Question

Suppose that a U.S. firm wants to identify the optimal amount of petroleum to extract. The U.S. petroleum market comprises 10 identical firms, and each firm extracts the same quantity of petroleum and sells each unit at the market price. The functional form of the U.S. market demand for petroleum is given by Q(P) = 475 −1/2P, and the inverse market supply function is given by P(Q) = 65 + 3Q. Prices are represented in U.S. dollars and quantities are measured in thousands of gallons.

(a) How much petroleum do you recommend that each firm extract in order to be efficient? What would be the net benefits for each firm?

(b) Graph the U.S. market for petroleum. For full credit, label the equilibrium point as well as all axes, curves, and intercepts.

(c) Indicate consumer and producer surplus on your graph.

(d) Compute and interpret the market price elasticity of demand at equilibrium. Does the price elasticity you calculated make sense for the petroleum market? Explain your answer in 20 words or less.

Answer 1

a)

Given the market demand and supply functions, the efficient level of output would be the level where market demand is equal to the market supply. Therefore calculating form demand = supply, we get,

Demand -

Q=475-(1/2)P

P=950-2Q

Supply-

P=65+3Q

950-2Q=65+3Q

950-65=5Q

Q=177 and P=596

Therefore, efficient level of output=177, given that their are 10 firms each firm should extract 17.7 units.

b)

The following graph shows the demand and the supply function where the market equilibrium is at point E where Q=177 and P=596

c)

The following graph shows the Producer and consumer surplus. The area os the triangle F depicts the consumer surplus and the area of the triangle G depicts the producers surplus.

d)

The price elasticity of demand is given by the following formula-

Ed= (dq/dp)*(p/q)

Therefore differentiating the deamand curve,

dq/dp=0-1/2

dq/dp=-1/2

Ed= (-1/2)*(596/177)

Ed=-1.683

The elasticity of demand shows that the demand curve is elastic, this is because the market has 10 firms with identical product knowledge therefore with a rise in price the corresponding change in quantity would be greater since the consumer can purchase from the other available 10 firms. Therefore, due to the existence of 10 firms, the demand is elastic.