EC201 LT

Question 1

Marshal’s consumer surplus

Answer 1

The most you would be willing to pay for good x if is no good x is the value of good x

Consumer surplus is value - cost

Consumer surplus is the difference between what consumer would have been prepared to pay compared to what they actually payed

Question 2

Completeness

Answer 2

Completeness - If a consumer is choosing between two bundles A and B one of the following possibilities holds: she prefers A to B or B to A or is indifferent

Can rank any two possibilities
U(X1A, X2A) > U(X1B, X2B) - prefers bundle A
U(X1A, X2A) < U(X1B, X2B) - prefers bundle B
U(X1A, X2A) = U(X1B, X2B) - indifferent (A and B equally attractive)

Question 3

Transitivity

Answer 3

If A is preferred to B and B to C then A is preferred to C

U(X1A, X2A) > U(X1B, X2B) and,
U(X1B, X2B) > U(X1C, X2C) then,
U(X1A, X2A) > U(X1C, X2C)

Question 4

Continuity

Answer 4

If A is preferred to B and C is close to B, then A is preferred to C

Question 5

Nonsatiation

Answer 5

More is better, Increasing consumption of goods increases utility -> implies that indifference curves slope downwards, points above indifference curve give higher utility than points on or below
If du/dx1 > 0 and du/dx2 > 0 then increasing x1 and or x2 increases utility. The indifference curve slopes downwards, the preferred set is above the indifference curve and nonsatiation is satisfied
Nonsatiation requires if X1B > X1A then U(X1B, X2A) is preferred to U(X1A, X2A)
Nonsatiation implies that points above an indifference curve are preferred to points on the indifference curve. These points are the preferred set

Question 6

Convexity

Answer 6

Any straight line joining two points lies inside the set/lies entirely on or above the graph, increasing first derivatives with positive second derivatives

Convex functions are functions with increasing first derivatives and positive second derivatives

The assumption of diminishing MRS is equivalent to the assumption that all combinations of x and y a preferred or indifferent to a particular combination of x,y for a convex set

If indifference curves are convex (if they obey the assumption of diminishing MRS), then the line joining any two points that are indifferent will contain point preferred to either of the initial combinations. Intuitively, balanced bundle of goods are preferred to extreme bundles

Mathematically a set is convex if any straight line joining two points in the set lies in the set

Question 7

Can indifference curves cross?

Answer 7

No because if u(a) = u(b) and u(b) = u(c), transitivity implies that a and c are indifferent but nonsatiation implies that a had higher utility than c

Question 8

MRS

Answer 8

Amount of good 1 given up, amount of extra good 2 needed to get back to the same u

Rate at which the consumer would be willing to give up one good for the other while maintaining the same level of utility

Question 9

Ordinal Utility

Answer 9

The order of number attached to indifference curves does not change

Relative utility ranking/utility of two bible

Any transformation that preserves the ordering will give the same ordering of utility
(can multiple by a positive number, take it at a power of a positive number, take logs)

Question 10

What is a utility function?

Answer 10

A utility function assigns a number to bundles then, to compares to bundles, it suffices to check which gives high utility

Question 11

Definition of uncompensated demand

Answer 11

The consumer’s demand functions x1(p1,p2,m) maximise utility u(x1,x2) subject to the budget constraint p1x1 + p2x2 <= m and non negativity constraints x1>=0, x2>=0

To get uncompensated demand, fix income and prices which fixes the budget line. Get onto highest possible indifference curve

Uncompensated demand is a function of prices and income

Question 12

Homogeneity of uncompensated demand

Answer 12

All uncompensated demand functions are homogeneous of degree 0 in prices and income
E.g. what happens to uncompensated demand when prices and income are all multiplied by 2? Demand does not change, the values of x1 and x2 do not change when p1,p2 and m are all multiplied by t>0 (draw diagram and show budget line/budget set doesn’t change)

Demand curves: if p1 increases, there is movement up the demand curve, if income m increases the demand curve shifts outwards and quantity demanded increases

Question 13

Own price elasticity

Answer 13

%change in quantity/%change in own price

Question 14

Income elasticity of demand

Answer 14

%change in quantity/%change in income

Question 15

Normal vs Inferior goods

Answer 15

A good is normal if consumption increases when income increases, positive income elasticity if x1 is a normal good

A good is inferior if consumption decreases when income increases, negative income elasticity if x1 is an inferior good

Question 16

Cobb Douglas Utility

Answer 16

With Cobb-Douglas utility, the consumer with income m>0 will never choose to be at a corner where the budget line meets one of the axes (Because Cobb-Douglas curves never touch the axes!)

