TERM 2 LECTURE 1 Flashcards
(16 cards)
What is a budget set?
Combination of two goods affordable under a given budget y
P1q1 + p2q2 /< y
Why would we get discontinued or kinked budget constraints in practical applications?
Could get taxed, or discounted past a certain quantity of the good
If q1 has a per unit tax once units exceed threshold E, price will increase post E, so…
If tax is only on the units consumed after the threshold:
- After this threshold, line becomes steeper, as when q1>E, p1q1 + p2q2 /< y-t(q1-E), so the x intercept becomes smaller
If the tax is on all units:
- we see the kinks, as if we consume up to E, it will be a normal curve, but if we consume past E, budget curve will shift to p1q1 + p2q2 /< y-tq1, as all units before are to be affected
What if there’s a discount past a given threshold?
Then the reverse as the tax occurs, so if the discount is only on the units past E, then it rotates up at the point of change, if its on all goods, it kinks up.
What are Marshallian demands?
Also known as uncompensated demands
- the consumer’s chosen quantities written as a function of y and p
- q = f(y,p)
What is the IEP?
Income Expansion Path, the path traced out by demands as y increases is called the IEP
- shows how the optimal consumption of q1,q2 changes with income m
What are Engel Curves? How do we find them?
Isolates the income - quantity consumed relationship for a single good
- find the demand functions for each good in terms of income and prices by solving the utility maximisation problem
- if you plot many Engel curves for goods q1 and q2 on the same diagram, with corresponding values of income m, then the points of intersection for different income levels will trace out the IEP
Total Budget Elasticity
- normal good?
- inferior good?
Ei = (y/qi)Dfi/Dy
- if demand for a good rises with total budget, Ei > 0, and it is a normal good
- if it falls, Ei < 0, we say it is an inferior good
Budget Share
- luxury goods?
- necessity goods?
Wi = piqi/y, rises with total budget, ei > 1, then it is a luxury good, if it falls, so ei<1, we say its a necessity
Dwi/dy = wi(ei-1)
Offer curve?
- path traced out by demands as pi increases is the offer curve
- demand curve for a good shows relationship between quantity and price for one good, so if you plot multiple demand curves for different price ratios, you can trace out the offer curve.
Own price elasticity?
- giffen good?
- price inelastic/ elastic good?
Nii = (pi/qi)(DFi/Dpi)
- if demand rises for a good with own price, Nii>0, so it is a giffen good
- if budget share rises with price, Nii>-1, we say it is a price inelastic good
- if budget share falls with price, Nii<-1, we say it is price elastic
Other price pj,
Cross price elasticity?
- substitute?
- complement?
Nij = (pj/fi)(Dqi/Dpj)
- if demand rises with the price of another, nij>0, we can say it is a substitute good
- if demand falls with the price of another, nij<0, we can say it is a complement good
We know demands must lie in the budget set:
P’f(y,p) /<y
- if consumer spending exhausts the total budget, then this holds as an equality
- this is known as adding up
- if all but one marshallian demand is specified, then the remaining demand can be inferred from adding up
Differentiating the adding up function with respect to your gives us the ____?
- what does this tell us?
Engel Aggregation, which is that the summation of the budget share weighted average of total budget elasticities = 1
Therefore:
- not all goods can be inferior
- not all goods can be luxuries
- not all goods can be necessities
Can all goods have constant income elasticities?
- cournot aggregation?
- only if a = 1, i,e, unitary income elasticity
If you differentiate the adding up function with respect to pj and manipulate you get:
Sum(wi.nij) = -wj
- the cournot aggregation which ensures that total spending remains the same given a price change.
How is homogeneity implied?
Multiplying y and p by the same factor does not affect the budget constraint, and if it doesn’t affect motivations for choice within budget sets, choices shouldn’t be affected either.
- therefore marshallian demands should be homogenous of degree 0
