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ec201 mt > 1.3 Expenditure minimisation > Flashcards

1.3 Expenditure minimisation Flashcards

1
Q

So what is uncompensated demand ?

A
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2
Q

Uncompensated demand depends on what.

A

It depends on prices and income

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3
Q

Show uncompensated demand on a diagram what do we fix and what do we move?

A

We fix the budget line and income, and we move the indifference curve till we get to the highest level of Utility.

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4
Q

What is compensated demand?

A
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5
Q

What is compensated demand depend on?

A

It is dependent on prices and utlitiy.

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6
Q

Show compensated demand on a diagram, what do we fix and what do we move?

A

We fix utlitiy and the indifference curve and we are trying to get on the lowest possible budget line.

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7
Q

When the price of good 1 changes, the change in uncompensated demand is??

A

captures the subsitution and income effect.

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8
Q

When the price of good 1 changes, the change in compensated demand is??

A

captures the subsitution effect.

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9
Q

What is the expenditure function and what is the formula?

A
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10
Q

How does the expenditure function look on the diagram for compensated as opposed to expenditure function for uncompensated demand

A

to get the axes you would just divide compensate demand of the goods by their prices to get the axes.

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11
Q

What are some properties of the Expenditure function?

A

1) Increasing in Utility
2) Homogeneous of degree 1 in prices
3) Shepard’s lemma.

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12
Q

What does the property increasing in utility mean?

A

It costs more to get higher utility

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13
Q

What does the property Shepherds lemma mean?

A

If you partially differientate the expenditure function in respect to p1 and p2, you should the compensate demand for h1 and h2

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14
Q

Mainly how do we calculate compensated demand?

A

Its very similar to how we find compensated demand

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15
Q

Now lets do an example, what is step 1?

A
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16
Q

Now do steps 2 and 3 for this example of CB

A
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17
Q

What is the property .

Non-decreasing in price mean when looking at the cobb douglas compensated demands?

A

The relative price makes sense, e.g. if the price of my own good goes up, i consume less and if the price of the other good goes up, i consume more of my good.

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18
Q

How would we draw this compensated demand curve for Cobb douglas? ( HINT, first rearrange compensate demand for h1 to find in terms of p1)

A
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19
Q

What are the 3 steps again to find out Compensated demand?

A
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20
Q

Now draw the compensated demand curve for good 1 and tell me the properties of it?

A

Compensated demand can never slope upwards( in general giffen goods slope upwards( these are inferior goods, but not all inferior goods have an upward sloping demand curve, only giffen goods.

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21
Q

Workout the expenditure function for the cobb douglas example?

A

Its always p1 and p2 that have be timzed by h1 and h2 outside the bracket, and the power of p1 refers to the power of x1 and vice versa.
In the square bracket the compensated demand is the fractions are such that of h1 and h2 and the same brackets, with u outside.

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22
Q

What is the answer and how do we analyse this?

A

The answer is C, we need to understand better what is happening in the income and subsitution effects.

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23
Q

Lets say good 1 is sushi and good 2 is sandwiches and the price of good 1 increases, lets say the budget is as follows p1x1 + p2x2 = m, illustrate this on a diagram, show the change in uncompensated demand, and what happens to the budget line( show the gradients)

A
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24
Q

To decompose a subsitution and income effect, what do we do?

A

We draw a fake budget line from the original budget line and go up until it is tangent towards the original indifference curve.

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25
Q

Analyse the subsitution and income effect, assuming the 2 goods are normal goods?

A

The subsistution effect ( movement from A to B): Sushi is relatively more expensive, which causes the student to substitute away from sushi towards
sandwiches.
The income effect( movement from B to C) the purchasing power of consumer has fallen due to the fact that income has fallen, hence as both goods are normal goods, the consumption of both goods fall

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26
Q

What are the overall effects of the subsitution and income effects, is the answer clear for both goods, if not what do we need to have for it to be clear?

A

1) overall the effects are reinforcing each other for sushi ( as prices of sushi goes up, the consumer consumes less for 2 reasons 1) sushi is expensive, so subistutes away 2) the consumer feels poorer, so buys less sushi anyway. ( for sure overall effect is less sushi)
2) for sandwiches we don’t know, the substation effect says you buy more sandwiches but the income effect says you buy less sandwiches, so the effect is unknown.
Its best to draw the point C parallel and mention ambiguity

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27
Q

Now thinking about our pole why was C correct and is C always the case?

A

Because of the (negative) substitution effect, you consume a bundle which is on the same IC but not the same bundle, as you change your consumption patterns.
C isn’t always the case, as if the subsitution effect was 0 then you would need exactly £100 ( perfect complements)

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28
Q

For quasi linear preferences, if x1 was the good being proritised and there was an increase price of p1 ( we are assuming an interior solution, so income is enough), which affects always dominates ?