Income has an effect in demand for good 1, income elasticity of demand for good 1 = 1

Question 17

Quasilinear utility

Answer 17

Quasilinear utility: u(x1,x2) = V(x1) + x2
V(x1) is increasing in x1 and concave

Demand for good 1 depends on prices and not income, demand for good two depends on prices and income (one good will not be dependent on income so there will be no income effect)

Income elasticity on a good with no income effect is equal to 1??

When m satisfies the inequality (=/>) -> income has no effect on demand for good 1, income elasticity of demand for good 1 = 0

If m doesn’t satisfy the inequality ( demand for good 1 depends on prices and income, there is an income effect on demand for good 1

Question 18

Substitute

Answer 18

If demand for good 1 increases when the price of good 2 increases

Question 19

Complements

Answer 19

If demand for good 1 decreases when the price of good 2 increases

Question 20

Cross Price Elasticity

Answer 20

measures responsiveness of demands for x1 following the change in price of good x2

Question 21

Perfect Complements

Answer 21

utility maximisation -> implies that (x1, x2) lies at the kink of the indifference curves

With a perfect complements utility function the ratio of consumptions of the goods does not vary with price or income

Price of good 1 is dependent on price of good 2

Demand curves: increase in p1 results in movement along demand curve, increase in p2 results in shift down the demand curve, increase in m results in shift up demand curve

Question 22

Perfect Substitutes

Answer 22

MRS is a/b which does not depend on x1 and x2, there is a jump in the demand curve, may be a point where no price equals demand and supply

Question 23

Price Consumption Curve

Answer 23

Indicates the various amounts of a commodity bought by a consumer when its price changes

A line drawn through all the equilibrium points between indifference curves and expenditure function/budget sets

Question 24

Income Consumption Curve

Answer 24

The locus of points showing the consumption bundles chosen at each of the various levels of income

How the consumer’s optimal bundle of purchases vary with corresponding income

Question 25

Compensated Demand

Answer 25

Minimises the cost of obtaining utility u at prices p1 and p2 and is function of obtaining utility u at prices p1 and p2 and is a function of utility u, p1, p2, notation h1(p1,p2,u), h2(p1,p2,u)

Compensated demand h1(p1,p2,u), h2(p1,p2,u) is the cheapest way of getting utility u at prices p1 and p2

To get uncompensated demand fix income and prices which fixes the budget line. Get onto the highest possible indifference curve

To get compensated demand fix utility and prices which fixes the indifference curve and gradient of the budget line. Get onto the lowest possible budget line

A demand curve composed solely of substitution effects

Question 26

The Expenditure Function

Answer 26

E(p1,p2,u) is the minimum amount of money you have to spend to get utility u with prices p1 and p2. It is function of p1,p2 and u

The cost of the cheapest way of getting utility u at prices p1 and p2

The amount of goods which minimises the cost of getting utility u is compensated demand h1(p1,p2,u), h2(p1,p2,u) so E(p1,p2,u) = p1h1(p1,p2,u) + p2h2(p1,p2,u)

Question 27

Homogeneity of Compensated Demand and Expenditure Function

Answer 27

Compensated demand is homogeneous of degree 0 in prices

The expenditure function is homogeneous of degree 1 in prices

If all prices are multiplied by t, the cheapest way of getting utility u doesn’t change (degree 0?)

The cost of the cheapest way of utility does change (degree 1?)

Question 28

Properties of the Expenditure Function

Answer 28

1) Increasing in utility
2) The expenditure function increases or does not change when a price increases
3) Homogeneous of degree 1 in prices
4) Shepherd’ s lemma - derivative of expenditure = compensated demand for good 1
5) Concave in prices

Question 29

The Slutsky Equation

Answer 29

It is way of knowing how big income and substitution 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 budget

For a normal good, income and sub effects work in the same direction
Income effects are small if the income elasticity or the budget share are small

Question 30

The Income Effect

Answer 30

The change in uncompensated demand due to an income change holding prices constant

Question 31

The Substitution Effect

Answer 31

is the change in compensated demand due to a price change holding utility constant

Question 32

Quasilinear Utility (C.D.)

