问一道题：NO.PZ2016010802000025

问题如下：

The market demand function for four-year private universities is given by the equation

Q^d_pr ​=84−3.1P_pr​+0.8I+0.9P_pu​

where Q pr d 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.

The income elasticity of demand for private universities is closest to:

选项：

0.5.

0.8.

1.3.

解释：

C is correct.

From the demand function:

Solve for Q^d_pr :
∆Q /∆I^d_pr = 0.8 (coefcient in front of the income variable)
Q^d_pr = 84 – 3.1P_pr + 0.8I + 0.9P_pu
= 84 – 3.1(38) + 0.8(100) + 0.9(18)
= 62.4

At I = 100, the income elasticity of demand

(ΔQ^d_pr​/ΔI)(I​/Q^d_pr​)​=(0.8)(100/62.4)=1.3

考点：需求收入弹性

解析：题目给出了需求函数的表达式，带入数字，先求的私立大学的需求量，即：

Q^d_pr = 84 – 3.1P_pr + 0.8I + 0.9P_pu
= 84 – 3.1(38) + 0.8(100) + 0.9(18)
= 62.4

之后我们再利用需求收入弹性公式求解，即，

(ΔQ^d_pr​/ΔI)(I​/Q^d_pr​)​=(0.8)(100/62.4)=1.3