Question

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

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

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%.

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%.

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%.

Key concepts

Equilibrium Price

The equilibrium price is when the demand for a product equals the supply, leading to a stable market where there is no pressure for the price to move up or down. In simple terms, it is the perfect match between what consumers are willing to pay and what producers are willing to accept.
For copper, the equilibrium price can be influenced by changes in demand or supply. When demand increases and supply remains constant, the equilibrium price typically rises. This happens because more buyers are willing to purchase copper at the current price, pushing it up due to increased competition.
Specifically, if the demand for copper increases by 20%, the formula to calculate the change in equilibrium price is:

• \( \%\Delta P = \frac{\%\Delta Q}{E_S - E_D} \)

Given that \(E_S = 1.5\) and \(E_D = -0.5\), substituting the values gives us a 10% increase in price.
Therefore, the equilibrium price climbs by 10% due to heightened demand.

Equilibrium Quantity

The equilibrium quantity is the amount of copper that is sold at the equilibrium price. This is the point where the quantity consumers want to buy equals the quantity producers want to sell. When we see changes in demand or supply, the equilibrium quantity shifts accordingly.
To find out how much the equilibrium quantity changes when demand increases, we use:

• \( \%\Delta Q^* = \frac{\%\Delta Q \cdot E_S}{E_S - E_D} \)

Substitute a 20% demand increase and the values of \(E_S = 1.5\) and \(E_D = -0.5\):

• \( \%\Delta Q^* = \frac{20\% \cdot 1.5}{1.5 - (-0.5)} = 30\% \)

This calculation tells us that the equilibrium quantity rises by 30% with the heightened demand. More copper is bought and sold at the new equilibrium price.

Copper Demand and Supply

Copper demand and supply are integral to determining the market's equilibrium price and quantity. When demand escalates but supply diminishes, it creates a complex dynamic that reshapes market equilibrium.
In our scenario, China's rising consumption catapults demand by 20%, while U.S. copper production falls, reducing supply by 20% during 2000-2003. When both events occur, it exacerbates the impact on market equilibrium.
To find the equilibrium impacts:

• First, calculate price change with varying supply: \(\%\Delta P = \frac{-20\%}{1.5 - (-0.5)} = -20\% \)
• Second, determine how equilibrium quantity changes: \(\%\Delta Q^* = \frac{-20\% \cdot 1.5}{1.5 - (-0.5)} = -30\% \)

This means the equilibrium price rises further by another 20%, while the equilibrium quantity drops by another 30%. These changes reflect how decreased supply pressures lead to higher prices and lower quantities available in the market. Understanding these shifts helps explain the fluctuating nature of copper markets worldwide.