Elasticity

 

I.       The Price Elasticity of Demand

A.      Def'n: The price elasticity of demand measures how responsive or sensitive to changes in price.

B.      How do you calculate the price elasticity of demand?

ed = ‑ (% change in quantity demanded)/(% change in price)

ed =  ‑ (dQ/Q)/(dP/P) = (P/Q)(dQ/dP)

C.      Definitions:

1.       ed > 1 ==>|dQ/Q| > |dP/P| ==> elastic demand

2.       ed < 1 ==>|dQ/Q| < |dP/P| ==> inelastic demand

3.       ed = 1 ==>|dQ/Q| = |dP/P| ==> unitary elastic demand

D.      Formulas:

1.       Example:

Point A: P = $25, Q = 40

Point B: P = $20, Q = 60

2.       The point formula: ed = ‑ (dQ/Q0)/(dP/P0)

From Point A to B: ed = (20/40)/(5/25)=(1/2)/(1/5)=2.5

From Point B to A: ed = (20/60)/(5/20)=(1/3)/(1/4)=4/3

3.       The arc formula or the midpoint method:

ed = ‑[dQ/(Q1+Q2)/2]/[dP/(P1+P2)/2]

ed = [20/(40+60)/2]/[5/(25+20)/2]=(20/100)/(5/45)

ed = (1/5)/(1/9)=9/5

E.      Elasticity is not slope

1.       ed = ‑(dQ/Q)/(dP/P)=‑(P/Q)(dQ/dP)=‑(P/Q)(1/slope)

2.       For a straight line, downward sloping demand curve, slope is constant. Decrease P, increase Q ==> decrease in the price elasticity of demand

F.       The relationship between elasticity and dP and dTR

1.       TR = PQ = area of rectangle on demand curve

2.       dTR/dQ = P + Q(dP/dQ) = P[1+(Q/P)(dP/dQ)]

dTR/dQ = P[1 ‑(1/ed)]

3.       If ed>1 ==> Decrease P, Increase Q ==> Increase TR

4.       If ed<1 ==> Decrease P, Increase Q ==> Decrease TR

5.       If ed=1 ==> No change in TR

G.      Special cases

1.       perfectly elastic demand

2.       perfectly inelastic demand

H.      Determinants of the price elasticity of demand

1.       The number of substitutes: Increase number of substitutes ==> students more sensitive to price changes ==> increase in the price elasticity of demand

2.       Percent of budget ==> If expenditures on the good is a larger % of the consumer's budget ==> more responsive to price changes ==> more elastic demand

3.       Passage of time ==> In the long run, consumer have more time to adjust ==> more responsive to price changes ==> demand more elastic in the long run

II.      The price elasticity of supply

A.      Def'n: The price elasticity of supply measures how responsive producers are to changes in price.

B.      How do you calculate it?

es = (% change in quantity supplied)/(%change in price)

point formula: es = (dQ/Q0)/(dP/0)

arc formula: es = [dQ/(Q0+Q1)/2]/[dP/(P0+P1)/2]

C.      Definitions:

1.       elastic supply: es>1

2.       inelastic supply: es<1

3.       unitary elastic supply: es=1

D.      The straight line upward sloping supply curve:

1.       cuts the origin: es=1

2.       cuts the horizontal axis: es < 1

3.       cuts the vertical axis: es > 1

4.       When two supply curves intersect the flatter one is more elastic

E.      Special cases

1.       perfectly elastic supply

2.       perfectly inelastic supply

F.       The determinants of the price elasticity of supply

1.       Can the product be stored? ==> more elastic.  If the product is perishable==> less elastic

2.       In long run ==> supply more elastic as firms have more time to respond to price change

III.    Other measures of elasticity

A.      The income elasticity of demand

1.       Def'n: measures how responsive the quantity demanded is to changes in income

2.       eY = [dQ/(Q0+Q1/2]/[dY/(Y0+Y1)/2]

3.       eY>0 ==> normal good

eY<0 ==> inferior of good

B.      The cross price elasticity of demand

1.       Def'n: measures how responsive the quantity demanded of X is to changes in the price of good Y, a related good.

2.       eXY = [dQX/(Qx0+QX1)/2]/[dPY/(PY0+PY1)/2]

3.       eXY > 0 ==> X and Y are substitutes

eXY < 0 ==> X and Y are complements

IV.     Exercises

A.      Effect of bumper crops on farmers revenue

1.       Assume inelastic demand                  

2.       improvement in farm technology ==> ­ supply ==> ¯ P and ­Q and ¯ revenue

B.      OPEC attempt to raise price

1.       In short run demand and supply for oil relatively inelastic

a.       quantity of known oil reserves and capacity for oil extraction cannot be changed immediately

b.       buying habits don’t respond immediately to changes in price

c.       ¯ S ==> large ­ P

2.       In long run demand and supply more elastic

a.       nonOPEC producers respond to higher price and ­ oil production and ­ extraction capacity

b.       consumers respond with ­ conservation

c.       in long run ¯ s ==> smaller ­P

C.      Illegal drugs

1.       Assume addicts finance habits with street crime.  Assume demand for drugs inelastic

2.       drug interdiction ==> ¯S ==> ­P ¯Q & ­ pushers’ revenue = ­addicts’ expenditures ==> ­ street crime