$[7\mathrm{.}52/14\mathrm{.}32$ Points$]$

WANEF$$MAC$814\mathrm{.}4\mathrm{.}037.$

A study of a country's colleges and universities resulted in the demand equation $q=20,000-2p,$ where $q$ is the enrollment at a public college or university and $p$ is the average annual tuition $($plus fees$)$ it charges. $+$ Officials at Enormous State University have developed a policy whereby the number of students it will accept per year at a tuition level of $p$ dollars is given by $q=10,000+0\mathrm{.}5p.$ Find the equilibrium tuition price $\frac{?}{\text{b}\text{a}\text{r}}(p)$ and the consumers' and producers' surpluses at this tuition level. What is the total social gain at the equilibrium price? $[$Hint: See Example $3.]$

equilibrium tuition price

$\frac{?}{\text{b}\text{a}\text{r}}(p)=$$

$CS=$$

$PS=$$

$$60000000x$

consumers' surplus

producers' surplus

total social gain

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