Elasticity

1
Elasticity

• Whats percentage change in A in response to an
  1 change in B, taking other things fixed?
• Income elasticity of demand
• The percent change in consumption that results
  from a 1 increase in income.
• Characterize the shape of an Engle curve
• Price elasticity of demand
• The percent change in consumption that results
  from a 1 increase in price.
• Characterize the shape of a demand curve
• Cross elasticity of demand
• The percent change in consumption that result
  from a 1 increase in the price of a related
  goods.

2
Examples of Income elasticity

• If income increases from 80 to 120, consumption
  of bagels increases from 6 to 12.
• What is the income elasticity of demand for
  bagels at the point of interest?

3
Examples of price elasticity

• When price increase from 20 to 30, the quantity
  demanded decreases from 3 to 2.
• What is the slope of demand curve at the point of
  interest?
• What is the price elasticity to demand at the
  point of interest?

• Slope of the demand curve (30-20)/(2-3)
• -10
• Price elas of demand

4
Example of cross elasticity

• Suppose that you rented a video tape once a week
  and spent 2 for each, and went see a movie once
  a month and spent 7 each time. Now, the rent of
  each video tape increases to 3, and the price of
  a movie ticket remains the same. You decide to
  rent a video tape three times a month, and go see
  a movie twice a month.

• What is your cross elasticity of demand for movie
  with respect to video tapes?
• (note video tapes and movies are substitutes)

5
Note

• For complements, the cross elasticity must be
  negative. (like coffee vs coffee mates)
• For substitutes, the cross elasticity must be
  positive. (like video tapes vs movies)
• Elasticity is always in terms of a percentage
  change, not a change in the number of units.

• Why do we prefer to measure elasticity using
  percentage changes?
• Get rid of scale effects.
• Thus, the price elasticity is not equal to the
  inverse of the slope of a demand curve.

6
Derive price elasticity for a given demand
function

• The above calculation is point-specific.
  Sometimes we have the entire picture about the
  demand behavior. Using calculus, we can determine
  price elasticity of demand for each point on the
  demand curve.
• Price elasticitys mathematical definition
• Letting P be price and Q be quantity demanded
  (sales).
• Price elasticity of demand (sales) is

7
Example

• Suppose the demand curve is Q100-P. What is the
  price elasticity of sales in terms of the unit of
  sales?
• When market price is 10, What is the value of
  price elasticity of sales?

• dQ/dP -1
• P/Q(100-Q)/Q
• Price elas of sales
• (-1)(100-Q)/Q
• When P10, Q 90.
• The price elas of sales
• (-1)(100-Q)/Q
• (-1)(100-90)/90 -.11
• Every 1 increase in price, sales falls by .11.