Question

Question Help Concept Question 7.4 The price elasticity of demand for natural gas is -0.9, and the price elasticity of supply for natural gas is 0.6. If the government imposes a ceiling price for natural gas that is 10 percent below the equilibrium price the result will be equal to percent of the equilibrium quantity. Enter your rosponse as a whole number. Do not use a percentage sign.)

Answer 1

Supposing the equilibrium quantity be Q. From the price elasticity of demand, we have $\dpi{80} \frac{percentage \; change \; in \; demand}{percentage \; change \; in \; price} = -0.9$ , and if price is decreased by 10 percent, then $\dpi{80} \frac{percentage \; change \; in \; demand}{-10} = -0.9$ or $\dpi{80} percentage \; change \; in \; demand = 9$ . If demand is increased by 9%, that mean the new quantity demanded is $\dpi{80} Q + Q*0.09$ or $\dpi{80} 1.09Q$.

From the price elasticity of supply, we have $\dpi{80} \frac{percentage \; change \; in \; supply}{percentage \; change \; in \; price} = 0.6$ , and if the price is decreased by 10 percent, then $\dpi{80} \frac{percentage \; change \; in \; supply}{-10} = 0.6$ or $\dpi{80} percentage \; change \; in \; supply = -6$ . If the supply is decreased by 6 percent, that means the new quantity supplied is $\dpi{80} Q - 0.06*Q$ or $\dpi{80} 0.94*Q$.

The excess demand would be of amount $\dpi{80} ED = Q_D - Q_S$ or $\dpi{80} ED = 1.09Q - 0.94Q$ or $\dpi{80} ED = 0.15Q$ . As can be seen, the ED is 15% of the equilibrium quantity.

Hence, the result will be a excess demand/market shortage equal to 15 percent of the equilibrium quantity.