elasticity & its applications

elasticity

the responsiveness of variable Y to the change in variable X

what does elasticity attempt to measure?

the relative change in Y to the relative change in X

elasticity formula

Ey1x = percent change in Y/ percent change in X

facts about elasticity:

1. always a percentage ratio

2. no units of measurement

3. computed along a curve

4. elasticity is not the same as slope

mid-point “averaging” method

computed as the average percentage change for two price points along a curve

midpoint method formula

A formula used to calculate elasticity by averaging the starting and ending values for both X and Y, typically expressed as (change in Y / average Y) / (change in X / average X)

• [q2-q1/(q2+q1)/2] divided by [p2 - p1/(p2+p1)/2]

midpoint method advantage

one obtains the same elasticity between two price points whether there is a price increase or decrease

• done because the formula uses the same base for both cases'

• negative numbers indicate the demand curve is downward sloping but are read as absolute values

price elasticity

the ratio between the percentage change in the quantity demanded (Qd) or supplied (Qs) and the corresponding percent change in price

price elasticity of demand

the percentage change in the quantity demanded of a good or service divided by the percentage change in the price

price elasticity of supply

the percentage change in quantity supplied divided by the change in price

three types of elasticity:

1. elastic

2. unitary

3. inelastic

elastic demand/supply

the elasticity is greater than one, indicating a high responsiveness to changes in price

elasticities that are more than 1 indicate that:

a high responsiveness to changes in price - elastic

elasticities that are less than 1 indicate that:

a low responsiveness to changes in price - inelastic

unitary elastic

indicates proportional responsiveness of either demand or supply

if % change in Q > % change in price then

% change in Q / % change in P > 1 aka elastic

if % change in Q = % change in price then

% change in Q / % change in P = 1 aka unitary

if % change in Q < % change in price then

% change in Q / % change in P < 1 aka inelastic

why do some sellers try to increase their revenue by lowering prices?

it may or may not result in an increase in quantity sold

• the seller may or may not bring in more revenue if they sell more goods at a lower price

perfectly inelastic

occurs when a price change has no effect on the Qd

• consumer needs the same amount of product regardless of price

perfectly elastic

situations where a price change will cause the quantity demanded to drop to zero

• rare and unusual

total revenue/total sales: price * quantity

with unitary elasticity, the percentage increase in price calls for an offsetting decrease in demand and vice versa, so either way revenue will remain the same

price elasticity demand

occurs when a reduction in price increases the quantity demanded so that the seller’s revenue increases

price inelastic demand

occurs when a price decreases calls for an increase in quantity that results in a decrease in revenue

since people demand a certain quantity of the product:

price changes will have little effect on the quantity demanded

• it will change a little bit, but not much

what does the elastic portion of demand do as you lower the price?

total revenue goes up

what does the elastic portion of demand do as you raise the price?

total revenue goes down

where is total revenue at its max?

in the middle of the demand curve - aka unitary

factors influencing elasticity of demand:

1. proportion/share of income spent on the good

2. availability of close substitutes

3. nature of commodities

4. number of uses

5. time (short run & long run)

proportion/share of income spent on the good

if the proportion of income spent on the purchase of a good is very small, the demand for such a good will be inelastic

availability of close substitutes

if a good has greater numbers of close substitutes available in the market, the demand for the good will be greatly elastic

nature of commodities

• the demand for goods that are necessities tend to be less elastic

• luxury goods tend to be greatly elastic

number of uses of a good

if a good can be put to several uses, its demand is greater elastic (Ed > 1)

time (short run)

when consumption of a good cannot be postponed, its demand will be less elastic

time (long run)

if the rising price persists, people will find out methods to reduce the consumption of goods; so, the demand for a good in the long run is elasitc as long as other factors remain constant

uses of price elasticity of demand

1. for firms to predict TR when price changes

2. to make pricing decisions

3. in the case of supermarkets, it helps to decide which goods to put on special offer

4. firms might use it to plan marketing

5. government uses it to predict changes in tax revenues & quantity when tariffs are used

cross price and elasticity of demand

measures the responsiveness in the Qd of one good (X) to changes in the price of another good (Y)

when is cross price used?

to determine whether two goods are substitutes/complements and the degree to which one good is too another

cross price elasticity of demand

responsiveness of quantity demanded of a good X to change in price of good Y

cross price elasticity of demand formula

(Q1x - Q0x / P1y - P0y) * (P1Y + P0y) / (Q1x + Q0x)

if the cross price elasticity is positive than the goods are

substitutes for each other

if the cross price elasticity is negaitve than the goods are

complements for each other

income elasticity of demand

measures the responsiveness of quantity demanded of good X to changes in consumer income

• % change in Qd of a good divided by the % change in income

if income elasticity of demand is positive (Ey > 0) then the good is

a normal good

how do firms use income elasticity of demand?

knowing IED can help a firm respond to changing macroecon situations to help a firm plan

price elasticity of supply

measures the responsiveness of Qs to changes in price

• % change in Qs of a good divided by % change in the price of the good