The cross-price elasticity of demand for private universities with respect to the average price of public universities

Question:

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

A. 0.3 .

B. 3.1.

C. 3.9.

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

\[ Q_{p r}^{d}=84-3.1 P_{p r}+0.8 I+0.9 P_{p u} \]

where $Q_{p r}^{d}$ is the number of applicants to private universities per year in thousands, $P_{p r}$ is the average price of private universities (in thousands of USD), $I$ is the household monthly income (in thousands of USD), and $P_{p u}$ is the average price of public (government-supported) universities (in thousands of USD). Assume that $P_{p r}$ is equal to $38, I$ is equal to 100 , and $P_{p u}$ is equal to 18.