Answer 32

Quasilinear utility -> uncompensated demand for good 1 does not depend on income except at low levels of income and is equal to compensated demand

Quasilinear utility: at a tangency compensated demand for good 1 depends only on prices and uncompensated demand for good one depends only on prices

There is no income effect on demand for good 1 with quasilinear utility

Question 33

Perfect Complements (C.D.)

Answer 33

Perfect complements utility -> Compensated demand does not depend on prices. No substitution effect

With perfect complements, compensated demand does not depend on prices (perfectly inelastic) -> No substitution effect
Compensated demand is completely inelastic and demand curve is vertical

Question 34

Price Changes for Normal Goods

Answer 34

If a good is Normal, substitution and income effects work in the same direction

When price falls, both effects lead to a rise in quantity demanded

When price rises, both effects lead to a drop in quantity demanded

Utility maximisation implies that a rise in price leads to a decline in quantity demanded

Sub effect causes less to be purchased as the individual moves along an indifference curve

Income effect causes less to be purchased because the resulting drop in purchasing power moves the individual to a lower indifference curve

Question 35

Price Changes for Inferior Goods

Answer 35

If a good is inferior, substitution and income effects move in opposite directions

Combined effect is indeterminate

When price rises, sub effect leads to a drop in q demanded, I.E is opposite

When price falls, sub effect leads to a rise in q demanded, I.E is opposite

Utility maximisation implies that no definite prediction can be made for changes in price

The sub an income effect move in opposite directions

Income effect outweighs sub effect then we have Giffen’s paradox

Question 36

The Base Weighted Price Index

Answer 36

The base weighted price index: measures the proportional increase in the cost of (x1A, x2A) which has utility uA

Initially prices at p1A, p2A, consumption (x1A,x2A) is optimal, income is p1Ax1A + P2Ax2A

Prices change to p1B, p2B if income changes at the same rate as the base weighted price index it changes to p1Bx1A+p2Bx2A

is a weighted average of proportionate price increases where weight for good I is the proportion of expenditure spent on good I at date A

Base weighted price index: proportional increase in income needed to continue to buy (x1a, x2a) after the price change

Question 37

Expenditure Function Price Index

Answer 37

Expenditure function price index: initially prices p1A, p2A, utility uA, income E(p1A,p2A,uA). Price changes to p1B,p2B, income changes at the same rate as the expenditure function price increase so changes to E(p1B,p2B,uA)

Expenditure function price index: proportional increase in income needed to continue to have utility uA after the price change
The expenditure function prices index is lower than or equal

Question 38

Fall in Consumer Surplus

Answer 38

Fall in consumer surplus: measures the reduction of the gain from trade (total value - total cost) in money

The fall in consumer surplus is the amount of extra money you would have to be given to get back to the same utility as before the price increase -> This is the compensating variation?

If demand is elastic/substitute available, fall in consumer surplus is smaller
Change in consumer surplus is the area bounded by the uncompensated demand curve

Question 39

Compensating Variation

Answer 39

Compensating variation for a price increase p1A to p2A is the amount of extra money the consumer needs to get back to the same level of utility as before the price change

Compensating variation is the area between the compensated demand curve and the vertical axis (why not uncompensated?) - the amount of extra money you need after the price increase to make you as well of as you were before the price increase

Compensating variation is the area bounded by the compensated demand curve with utility uA

Question 40

Equivalent Variation

Answer 40

Equivalent variation: EV is the amount of money that taken away from the consumer without changing prices has the same effect on utility as the price change

E(p1B,p2,uB) - E(p1A,p2,uB)

EV if it is what is the monetary equivalent of the price change
Assume the price of good 2 is 1. The equivalent variation is a line on the indifference curve diagram and an area of the demand curve diagram

Question 41

EV vs CS vs CV

Answer 41

For a price rise of a normal good: EV < change in consumer surplus < CV because EV is measured at a lower level of utility

When there are no income effects, e.g. with quasilinear utility at a tangency, uncompensated and compensated demand are the same so the loss in consumer surplus due to an increase in p1 is the same as the CV & EV

There is no difference between compensating variation, equivalent variation and change in consumer surplus with quasilinear utility as there is no income effect
• EV = tax revenue if no sub effect
• EV = CV if no income effect
• CV = CS in quasilinear utility (no income effect)

The difference between CV and EV and the change in consumer surplus is due to income effect

