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Chapter 2: Problem 9

In Example 2.8 (page 76 ), we discussed the recent increase in world demand for copper, due in part to China's rising consumption. a. Using the original elasticities of demand and supply (i.e., \(\left.E_{S}=1.5 \text { and } E_{D}=-0.5\right),\) calculate the effect of a 20 -percent increase in copper demand on the price of copper. b. Now calculate the effect of this increase in demand on the equilibrium quantity, \(Q^{*}\) c. As we discussed in Example 2.8 , the U.S. production of copper declined between 2000 and 2003 Calculate the effect on the equilibrium price and quantity of both a 20 -percent increase in copper demand (as you just did in part a) and of a 20 -percent decline in copper supply.

Short Answer

Expert verified
a) The price of copper increases by 10% due to a 20% increase in demand; b) The equilibrium quantity increases by 30% as a result of this increase in demand; c) With a 20% increase in demand and a 20% decrease in supply, the equilibrium price increases by an additional 20% and the equilibrium quantity decreases by an additional 30%.

Step by step solution

01

Calculate Effect of Increase in Demand on Price

We start with the formula for percentage change in price given percentage change in quantity (demand) and elasticity of demand and supply: \(\%\Delta P = \(\%\Delta Q / (E_{S} - E_{D})\)\). Substituting the given values, we get: \(\%\Delta P = 20% / (1.5 - (-0.5)) = 10%\). So, the price of copper increases by 10%.
02

Calculate Effect of Increase in Demand on Equilibrium Quantity

Next, we calculate the effect of the increase in demand on the equilibrium quantity. Using the formula for percentage change in equilibrium quantity, \(\%\Delta Q^* = \%\Delta Q * E_{S} / (E_{S} - E_{D})\), substituting the values we get: \(\%\Delta Q^* = 20% * 1.5 / (1.5 - (-0.5)) = 30%\). So, the equilibrium quantity increases by 30%.
03

Calculate Effect of Increase in Demand and Decrease in Supply on Price and Quantity

Finally, we calculate the effect of both an increase in demand and decrease in supply on price and quantity using the same formulas but adjusting the percentage change in quantity and the supply elasticity. \(\%\Delta P = -20% / (1.5- (-0.5)) = -20%\). The price increases by an additional 20%. \(\%\Delta Q^* = -20% * 1.5 / (1.5 - (-0.5)) = -30%\). The equilibrium quantity decreases by a further 30%.

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Most popular questions from this chapter

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