Question: The demand curve for a product has equation \(p=100{{e}^{-0.008q}}\) and the supply curve has equation \(p=4\sqrt{q}+10\) for \(0\le q\le 500\), where q is the quantity and p is the price.

(a) At a price of $50, what quantity are consumers willing to buy and what quantity are producers willing to supply? Will the market push prices up or down?

(b) Find the equilibrium price and quantity. Does your answer to part (a) support the observation that market forces to push prices closer to the equilibrium price?

(c) At the equilibrium price, calculate and interpret the consumer and producer surplus.