When there is no income effect (quasilinear), dealing only with sub effects and so compensated demand meaning that CV = change in CS, because income elasticity = 0, demand for good 1 is inelastic meaning same quantity of good 1 is consumed each time which means utility for good 1 remains constant there is no difference between CV and EV

Income effects are small when either or both of the income elasticity of uncompensated demand and the budgets share are small

If income effects are small the change in consumer surplus is a good approximation to the compensating variation

The difference between CV, EV and CS is small when the income effect is small and/or when the share of the budget spent on a good is small

There is no measurement consumer surplus in compensated demand because the demand function corresponds to changes in utility and utility expenditures and not income

Question 42

Excess Burden

Answer 42

The excess burden of an excise tax is equivalent variation - tax revenue = loss to consumer - tax revenue (With an excise tax there is an excess burden)

Question 43

Lump Sum Tax

Answer 43

A tax is lump sump if the amount paid does not depend on anything the consumer can change e.g. does not depends on income, wealth, spending and saving etc..

Suppose the government wants to raise revenue R from a household: a lump sum tax that reduces income by R that does not depend on anything consumer does reduces utility by less than a non lump tax which raises the same revenue

A poll tax is a lump sum tax which is the same for everyone

Does compensating a consumer for a price increase imply that the price increase has no effect on demand?

A price increase reduces demand even if the consumer is compensated

If income effects are small compensation has little effect on the demand for the good

Question 44

Value Judgement

Answer 44

Adding up consumer surplus geometrically implies a value judgement that giving £1 to one consumer has the same social benefit as giving £1 to any other consumer

You want to evaluate the losses to each group, and then consider how to use them as input into a decision

Question 45

Budget Constraint and Utility Assumptions

Answer 45

Budget constraint and utility assumptions:

Utility u(c,n) depends on consumption c and time outside paid employment (leisure) n, households can choose how many days of hours to work (e.g. gig economy)

Nonsatiation: utility is increasing in both consumption and leisure (also completeness, transitivity, continuity and convexity)

Spending on conusumption <= total earnings

Nonsatiation implies that that budget constraint is satisfied as an equality c + wn =wT

MRS = w = real wage

Question 46

Substitution and Income effect (Labour supply)

Answer 46

Sub effects dominates -> labour supply increases when wage rises (workers prefer to work as opportunity cost of leisure increases)

Income effect dominates -> labour supply decreases when wage rises (more wealth gained per unit of time work means workers can increase leisure time)

The labour supply curve is backward-bending when the substitution effect dominates the income effect for wages below a certain w, and the income effect dominates the substitution effect above w

Cut in marginal tax rate for incomes:
Substitution effect increases labour supply
Income effect decreases labour supply

Question 47

Income v Consumption tax

Answer 47

Income tax is a proportion of total earnings

Consumption tax is a proportion of total spending

In general a Proportional income tax at rate tm and a promotional consumption tax at rate tc raise the same revenue and have the same effect on the budget constraint if (1-tm)(1+tc) = 1

Question 48

Equivalent Variation for a Price Change

Answer 48

Definition for Equivalent Variation for a price change: taking away EV without changing p1 from p1A has the same effect on utility as increasing p1 from p1A to p1B without changing income

Question 49

Equivalent Variation for a Tax

Answer 49

Definition for Equivalent Variation for a tax: Taking away the equivalent variation without changing the price of leisure has the same effect on utility as imposing the tax

Question 50

Lump Sum Tax

Answer 50

Budget constraint with lump sum tax raising same revenue as income tax. This gives higher utility than the income tax

A lump sum tax that reduces income by a fixed amount that does not depend on anything the consumer does reduces utility by less than a tax raising the same amount of revenue where the revenue can be changed by changing consumption, work or saving

The only feasible lump sum tax is a poll tax where everyone pays the same amount

Question 51

Marginal Income Tax Rate

Answer 51

Marginal income tax rate is the number of extra pennies tax you pay on £1 extra earnings

Question 52

Average Income Tax Rate

Answer 52

Average income tax rate = total income tax/total income

Question 53

The Benefit Withdrawal Rate

Answer 53

The benefit withdrawal rate: this is the amount by which the benefit is withdrawn if someone earns £1 more

Question 54

Upward Sloping Indifference Curves

Answer 54

Pre-tax and post-tax income: Indifference curves are upward sloping (less pre-tax income is equivalent to more leisure, more post-tax income is equivalent to more consumption)

Hours worked and post-tax income: Indifference curves are upward sloping (less hours worked is equivalent to more leisure, more post-tax income is equivalent to more consumption)

