Read: Supply & Demand $+$ Market Equilibrium

Read: Consumer and Producer Surplus

Question $2$ Let DemandPrice $(q)=110-\frac{q}{3}$ and SupplyPrice$(q)=10+\frac{q}{2}.$

Assume we have a free market and that goods are sold at market equilibrium.

consumer surplus $={\displaystyle \underset{0}{\overset{q_s}{}}}($ demand function $(q)-p_s)dq$

producer surplus $={\displaystyle \underset{0}{\overset{q_s}{}}}(p_s-$supply function $(q))dq$

a$.$ Find the point of equilibrium.

b$.$ Find the consumer surplus.

c$.$ Find the producer surplus.

d$.$ Find the total social gain.