Question

4. There are two types of buyers of ale in Temeria: nobles and common people. The ale demand for nobles is QN=40-P (for P ≤ 40). The ale demand for common people is QF=100-4P (for P ≤ 25).

a. Graph the ale demand curves for both types of buyers. (3 points)

b. Find an equation for the market demand, QM as a function of P. (5 points)

c. Graph the market demand curve. At what price(s) is the market demand curve kinked? (4 points)

d. Calculate the price elasticity of market demand at P=20. (4 points)

Answer 1

a.





b.
Market demand = Demand by nobles + Demand by common
Market demand function = demand function of nobles + demand function of common

Market demand function will be:
QM = 140 - 5P (for P <=25) and
QM = 40 - P (for P > 25)


c.


Market demand curve kinked at the price of 25 a unit of Ale.


d.
Price elasticity of market demand at P=20

It was: At price 19, Qty demanded is 45
It is: At price 20, Qty demanded is 40

Now let us calculate Price elasticity of demand:

We know that:
Ed = (-) ΔQ/ΔP * P/Q

Putting the values, we get:
Ed = (-) (40-45)/(20-19) * 19/45
Ed = (-) -5/1 * 19/45
Ed = 2.11 (times)