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Question 1

What are the three assumptions of preferences and their meanings?

Answer 1

1. Completeness - can compare between any two goods/baskets (ALWAYS ASSUMED)
2. Transitivity - preferences are internally consistent (ALWAYS ASSUMED)
3. Monotonicity - if a good is desirable, then consuming more of the good increases utility (i.e. MU > 0)

Question 2

Define Marginal Rate of Substitution (MRS)

Answer 2

Rate at which consumer is whilling to give up y for one more unit of x, maintaining the same level of utility.

Question 3

How do indifference curves show monotonicity?

Answer 3

Downward slope

same utility, qx increases utility increases so qy must decrease to maintain the same level of utility

Question 4

What does a convex indifference curve mean?

Answer 4

Diminishing MRS

willing to give up less y as x increases hence decreasing rate of decrease in y, decreasing MRS

Question 5

What is the formula for MRS?

Answer 5

-(change in y)/(change in x) AND MUx/MUy

i.e. -ve dy/dx

negative of slope of indifference curve. MUx/MUy formula is derived from utility equation (change in U = MUx(change in x) + MUy(change in y))

Question 6

What is the principle of diminishing marginal utility?

Answer 6

MUx decreases as x increases, holding y constant

MUy decreases as y increases, holding x constant

Question 7

What is the utility function for perfect substitutes?

Answer 7

U(x,y) = αx + βy

Question 8

What are the conditions for perfect substitutes?

Answer 8

1. Linear indifference curve
2. Linear utility function
3. Constant MRS

Constant MRS means that MRS is independent of the quantity of x or y consumed

Question 9

What is the utility function for perfect complements?

Answer 9

U(x,y) = min {αx, βy}

Question 10

What is the MRS of a perfect complement graph in the horizontal part?

Answer 10

MRS = 0 as the consumer is not willing to give up any more y for one more unit of x at the same level of utility

Question 11

What is the MRS of a perfect complement graph in the vertical part?

Answer 11

MRS = ∞ as consumer is willing to give up infinite units of y to gain one more unit of x at the same level of utility

Question 12

What is the MRS at the kink of the perfect complements graph?

Answer 12

MRS is undefined

Question 13

What is the form of a Cobb Douglas utility function?

Answer 13

U(x,y) = A(x^α)(y^β), for A,α and β > 0

Question 14

What are the properties of a Cobb Douglas utility function with regards to marginal utility? What are the implications?

Answer 14

MU always positive (α and β > 0) –> monotonicity holds for both goods –> indifference curves are downward sloping

MU may or may not be diminishing (depending on value of α and β, value of α-1 and β-1 may be <0)

Question 15

What are the properties of a Cobb Douglas utility function with regards to MRS? What are the implications?

Answer 15

MRS is diminishing –> indifference curves are convex

sub in eqn of MUx/Muy, MUx/MUy cancels out to equal αy/βx. x increases, y decreases, αy/βx decreases.

Question 16

What is the formula for budget line slope?

Answer 16

-px/py

derived from -(M/py)/(M/px), which is rise (max y within budget) over run (max x within budget)

Question 17

What is the constrained optimisation problem? How is it shown graphically?

Answer 17

Max U(x,y) subject to Px(x) + Py(y) = M

Optimal choice is highest possible indifference curve tangent to the budget line

Question 18

What is the tangency condition?

Answer 18

MRSx,y = MUx/MUy = Px/Py

rate at which consumer is willing to substitute the two goods, holding utility constant, is equal to the rate at which the two goods are exchanged in the market

Question 19

What is the equal marginal principle?

Answer 19

MUx/Px = MUy/Py

at max utility, MU per dollar spent on x = MU per dollar spent on y

if MU per dollar for x is higher than y, then more x should be purchased and vice versa (greater gains in utility per dollar given limited money)

Question 20

What is the BLTC method?

Answer 20

1. Budget line eqn
2. Tangency condition

solve the simultaneous eqn

Question 21

What is the Lagrange Multiplier method?

Answer 21

Λ(x,y,λ) = U(x,y) + λ(M-pxx-pyy)

Find tangency condition: partially differentiated wrt x and y, first order = 0

partially differentiate wrt λ, budget line eqn = 0

solve simultaneous equations

Question 22

What is the constrained maximisation problem?

