Question

The market demand function for four-year private universities is given by the equation:  Q^d_pr = 84 - 3.1P_pr + .8I +.9P_pu

Where Q^d_pr is the number of applicants to private universities per year in thousands,P_pr is the average price of private universities (in thousands of USD),  I is the household monthly income (in thousands of USD), and P_pu is the average price of public (government-supported) universities (in thousands of USD). Assume that P_pr is equal to 38, I is equal to 100, and P_pu is equal to 18

a- Compute the price elasticity of demand for private universities

b- Compute the income elasticity for private universities

c- Compute the cross-elasticity of demand for private universities

d- If the two goods are classified as complementary, the cross elasticity between them is

e- What will be the cross elasticity of demand between two goods, if the two goods are classified as substitutes

Answer 1

The market demand is given as

Qd = 84 - 3.1.Ppr + 0.8.I + 0.9.Ppu

Where Qd is the number of applicants to private universities per year in thousands,P_pr is the average price of private universities (in thousands of USD),  I is the household monthly income (in thousands of USD), and P_pu is the average price of public (government-supported) universities (in thousands of USD).

Now, we are given that,

Ppr = 38

I = 100

Ppu = 18

Puttimg these in Qd we get

Qd = 84 - 3.1×38 + 0.8×100 + 0.9×18

or, Qd = 62.4

Also, from the demand function, we get

dQd/dPpr = -3.1

dQd/dI = 0.8

dQd/dPpu = 0.9

Let's answer the following questions one by one.

(a) The price elasticity of demand for private universities is

Epr = (dQd/dPpr).(Ppr/Qd)

or, Epr = (-3.1)×(38/62.4)

or, Epr ~ -2

The price elasticity of demand for private universities is (-2).

(b) The income elasiticity of demand for private universities is

EI = (dQd/dI).(I/Qd)

or, EI = (0.8)×(100/62.4)

or, EI = 1.3

The income elasiticity of demand for private universities is 1.3.

(c) The cross elasiticity is

Ec = (dQd/dPpu).(Ppu/Qd)

or, Ec = (0.9)×(18/62.4)

or, Ec = 0.26

The cross elasticity is 0.26.

(d) If two goods are complements, then if price of one good rises, then the demand for the other good falls.

Hence, the cross elasticity of demand is negative between two complements.

(e) If two goods are substitutes, then if price of one good increases, then the demand for the other good increases.

Hence, the cross elasiticity of demand is positive between two substitutes.

Hope the solutions are clear to you my friend.