ec2101 Flashcards
What are the three assumptions of preferences and their meanings?
- Completeness - can compare between any two goods/baskets (ALWAYS ASSUMED)
- Transitivity - preferences are internally consistent (ALWAYS ASSUMED)
- Monotonicity - if a good is desirable, then consuming more of the good increases utility (i.e. MU > 0)
Define Marginal Rate of Substitution (MRS)
Rate at which consumer is whilling to give up y for one more unit of x, maintaining the same level of utility.
How do indifference curves show monotonicity?
Downward slope
same utility, qx increases utility increases so qy must decrease to maintain the same level of utility
What does a convex indifference curve mean?
Diminishing MRS
willing to give up less y as x increases hence decreasing rate of decrease in y, decreasing MRS
What is the formula for MRS?
-(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))
What is the principle of diminishing marginal utility?
MUx decreases as x increases, holding y constant
MUy decreases as y increases, holding x constant
What is the utility function for perfect substitutes?
U(x,y) = αx + βy
What are the conditions for perfect substitutes?
- Linear indifference curve
- Linear utility function
- Constant MRS
Constant MRS means that MRS is independent of the quantity of x or y consumed
What is the utility function for perfect complements?
U(x,y) = min {αx, βy}
What is the MRS of a perfect complement graph in the horizontal part?
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
What is the MRS of a perfect complement graph in the vertical part?
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
What is the MRS at the kink of the perfect complements graph?
MRS is undefined
What is the form of a Cobb Douglas utility function?
U(x,y) = A(x^α)(y^β), for A,α and β > 0
What are the properties of a Cobb Douglas utility function with regards to marginal utility? What are the implications?
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)
What are the properties of a Cobb Douglas utility function with regards to MRS? What are the implications?
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.
What is the formula for budget line slope?
-px/py
derived from -(M/py)/(M/px), which is rise (max y within budget) over run (max x within budget)
What is the constrained optimisation problem? How is it shown graphically?
Max U(x,y) subject to Px(x) + Py(y) = M
Optimal choice is highest possible indifference curve tangent to the budget line
What is the tangency condition?
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
What is the equal marginal principle?
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)
What is the BLTC method?
- Budget line eqn
- Tangency condition
solve the simultaneous eqn
What is the Lagrange Multiplier method?
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
What is the constrained maximisation problem?
Max U(x,y) subject to M-pxx-pyy = 0
When is something a binding constraint?
When the solution for the Umax problem is negative, then variable >=0 is binding
cannot have negative quantity of a good
What is an interior solution?
The optimal basket where strictly positive amounts of both goods are consumed
What is a corner solution?
Optimal basket where consumption of at least one good is zero.
for corner solutions, the indifference curve may not be a tangent to the budget line
What is the budget constraint equation when there is a voucher?
Px(x) + Py(y) = M + voucher
optimal is calculated without constraint of M/py vs M+voucher/px
assuming x is the good w the voucher
Which types of goods affected by changes in income?
normal and inferior goods
normal: income up, qd up. inferior: income up, qd down
Which types of goods are affected by changes in price?
- Ordinary (px up, qd down)
- Giffen (px up, qd up)
- Veblen (px up, qd up)
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
What is the income expansion path?
The curve connecting consumer’s optimal choices at different income levels
What is the Engel curve?
The relationship between income and optimal consumption of a good, ceteris paribus
What is the slope of the engel curve for normal and inferior goods respectively?
- Normal: upward sloping
- Inferior: downward sloping
normal: up income, up optimal consumption
inferior: up income, down optimal consumption
What is a Giffen good?
An inferior good where the income effect dominates the substitution effect (px increase, qd increases and vice versa)
change in demand can be directly attributed to change in price
What is a Veblen good?
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
change in demand reflects consumers preferences, which depends partially on the change in price
What is an offer curve?
Optimal choices at different prices of the good
What are the properties of a Cobb Douglas utility function?
- Demand for one good does not depend on the price of the other good (i.e. the goods are neither substitutes nor complements)
- Consumer always spends a fixed proportion of income on the good
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)
Offer curves are related to price. What are the slopes of offer curves for substitutes and complements (assuming ordinary good)?
Substitutes: downward sloping (as py decreases, qy decreases, qx increases)
Complements: upward sloping (as px decreases and qy increases, qx increases)
What is compensating variation?
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
What is equivalent variation?
The amount of income would need before the price drop to obtain the post price drop utility level
What are network externalities?
Externalities that occur when a consumer’s demand for a good depends on how many other consumers are purchasing the good
What are positive network externalities?
Consumer demand for a good increases with the number of other consumers that buy the good
Increase in Qd is called the bandwagon effect
What are negative network externalities?
Consumer demand for a good decreases with the number of other consumers who buy the good
decrease in Qd is called the snob effect
How is the Slutsky decomposition different from the Hicks decomposition?
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.”
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
