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Suppose that the world price of oil is roughtly $80 per barrel and that the world demand and total world supply of oil equal 34 billion barrels per year (bb/yr), with a competitive supply of 20 bb/yr and 14bb/yr from OPEC. Statistical studies have shown that the short-run price elasticity of demand for oil is -0.05, and the short-run competitive price elasticity of supply is 0.10. Using this information, derive linear demand and competitive supply curves for oil.

Let the demand curve be of the general for Q=a-bP and the competitive supply curve be of the general form Q=c+dP, where a, b, c, and d are constants.

The equation for the short-run demand curve is: Q= ______

The equationfor the short-run competitive supply curve is: Q= ______

Explanation / Answer

(1) Linear demand curve

Let the linear demand curve be

Q = a - bP

Given:

When P = 60, Quantity demanded Qd = 34

Lng run price elasticity of demand = - 0.4, implying that with every 1% change in price, total demand changes by 0.4% in the opposite direction.

Let P increase 250% to 210. Then Q decreases by 100%, and new Qd = 0

So, the Y-intercept of demand curve is P = 210

[P = 210 - bQ]

Let P increase 10% to 66. Then Qd will decrease by 4%, and new Qd = 32.64

So, 66 = 210 - b x 32.64

Or, b = (210 - 66) / 32.64 = 4.41

So, the equation for linear demand curve is

P = 210 - 4.41 Q

(2) Long run supply curve

The supply curve is

Q = c + dP

When p = 60, Qs = 20

20 = c + 60d

elasticity of supply = 0.40

So, every 1% increase (decrease) in price, quantity supplied increases (decreases) by 0.4%.

If P increases by 10% to 66, Qs increases 4% to 20.8

So, we get

20.8 = c + 66 d ....(1)

20 = c + 60d .... (2)

(1) - (2):

0.80 = 6d

So, d = 0.80 / 6 = 13.33

Substituting in (2):

20 = c + (13.33 x 60)

c = - 779.80

So the supply curve equation is:

Q = - 779.80 + 13.33P

(3) In the long run, price is expressed as a function of quantity. So,

(a) Long run demand curve: P = (a - Q) / b

(b) Long run competitive supply curve: P = (Q - c) / d

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