasible in many
countries, and in the judgement of most people ethically unacceptable.
What is a lump sum tax, if the government replaces the excise tax by a lump sum tax which raises the same revenue as the exicse tax is the consumer better or worse off?
A tax is lump sum if nothing the consumer does can change the amount paid. The effect of a lump sum tax is to shift the orgiinal budget line down to the parallel dashed budget line. Point B is chosen with excise tax is still feasible so the consumers cannot be worse off, the consumer is better off and will be at bundle D if substitution is possible.
