Suppose that, at the market equilibrium price of natural gas, the price elasticity of demand is -1.2 and the p?

Suppose that, at the market equilibrium price of natural gas, the price elasticity of demand is -1.2 and the price elasticity of supply is 0.6. What will result from a price ceiling that is 10 percent below the market equilibrium price?

A) A shortage equal to 1.8 percent of the market equilibrium quantity.
B) A shortage equal to 0.6 percent of the market equilibrium quantity.
C) A shortage equal to 18 percent of the market equilibrium quantity.
D) A shortage equal to 6 percent of the market equilibrium quantity.

can anyone explain this problem to me? thanks alot.

2 Responses to “Suppose that, at the market equilibrium price of natural gas, the price elasticity of demand is -1.2 and the p?”

  1. Faz Says:

    Let d be % change in qty demanded, then
    d / -10 = -1.2, so d = 12

    Let s be % change in qty supplied, then
    s / -10 = 0.6, so s = -6

    12 – (-6) = 18
    C) A shortage equal to 18 percent of the market equilibrium quantity.

  2. jerry w Says:

    Since you are asked to compare the shortage to the equilibrium quantity, then you will only need to figure out how the quantity that is actually traded in the market differs from the equilibrium (with no price ceiling) would be. You don’t need to know what the total shortage at the price ceiling is, only the portion of the shortage that is below equilibrium.

    For this reason, you do not need to use both the price elasticity of demand and the elasticity of supply in your calculations. All you need to do is use the one that sets the limit below equilibrium. Since the demand curve slopes downward and the supply curve slopes upward, the quantity traded in the market at a price below equilibrium will be limited by the supply curve. The demand curve would be at a quantity above equilibrium, but that quantity cannot be traded in the marketplace; the supply curve limitation would be all the quantity that would be available for purchase, thus a shortage.

    So just figure the change in quantity as it relates to the supply curve. At a price elasticity of supply of +0.6, and a 10% decrease in price, use the formula p.e.s = %change in quantity divided by %change in price, you get:

    0.6 = x / 10; x = 6. So the change in quantity, compared to the equilibrium quantity, will be 6% less than the equilibrium quantity.

    the answer is D.