A

Subsitution effects always dominates, as there is no income effect for good 1.

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29
Q

Show the Poll question on the diagram

1) explain why you wouldn’t need to give the full £100

A

The green line represents the amount of money to consume the same bundle, which is £100, but we don’t need to give this £100, to be as well off as b4.

30
Q

With good 1 being an inferior good and good 2 being a normal good, when price rise for good 1 AND FALLS what is the overall effect summarise?

A

When price rise for good 1 : The SE> IE( OVERALL YOU BUY LESS OF GOOD 1.)
For good 2 IE>SE meaning overall you buy less of good 2

When price falls for good 1: The SE>IE ( Overall you buy more of good 1) For good 2 IE>SE meaning overall you buy more of good 2.

31
Q

Show the income and subsitution effect of an inferior good lets say good 1 is an inferior good and good 2 is a normal good show the effect and the price rises for good 1

A

The income effect for sushi is positive as opposed to negative if it was a normal good.
The effect is ambigious we cant tell which one dominates.
( overall there is a fall in sushi consumption)

32
Q

Decompose the overall effect when good 1 is inferior and good 2 is a normal good, and the price of good 1 goes up using SE AND IE
Label diagram and Show subsitution and income effect mathematically. Talk about both effects.

A

For inferior goods subsitution effect always dominates income effect for inferior goods in absolute terms.
For good 2 the income effect dominates the substitution effect

33
Q

Decompose the overall effect when good 1 is inferior and good 2 is a normal good, and the price of good 1 goes down using SE AND IE
Label diagram and Show subsitution and income effect mathematically. Talk about both effects. ( HINT THE SIGNS OF THE OF IE AND SE CHANGE FROM WHEN THE PRICE WENT UP)

A

For good 2 the income effect dominates subsitution effect.

34
Q

What is true about Giffen goods if good 1 is the giffen good and prices rise and falls and what which effect dominates for good 2.

A

• Giffen good: if the income effect outweighs the substitution effect
If price rise : you buy overall more of good 1, IE > SE FOR GOOD 2 ( OVERALL YOU BUY LESS OF GOOD 2)
If price falls : you buy overall less of good 2, IE> SE FOR GOOD 2 ( OVERALL YOU BUY MORE OF GOOD 2

35
Q

Decompose the overall effect when good 1 is a giffen good and good 2 is a normal good, and the price of good 1 rises using SE AND IE
Label diagram and Show subsitution and income effect mathematically. Talk about both effects. ( HINT THE SIGNS OF THE OF IE AND SE CHANGE FROM WHEN THE PRICE WENT UP)

A

For good 2 overall you buy less of good 2 as IE> SE

36
Q

Decompose the overall effect when good 1 is giffenand good 2 is a normal good, and the price of good 1 goes down using SE AND IE
Label diagram and Show subsitution and income effect mathematically. Talk about both effects. ( HINT THE SIGNS OF THE OF IE AND SE CHANGE FROM WHEN THE PRICE WENT UP)

A

For good 2 the iE>SE, SO OVERALL YOU BUY MORE OF GOOD 2.

37
Q 
In the UK, people over 80 years old who
live alone receive a £300 Winter Fuel
Allowance
When fuel prices rise, you advise the
government to adjust the allowance in
order to leave the elderly as well off as
before.
Does this mean they will be as warm as
before?
A. Probably as warm
B. Probably less warm
C. I don’t know
A

The answer is B. as if prices rise you don’t substitute to consume more fuel( positive subsitution affect doesn’t exist.

38
Q

We know that the subistuiton and income effects can go in different directions or reinforce each other, and it is important to evaluate the direction and magnitude of the effects to design policy. What do we need to do this?

A

The slutsky equation.

39
Q

What is the slutsky equation and what does it tell us?

A

Slutsky equation shows us how big income and substitute effects are.

40
Q

What is the stusky equation with elasticities, what does it tell us for good 1?tell us the different proportions of the equation using sushi example?

A

Slutsky equation shows us how big income and substitute effects are. Combined with
elasticity estimates it tells us that income effects are too small to bother with except for
goods that are a large proportion of the budge
1) first part =PED OF demand for sushi for uncompensated demand.
2)second part = pED of compensated demand for sushi.
3) income elasticity of demand for sushi
4) Budget share( proportion of income spent on good 1)

41
Q

For Sushi are people income sensitive and is the budget share big?

A

No income effects are small( some income insensitive ) and its budget share is small( proportion of income spent on good 1), hence for the slustksy equation with elastiticites it will be quite small. Hence income effects are small.

42
Q

What does income sensitive mean?

A

We respond a lot to consumption of that good when income changes.

43
Q

Give an example of a good that is income sensitive and forms a large proportion of our income, hence income effect is big?

