In: Advanced Math
One of the luxury car manufacturers usually wants to make a limited number of automobiles in a given year and the company’s aim is to expand their profit margins in each car sold. After doing the analysis on the sales of their cars, the company determined the below supply and demand functions of the cars sold:
Supply function: P = 1000 + Q^2
Demand function: P = 21000 – Q^2
a) Calculate the producer, consumer and total surplus at the market equilibrium.
b) If the manufacturer restricts the number of cars manufactured and sold to 800 at the demand price of $15,000, how much is the total producer surplus?
c) A manufacturer wants to maximize the producer surplus and hence determine the quantity (give the whole number) at which this can be possible. Also determine the producer surplus at this quantity.