$1(10$ points$)$ Two Extremes

Suppose the inverse demand function for ice cream at Guelph is $\backslash ($ p$=120-2$ q $\backslash ),$ where $\backslash ($ p $\backslash )$ is price, and $\backslash ($ q $\backslash )$ is quantity. There is only one ice cream seller at Guelph, and the firm's cost function is $\backslash ($ C$($q$)=2$ q$^\{2\}\backslash ).$

$1\mathrm{.}1$ Perfectly Competitive Market

$1.(1$ point$)$ Suppose the firm is a price taker, set up the profit maximization problem.

$2.(1$ point$)$ Derive the supply curve.

$3.(1$ point$)$ Find the equilibrium price and quantity when the firm is a price taker. $($hint: demand $=$ supply$).$

$4.(1$ point$)$ Find the consumer surplus. $($hint$,$ it will be helpful to draw the supply and demand curve$)$

$*$Submit the solutions on Courselink.

$5.(1$ point$)$ Find the producer surplus.