Lecture 4- Elasticity Flashcards
Define price elasticity of demand (PED)
A measure of the responsiveness of the quantity demanded of a good to
a change in the price of the good, ceteris paribus
Define price elasticity of supply (PES)
A measure of the responsiveness of the quantity supplied of a good to a
change in the price of the good, ceteris paribus
Define income elasticity of demands (YED)
A measure of the responsiveness of the quantity demanded of a good to a change in consumers’ income, ceteris paribus
Define interest elasticity of borrowing
A measure of the responsiveness of borrowing to a change in the rate of
interest, ceteris paribus
Define tax elasticity of consumption
A measure of the responsiveness of private consumption to a change in the rate of tax, ceteris paribus
Define wage elasticity of employment
A measure of the responsiveness of employment to a change in the wage rate, ceteris paribus
What is what is y=f(x) in terms of elasticity?
So the x elasticity of y would mean that (using price elasticity of demand/supply) as an example that x=price and y=demand/supply
… you would calculate the arc price/x elasticity of demand/supply/y by placing the % change in y/demand/supply over the % change in x/price
What are the 2 measures of elasticity?
1) Arc price elasticity
2) Point price elasticity
What is arc price elasticity?
The elasticity I learnt at A-level- works the elasticity between 2 points along the demand/supply curve
What is point price elasticity?
More widely used and more specific form of elasticity where use the derivative to find the elasticity at a particular point along the demand/supply curve
How do calculate arc price elasticity of demand/supply?
(% change in y/demand/supply) / (% change in x/price)
How do calculate point price elasticity of demand/supply?
Multiply the derivative of the function by (initial price/initial quantity)
Where x=price and y=quantity demanded/supplied
So either:
dy/dx * x/y- where x=price and y=quantity demanded/supplied
dq/dp * p/q- where p=price and q=quantity demanded/supplied
What do you do when the derivative of your function is not a whole number but carries some variable e.g. p or x etc?
What should you substitute in for this variable?
Substitute what we p or x is
The question will typically state it so substitute wherever this letter arises
For example if a question asks you to find the point price elasticity of demand when price is equal to 5 then substitute 5 whenever there is a p
What should you do when a question asks you to calculate the PED OR PES whilst giving an initial and final price or quantity?
Calculate using arc price elasticity of demand as opposed to point price elasticity of demand as you are given 2 points rather than just 1
… calculate the % change in price and quantity respectively and solve
Substitute the price or quantity values provided to get values for the other
What should you do when a question asks you to calculate the PED OR PES at a certain price or quantity?
Calculate using point price elasticity of demand as opposed to arc price elasticity of demand as you are given just 1 point rather than 2
… differentiate the equation provided linking price and quantity to find dq/dp and then multiply this value by the price over the quantity
Use the price or quantity value for which the question wants you to find the PED or PES and substitute the value into the equation provided to find the other corresponding value
If asked, how would you comment on 2 arc or point price elasticities of demand (one can be point and the other can be arc) which are the same despite using slightly different figures to calculate it?
The main thing you would need to state is that the fact that they are the same is a property of elasticity of a linear function
If asked, how would you comment on 2 price elasticities of demand which are the different despite using slightly different figures to calculate it?
The main thing you need to state is that this is the asymmetric property of arc elasticity where the direction of the change in price matters
An increase and a decrease will not yield the same elasticity even if they are movements between the same two points on the function
Point elasticity does not have this asymmetry problem
What MUST you remember when you have a question asking you to find an equation of the price elasticity of demand AND then to use it to find marginal revenue?
Begin by trying to find PED (typically and mostly point price elasticity of demand)
So differentiate the equation they provide which should include q and p
Multiply this (dq/dp) by p/q
dq/dp should be in terms of p so substitute the equation they give you for q so that everything is in terms of p
THEN REMEMBER the equation:
MR = p(1/PED +1)
… flip the equation for point PED you found and substitute it in the above equation
ALWAYS USE THE ABOVE EQUATION WHEN YOU NEED TO FIND AN EQUATION FOR MR
How do you prove that when demand is elastic then marginal revenue is positive
See maths for econ key images word doc
What is dp/dq * q/p equal to where p=price and q=quantity demanded/supplied?
It is equal to 1/PED (more specifically point price elasticity of demand)
What do the values found for PED and PES mean and signify?
In calculations PED is always negative and PES is always positive but use the positive/absolute/modulus values when talking about either in answers etc
If the absolute or modulus value of either PES OR PED is greater than 1 then it is elastic
If the absolute or modulus value of either PES OR PED is between 0 and 1 then it is inelastic If the absolute or modulus value of either PES OR PED is equal to 1 then it is unitary
If the absolute or modulus value of either PES OR PED is equal to 0 then it shows no correlation/responsiveness
What must you remember about linear demand functions?
Top half elastic
Middle is unitary
Bottom half inelastic
What are rectangular hyperbolas and what must you remember about them in terms of elasticity?
Rectangular hyperbolas are essentially 1/x graphs where the graphs are in 2 diagonally opposite quadrants
In terms of elasticity, they have constant elasticity (same)
