Suppose the demand in any given month for a commodity is represented by the foll

Question

Suppose the demand in any given month for a commodity is represented by the following equation: QD = 40,000 - 4.0 P, where P represents the price per unit and QD is quantity demanded. Next, suppose QS represents quantity supplied. The relationship between QS and the price per unit is given by the following equation: P = 200 + .20 . QS. Given this information, what is the market clearing ("equilibrium") price? What is the equilibrium quantity? How much revenue will sellers of the commodity receive from sales of the commodity each month? At the equilibrium quantity demanded and equilibrium price, how much will purchasers of this commodity spend per month? What is the amount of consumer surplus received by buyers of the commodity? What is the amount of producer surplus received bv sellers of the commodity

Explanation / Answer

Equilirbium is where the demand is equal to supply.

Q=40000-4P

P= 10000-0.25Q

Demand = Supply

10000-0.25Q=200+0.2Q

9800=0.45Q

Q = 980000/45 = 21777.78 = 21778

P=$4555.5

Seller will receive:

TR=PQ = 4555.5 x 21778=$99210888

The amount that purchaser will spend each month will always be equal to what sellers receive each month, $99210888.

Consumer surplus:

0.5x (PQ=0-P) x Q

0.5x(10000-4555.55) x 21778

=59284616.05

Producer surplus:

0.5 x P xQ

0.5x 4555.55 x 21778

=$49605383.95

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