6. The demand curve for a product has equation p = 100 e^(-0.008q) and the supply curve has equation p = (4√q) + 10 , where q is the quantity and p is the price in dollars/unit.
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 tend to push the prices closer to the equilibrium price?
c) At the equilibrium price, calculate and interpret the consumer and producer surplus.
Supply, demand and equilibrium are analyzed using integrals. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.