Question

3) PED and Total Revenue (7 points) A demand curve is represented by the equation P = 60 - 20. The price has changed from $40 to $30. a. Graph this demand curve, labeling the two price points and their corresponding quantities demanded. (Hint: In addition to using the graph, you may also use the demand equation to find the quantities demanded for each price point b. On your graph, draw and label the total revenue, price effect and quantity effect as price changes from $40 to $30. C. Which effect from (a) is larger? What does that tell us about the effect of the price change on Total Revenue? Explain briefly how you know this is the case without necessarily calculating total revenue. d. Calculate the Total Revenue before and after the price change (at P=$40 and P=$30). Does this confirm your answer from part (b)? What does this tell us about the elasticity of demand between these points? e. Calculate the elasticity of demand between these points and briefly interpret. Does this confirm your answer from (d)?

Answer 1

=4 -- G=300

a) At price = 40,

40 = 60 - 2Q

Q = 10 units are demanded

At price = 30,

30 = 60 - 2Q

Q = 15 units are demanded.

b) When price falls from $40 to $30, quantity demanded rises from 10 to 15.

When price is $40, total revenue is CDEF

When price is $30, total revenue is GHIF

c) As price falls cause quantity demanded to rise, it is an example of normal good which induces consumers to buy more of the good when price rises as it raises the real income of consumers. It is an example of normal good with substitution effect dominating income effect, which says that people shifts to other goods faster or they are not stuck to this good which means this is not necessary good. Total revenue for luxury good when its price falls as more consumers consumes it. Elasticity of necessary good is elastic.

d) Total revenue

Total revenue when price is 40 = 40 * 10 = 400

Total revenue when price is 30 = 30 * 15 = 450

When price falls and revenue rises, demand is elastic.

e) Elasticity of demand = %change in quantity demanded / %change in price

%change in quantity demanded = [(15 - 10) / 10] * 100 = 50%

%change in price = [( 30 - 40 ) / 40] * 100 = -25%

Elasticity of demand = 50% / -25% = -2

We can ignore the negative sign here due to negative relationship between price and quantity demanded. So elasticity of demand is 2.

If Elasticity of demand is greater than 1, is is said to be elastic which confirms part d.

=4 -- G=300