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One of the luxury car manufacturers usually wants to make a limited number of automobiles in...

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Advance Math

One of the luxury car manufacturers usually wants to make alimited number of automobiles in a given year and the company’s aimis to expand their profit margins in each car sold. After doing theanalysis on the sales of their cars, the company determined thebelow 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 themarket equilibrium.

b) If the manufacturer restricts the number of cars manufacturedand sold to 800 at the demand price of $15,000, how much is thetotal producer surplus?

c) A manufacturer wants to maximize the producer surplus andhence determine the quantity (give the whole number) at which thiscan be possible. Also determine the producer surplus at thisquantity.

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