Objective $2$ The consumers' surplus, the producers' surplus, the equilibrium quantity

and the equilibrium price.

Example College tuition vs enrollment A study of U$.$S$.$ Colleges and universities resulted in the

demand equation $D(p)=q=20,000-2p,$ where $q$ is the enrollment at a public college or

university and $p$ is the average annual tuition $($plus fees$)$ it charges. Officials at Some 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 $S(p)=q=7,500+0\mathrm{.}5p.$

a$.$ Find the equilibrium tuition price and the equilibrium number of students the university will

accept per year. Write an interpretation.

b$.$ Find the consumers' surplus at this tuition level. Write an interpretation. $($Hint: write the

demand equation in terms of $q,D(q),$ first$)$

c$.$ Find the producers' surplus at this tuition level. Write an interpretation. $($Hint: write the

supply equation in terms of $q,S(q)$ first$).$

d$.$ Graph using Desmos the demand and supply equations and indicate the equilibrium point, the

consumers' surplus and the producers' surplus.