A

Housing

44
Q

When are income effects small for the slutsky equation

A

• Income effects are small if the income elasticity or the budget share are small

45
Q

Lets analyse slutsky equation further, lets look at the PED for sushi for uncompensated demand? if the price of sushi goes up what is the PED of uncompensated demand for normal good, inferior good and Giffen good ( its opposite if prices go down for sushi)

A

generally demand curves are downward sloping so we can infer here at for a normal good its negative ( price goes up you buy less of sushi.
If sushi was an inferior good and price goes up the pED is negative and for a giffen good it is Positive( when price goes up i buy more of the good)

46
Q

Lets analyse the slutsky equation further, when the price of sushi goes up, what is the PED for compensated demand. ( subsitution effect) when the good is a normal, inferior or giffen good?

A

All cases its negative or 0 ( if prices of go up you don’t buy more of the expensive good), here when its 0 these are PC’s ( so you don’t do anything if prices go up).

47
Q

Lets look at income elasticity of uncompensated demand, look at the case if sushi was a normal good, inferior or giffen good, what happens when income increases?

A

1) Normal good - positive ( more income buy more of the good
2) Inferior good - negative ( more income you buy more of the good.
3) Giffen good - negative ( remember giffen goods are low income goods so you don’t buy more)

48
Q

What is the budget share( proportion of income spent on good 1) of sushi for if it was Normal, inferior and giffen?

A

All positive

49
Q

What degree of homoegenoutiy do compensate demand functions have, show mathematically and diagramtically?

A

Compensated demand is homogeneous

of degree 0 in prices ( for uncompensated it was in prices and income)

50
Q

What does the property mean its homogeneous to degree 1 in prices

A
51
Q
A

B is correct
D is correct ( corner solution here)
E is correct

52
Q

A. The uncompensated demand curve can never slope upwards
B. The uncompensated demand curve can never slope upwards for a normal good
C. The compensated demand curve can never slope upwards
D. The uncompensated demand curve must always slope upwards for an inferior good.
Which of the following are TRUE?

A

B ( the income and substation effect will reinforce each other moving in the same direction)
C ( compensated demand captures the subsitution effect, which can only be negative or 0, not positive

Wrong answers
A) giffen goods can have an upward sloping demand curve
D) False While giffen goods are inferior not all inferior goods are giffen. it says must always.

53
Q

What is key when calculating compensated demand as opposed to uncompensated demands?

A

We use the utlitiy function and mrs=p1/p2 to find the 2 unknowns ( whereas with uncompensated we used the budget constraint and

54
Q

Find the compensated demands for this function, draw the graphs, and say what the mrs is fall both and find the expenditure function for both. part 1)

A
55
Q

Find the compensated demands for this function, draw the graphs, and say what the mrs is fall both and find the expenditure function for both. part 2

A
56
Q

Show the expenditure function for the interior solution?

A
57
Q

How would we draw the compensated demand curve for this quasi linear example?

A

1) Same thing rearrange compensated demand for h1
2) the demand curve is downwards sloping ( as h1 goes up p1 goes down vice versa).
The demand curve is constant after then it gets to corner solution why?

58
Q

What do we find when income is large enough for the quasi linear example and in uncompensated and compensated demand?

A

They are the same.

59
Q

What does it mean also that they are the same when income is high income?

A

The same as no income effect on demand for good 1 if not a corner! ( there is an income effect if at corner)

60
Q

Show that income effect is 0 at if not at corner and substation effect is negative if not at corner? ( hint use deratives?

A
61
Q

Show no income effect for quasi linear but preferences in good 1 ( draw diagram showing this, no need for maths)

A
62
Q

Find solutions compensated demand solutions for this ( HINT 3 CASES)

A
63
Q

Now draw the compensated demand curve for this example ( HINT the diagram has to show 3 cases), also show expenditure function for each case)

A

1) rearrange to find p1. p1/p2 = 3/2, hence p1=3/2p2.

64
Q

Quickly what is a key result from slutsky equation?

A

• Key result from the Slutsky equation: the income effect is small if the
budget share is small!

65
Q

Whenever there are fractions when solving compensated demand what should you do?

A

You should mutiply by the denominator to get rid of them.

66
Q

Also find h1 and h2 when there is a corner solution

A
67
Q

PROBLEM SET

A

Compensated demand = demand of a consumer over a bundle of goods that minimises their expenditure while delivering a fixed level of utiliy.
Expenditure function = minimum amount of expenditure that needs to be spent to get fixed level of utility.

68
Q

PROBLEM SET

A
69
Q

PROBLEM SET

A
70
Q

Remember label everything

A
71
Q

And BTW how would the demand curve look?

A

Vertical for good 1

72
Q

Just to remember the expenditure function is homegeonous to what and the compensated demand functions is homeogeonus to what?

A

Expenditure function = homogeneous to degree 1 in prices

Compensated demand functions is homogeneous to degree 0 in prices.

ec201 mt (11 decks)

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