Topic 4 - Optimisation Flashcards
Where is the point of optimisation?
on a diagram with budget constraint and indifference curve plotted: optimise where ratio of marginal utilities = ratio of prices
i.e slope of budget constraint equals slope of indifference curve
this occurs where there is a tangency solution
Why must price ratios and marginal utilities be equal at point of optimisation
if consumer is willing to give up more of y (MRS) than what the market requires her too in order to conumer 1 more X (slope of budget constraint), she will certianly give up the smaller amount required of her
SO consumption of X will rise and Y will fall until price and marginal utility ratios are equal
In which situation is the tangency conditon a necessary condition
If the optimal choice involved consuming both gooods then tangency condition is a necessary condition
What is a corner solution
With IC slopes that have a very small slope (small MRS)
- MRS < Px/Py for all Pi, and with diminishing MRS rhe slope will never be equal (or MRS > Px/Py)
- so consumer optimisises in axes at a corner (on highest possible IC curve)
How does optimisation occur in a non-convexity situation
- Tangency condition is necessary for optimality but is not sufficient unless preference are convex
- (e,g think of a waves graph)
How do we optimise with perfect substitutes
- if MRS > P1/P2 = consume only x1 so M/P1
- if MRS = P1/P2 : 0<x1*<M/P1
- If MRS > P1/P ; 0
essentially compare the slopes of BC and IC to determine which good is consumer. max utility on highest IC subject to BC
Where does consumer optimise for perfect complements
- optimise at KINK (l shape)
- but MRS is undefined at kink so find a expression at the kink and combine with BC to solve
What is a normal good and inferior good
normal:
- price falls, consumption rise
- income rises, consumption rises
Inferior good:
- price falls, consumpton falls
- income rises, consumption falls
What is a giffen good
very very inferior good
- as price falls, consumption falls
- as income rises, consumption falls
What does engel curve show
How demand for a good varies with income: x axis is demand for a god and y axis is income
inferior good: downward sloping
normal good: upward sloping
What does price consumption curve show
if income is held constant, how does consumption change if we change price
What is the substitution effect
As price of X falls, good Y becomes relatively more expensive and less attractive to the consumer
- optimal demand will change to where MRS= new price ratio
(new BC)
What is the income effect
As price of x falls, real income rises and consumer now feels richer so Q demanded changes
- real income changes, the consumer must move to a new IC
What is perfectly inelastic demand and perfectly elastic demand
0 change in demand for a good in response to change in price
any change in price causes demand to fall to zero so PED is - infinity
-1< PED < 0 : inelastic
- infinity < PED < -1: elastic
What is income elasticity of demand
measures the percenatge change in QD in repsonse to % change in income
