算出来是0.259，直接就约等于0.3？？是不是有点太多了

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​

whereQ^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.

The cross-price elasticity of demand for private universities with respect to the price of public universities is closest to:

选项：

A.

0.3.

B.

3.1.

C.

3.9.

解释：

A is correct.

From the demand function:

ΔQ^d_pr/ΔP_pu​=0.9(the coefficient in front of P_pu​ )

Solve for Q^d_pr = 8r−3.1P_pr​+0.8I+0.9P_pu

=84−3.1(38)+0.8(100)+0.9(18)=62.4

At P_pu = 18, price elasticity of demand=(ΔQ^d_pr​/ΔP_pu)(P_pu​/Q^d_pr​)​=(0.9)(18/62.4)=0.3

考点：交叉价格弹性

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 = 8r−3.1P_pr​+0.8I+0.9P_pu

=84−3.1(38)+0.8(100)+0.9(18)=62.4

之后我们再利用交叉价格弹性公式求解，即，

(ΔQ^d_pr​/ΔP_pu)(P_pu​/Q^d_pr​)​=(0.9)(18/62.4)=0.3