5: Elasticities

Question 1

What do elasticities show us?

Answer 1

Elasticities show us how strongly one variable reacts if one other variable is changing.

“If the independent variable increases by 1 percent, by how many percent does the dependent variable increase or decrease?”

Question 2

What is one main application of elasticities?

Answer 2

The analysis of the price elasticity of supply and demand.

Example: a monopolist might want to know how the market demand reacts if he increases the prices.

Question 3

How do you compute the elasticity (expressed with words)?

Answer 3

%change of dependent variable/%change of the independent variable

Example: By how many percent does the demand for good x decrease if the price for this good p increases by 1%?

Question 4

There are two different ways to compute an elasticity.
What are they called?

Answer 4

Point elasticity and arc elasticity

Question 5

What is the point elasticity? What does the point elasticity determine?

Answer 5

The point elasticity determines the effect of a 1% in the independent variable (the price p) on the dependent variable (the demand x(p)), measured in % by computing the derivative (slope) at a particular point.

Question 6

How do you compute the point elasticity?

Answer 6

derivative of given function in respect to p * p/x

Question 7

What is the problem of the point elasticity?

Answer 7

In reality, changes are usually not marginal (= infinitely small), but sometimes quite big.

Thus, if we use the point elasticity (which uses the derivative, that is a marginal change) to analyze quite large changes, we might make a sizable mistake in our computation.

Question 8

What does the arc elasticity determine?

Answer 8

The arc elasticity determines the effect of a discrete (that is not marginal) change in the price on the demand x(p)

Question 9

How do you compute the arc elasticity?

Answer 9

the change of x over the change of p * p/x

you calculate the change of x and p with the derivative of the function in respect to p

Question 10

What do you have to consider when solving a question using the arc elasticity?

Answer 10

Which point of reference should be used?

Example:
The demand changes by -10 and the price changes by +5 (using the derivative of the function in respect to p for the rate of change, in the example in the book its -2) then you can either compute -10/5 * 50/50 (original values) or -10/5 * 40/55 (new values)

Question 11

Which three different types of elasticities of demand are there?

Answer 11

• Price elasticity of demand
• cross elasticity of demand
• income elasticity of demand

Question 12

What is the price elasticity of demand?

Answer 12

By how many % does the demand for good i change if the price of good i increases by 1%?

Question 13

What is the cross elasticity of demand?

Answer 13

By how many % does the demand for good i change if the price of good j increases by 1%?

Question 14

What is the income elasitcity of demand?

Answer 14

By how many % does the demand for good i change if the income increases by 1%?

Question 15

How do you compute the cross elasticity?

Answer 15

derivative of function in respect to p2 * p2/x1

Question 16

How do you compute the income elasticity?

Answer 16

Derivative of the function with respect to b * b/x1

Question 17

What does it mean if the demand is elastic?

Answer 17

The demand is elastic if a 1% increase in the price triggers a decrease in demand by more than 1%.
That is the (absolute) elasticity is larger than 1

Question 18

What does it mean if a demand is inelastic?

Answer 18

The demand is inelastic if a 1% increase in the price triggers a decrease in demand by less than 1%.
That is, the (absolute) elasticity is smaller than 1

Question 19

What does it mean if the demand is unit elastic?

Answer 19

The demand is unit elastic, if a 1% increase in the price triggers a decrease in demand by exactly 1%. That is, the (absolute) elasticity is exactly equal to 1

Question 20

What does the exact elasticity of a demand function depend on?

Answer 20

The exact elasticity of a demand function depens on the point (x, p) at which we compute it.

Thus, most demand functions have an area in which they are inelastic and another one in which they are elastic.

We can use a linear demand function to illustrate this. The slope (derivative) is identical for all points on the straight line, but the numbers for p/x with which we multiplay the slope to obtain the elasticity are changing.

Question 21

What does the elasticity of supply show us?

Answer 21

The elasticity of supply shows us the increase of supply (in percent) that is triggered by an increase in the price by 1 percent.

By how many % does the supply of good i change if the price of good i increases by 1%?