Indifference curves upward sloping for the withdrawal rate (More income before benefits implies more work, less leisure, More income after benefits implies more consumption)

Reducing the withdrawal rate from 100% to 50% improves work incentive for people earning less than £200 but worsens work incentives for people earning between £200 and £400

More generally lower withdrawal rates improve work incentives for low earners and worsen work incentives for moderate earners
Lower withdrawal rates result in more benefits being paid so are more expensive

Question 55

Universal Credit

Answer 55

Intends to integrate part of the tax and benefit system to make it easier to understand and improve work incentives

Question 56

Present Discounted Value

Answer 56

The present discounted value at date 0 of income stream y0,y1,y2…yt,yT paying yt at date t, discounted at an interest rate r…..

The pdv of y1,y2…… is the maximum amount of debt at date 0 which you could repay using the entire income stream

If you get the income stream y0,y1…… at interest rate r, start with no saving and no debt at date 0, you can follow any consumption path and leave no debt or savings at date T whose pdv is equal to the pdv of the income stream

The consumer consumes his/her endowment bundle if savings are exactly zero (s=0) and no borrowing takes place

Question 57

Perfect Capital Markets

Answer 57

1) No uncertainty
2) You can borrow and lend at the same interest rate r
3) The only constraint on borrowing is that you must have enough income too repay your debt
4) There is a perfect and costless mechanism which ensures that no one takes on loans which they cannot repay and that all debts are paid

Question 58

No Arbitrage Argument

Answer 58

The market can only clear if current price = pdv -> no arbitrage argument

Question 59

Change in Asset Prices

Answer 59

If an increase in current asset prices leads people to expect that future asset prices will be even higher, an increase in asset prices can increase demand and further increase prices

If a fall in current asset prices leads to people to expect that futureP asset prices will be even lower, a decrease in asset prices can decrease demand and further decrease prices

Question 60

Interest Rate Increase and Income and Substitution Effects

Answer 60

Interest increase: never makes a saver worse off, usually makes a borrower worse off

Borrowing is more expensive so the sub effect decreases borrowing

Borrowing is more expensive so the household is poorer. If current consumption is a normal good this reduces current consumption so decreases borrowing

Income and substitution effects on borrowing work in the same direction. Both decrease current consumption and borrowing

Saving is more rewarding so the substitution effect increases saving

The higher interest rate makes the household richer. If current consumption is a normal good this increases current consumption so decreases saving

Income and sub effects work in opposite directions: If the SE dominates current consumption falls and saving increases, if the IE dominates current consumption increases & saving decreases

In reality the interest rate at which you borrow is higher than the rate at which you can save
If there are different interest rates for borrowing and lending or credit limits the choice between income streams depends on preferences

Question 61

Compensated Demand curves cannot slope upwards

Answer 61

The substitution effect of an increase in the price of a good decreases or leaves unchanged the demand for the good

Compensated demand is by definition the cheapest way of getting utility u at prices (p1,p2)

At prices (p1,p2) any other way of getting utility u must cost the same or more than (h1.h2) so must lie on or above the budget line through (h1,h2) withnslope -p1/p2

Any other (x1,x2) with Utility u cannot lie in the shaded area below the budget line through (h1,h2) with slope -p1/p2

H1a, h2a is the cheapest way of getting utility u at prices p1A, p2

H1b, h2b is another way of getting utility u, therefore h1b, h2b cannot cost less than h1a, h2a at prices p1A, p2

H1b, h2b, cannot cost less than h1a, h2a at prices p1A, p2 so (H1b, h2b) cannot lie in shaded area below budget line

Question 62

Saving and Borrowing Decisions

Answer 62

Assume preferences satisfy the standard assumptions of completeness, transitivity, continuity, nonsatiation and convexity so can be represented by a utility function u(c0,c1)

The consumer maximises u(c0,c1) subject to the budget & non-negativity constraints where c0+c1/(1+r) <= y0 + y1/(1+r), c0 >= 0, c1 >= 0

If the household can continue to do after the rate change what it did before the rate change, the rate change can’t make it worse off and usually makes it better off

Nonsatiation Implies that any consumer would the income stream with higher present value

In reality the interest rate at which you borrow is higher than the rate at which you can save

If there are different interest rates for borrowing and lending or credit limits the choice between income streams depends on preferences

It is optimal to choose the income stream with the highest pdv regardless of preferences