Answer 22

Max U(x,y) subject to M-pxx-pyy = 0

Question 23

When is something a binding constraint?

Answer 23

When the solution for the Umax problem is negative, then variable >=0 is binding

cannot have negative quantity of a good

Question 24

What is an interior solution?

Answer 24

The optimal basket where strictly positive amounts of both goods are consumed

Question 25

What is a corner solution?

Answer 25

Optimal basket where consumption of at least one good is zero. ## Footnote for corner solutions, the indifference curve may not be a tangent to the budget line

Question 26

What is the budget constraint equation when there is a voucher?

Answer 26

Px(x) + Py(y) = M + voucher | optimal is calculated without constraint of M/py vs M+voucher/px ## Footnote assuming x is the good w the voucher

Question 27

Which types of goods affected by changes in income?

Answer 27

normal and inferior goods | normal: income up, qd up. inferior: income up, qd down

Question 28

Which types of goods are affected by changes in price?

Answer 28

1. Ordinary (px up, qd down) 2. Giffen (px up, qd up) 3. Veblen (px up, qd up) ## Footnote For a Giffen good, the increase in demand is directly attributable to the increase in price. For a Veblen good, the increase in demand reflects the consumer’s preference (utility function), which in turn partially depends on the increase in price

Question 29

What is the income expansion path?

Answer 29

The curve connecting consumer's optimal choices at different income levels

Question 30

What is the Engel curve?

Answer 30

The relationship between income and optimal consumption of a good, ceteris paribus

Question 31

What is the slope of the engel curve for normal and inferior goods respectively?

Answer 31

1. Normal: upward sloping 2. Inferior: downward sloping ## Footnote normal: up income, up optimal consumption inferior: up income, down optimal consumption

Question 32

What is a Giffen good?

Answer 32

An inferior good where the income effect dominates the substitution effect (px increase, qd increases and vice versa) ## Footnote change in demand can be directly attributed to change in price

Question 33

What is a Veblen good?

Answer 33

Goods that are in demand due to their high price that acts as status symbols. when price falls, quantity demanded falls | value as status symbol is partially derived from the price ## Footnote change in demand reflects consumers preferences, which depends partially on the change in price

Question 35

What is an offer curve?

Answer 35

Optimal choices at different prices of the good

Question 36

What are the properties of a Cobb Douglas utility function?

Answer 36

1. Demand for one good does not depend on the price of the other good (i.e. the goods are neither substitutes nor complements) 2. Consumer always spends a fixed proportion of income on the good ## Footnote for 1, solve for the demand function to prove by using budget line and tangency condition to solve for eqn for x or y. for 2, expenditure does not depend on prices (calculate pxx or pyy)

Question 37

Offer curves are related to price. What are the slopes of offer curves for substitutes and complements (assuming ordinary good)?

Answer 37

Substitutes: downward sloping (as py decreases, qy decreases, qx increases) Complements: upward sloping (as px decreases and qy increases, qx increases)

Question 38

What is compensating variation?

Answer 38

Amount of income that the consumer is willing to give up after the price drop in order to maintain the pre price drop utility level | same indifference curve

Question 39

What is equivalent variation?

Answer 39

The amount of income would need before the price drop to obtain the post price drop utility level

Question 40

What are network externalities?

Answer 40

Externalities that occur when a consumer's demand for a good depends on how many other consumers are purchasing the good

Question 41

What are positive network externalities?

Answer 41

Consumer demand for a good increases with the number of other consumers that buy the good | Increase in Qd is called the bandwagon effect

Question 42

What are negative network externalities?

Answer 42

Consumer demand for a good decreases with the number of other consumers who buy the good | decrease in Qd is called the snob effect

Question 43

How is the Slutsky decomposition different from the Hicks decomposition?

Answer 43

The Hicks decomposition interprets “holding purchasing power constant” as “maintaining the same level of utility as the original optimal basket.” The Slutsky decomposition interprets “holding purchasing power constant” as “being able to afford the original optimal basket.” ## Footnote In the Hicks decomposition, the intermediate basket is on the same indifference curve as the original basket. In the Slutsky decomposition, given the hypothetical budget line, the consumer reoptimizes; the intermediate basket is on a higher indifference curve than the original basket