Question

1. In Example 2.8 (page 74), we discussed the recent decline in world demand for copper, due in part to China’s decreasing consumption. What would happen, however, if China’s demand were increasing?

2. Using the original elasticities of demand and supply (i.e., ES = 1.5 and ED = -0.5), calculate the effect of a 20-percent increase in copper demand on the price of copper.

3. Now calculate the effect of this increase in demand on the equilibrium quantity, Q*.

4. 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

1. The price increased by 9.67%.

2. The quantity rises by 14.5%.

3. The price increases 22.33%, and quantity will increase by 6.78%.

Step-by-step solution

Explanation for part (a)

The demand curve is Q_D=27 - 3P, and the supply curve is Q_S= -9 + 9P.

The demand increases by 20%; thus, the new demand curve will be:

$$\begin{gathered} Q_D^{\text{'}}=1.2Q_D \\ =1.2(27-3P) \\ =32.4-3.6P \\ \mathrm{At}\mathrm{equilibrium}, \\ \mathrm{D}=\mathrm{S} \\ 32.4-3.6\mathrm{P}=-9+9\mathrm{P} \\ 9\mathrm{P}+3.6\mathrm{P}=32.4+9 \\ 12.6\mathrm{P}=41.4\mathrm{P} \\ \mathrm{P}=\$3.29 \end{gathered}$$

Before the change in demand, the price was $3; thus, with the rise in demand by 20%, the price changes by 9.67%$\left(\frac{3.29-3}{3}\times 100=9.67\%\right)$

Explanation for part (b)

At $3.29, the equilibrium quantity will be:

Q = -9 +9(3.29)

=-9 + 29.61

= 20.61

The equilibrium quantity will be 20.61 million metrics.

Before the demand changes, the quantity was 18 million metrics; thus, with the rise in demand by 20%, the quantity changed by 14.5%$\left(\frac{20.61-18}{18}\times 100=14.5\%\right)$

Explanation for part (c)

The demand increases by 20%. The supply declined by 20%; thus, the new supply curve will be:

Q_S^'= 0.8Q_S

= 0.8(-9 + 9P)

= -7.2-7.2P

At equilibrium,

$$\begin{gathered} \mathrm{Q}{\text{'}}_{\mathrm{D}}=\mathrm{Q}{\text{'}}_{\mathrm{S}} \\ 32.4-3.6\mathrm{P}=-7.2+7.2\mathrm{P} \\ 7.2\mathrm{P}+3.6\mathrm{P}=32.4+7.2 \\ 10.8\mathrm{P}=39.6\mathrm{P} \\ \mathrm{P}=\$3.67 \\ Q=-7.2+7.2\left(3.67\right) \\ =-7.2+26.424 \\ =19.22 \end{gathered}$$

The new equilibrium price will be $3.67, and the quantity will be 19.22 million metrics.

The demand increases by 20% and supply decreases by 20%; before the change, the price is $3, and quantity is 18 million metrics; thus, the change in price and quantity will be:

$$\begin{gathered} △P\%=\frac{3.67-3}{3}=22.33\% \\ △Q\%=\frac{19.22-18}{18}=6.78\% \end{gathered}$$

The demand increases by 20%, supply decreases by 20%; then, price rises by 22.33%, and quantity rises by 6.78%.