Question

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? 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) A 20 percent increase in copper demand would cause the price of copper to rise by 30 percent. b) The effect of this increase in demand would cause the equilibrium quantity to decrease by 10 percent. c) When considering both a 20 percent increase in demand and a 20 percent decrease in supply, the equilibrium price would remain the same and the equilibrium quantity would decrease by 20 percent.

Step-by-step solution

Calculate the effect of increase in demand

We are given that the elasticity of supply \(E_{s}\) is 1.5 and the elasticity of demand \(E_{D}\) is -0.5. There's a 20% increase in demand. The formula for percentage change in price is \(\Delta P=\frac{E_{s}}{E_{s}-E_{D}} \times \Delta D\). By inserting the values we get, \(\Delta P = \frac{1.5}{1.5 - (-0.5)} * 20% = 30%\). Thus, the price of copper would rise by 30%.

Calculate the effect on equilibrium quantity

The formula for the percentage change in quantity is \(\Delta Q = \frac{E_{D}}{E_{s}-E_{D}} \times \Delta D\). Inserting the given values, we calculate \(\Delta Q = \frac{-0.5}{1.5 - (-0.5)} \times 20% = -10%\). So, the equilibrium quantity \(Q^{*}\) would decrease by 10%.

Calculate the effects of increase in demand and decrease in supply

Now, with a 20% increase in demand and a 20% decrease in supply, the percentage change in price is given by \(\Delta P = \frac{E_{s}}{E_{s}-E_{D}} \times \Delta D + \frac{E_{s}}{E_{s}-E_{D}} \times -\Delta S\). Inserting the values, we get \(\Delta P = \frac{1.5}{2.0} \times 20% + \frac{1.5}{2.0} \times -20% = 0\). There is no change in price. The percentage change in quantity is given by \(\Delta Q = \frac{E_{D}}{E_{s}-E_{D}} \times \Delta D + \frac{E_{s}}{E_{s}-E_{D}} \times -\Delta S\). Inserting the values, we get \(\Delta Q = \frac{-0.5}{2.0} \times 20% + \frac{1.5}{2.0} \times -20% = -20%\). Thus, the equilibrium quantity \(Q^{*}\) would decrease by 20%.

Key concepts

Elasticity of Demand

Elasticity of demand is a crucial concept in economics that measures how a change in price leads to a change in quantity demanded. To understand it deeply, picture this scenario. Imagine you're at a store eying your favorite chocolate, which has been priced higher than last time. Will you buy the same amount, less, or possibly none at all? Your response reflects demand elasticity. When the chocolate's price hike doesn't significantly affect the amount you buy, your demand is inelastic. But if you decide to buy much less or skip it altogether, your demand shows elasticity.

In technical terms, demand elasticity, often denoted as \( E_{D} \) , is calculated by dividing the percentage change in the quantity demanded by the percentage change in price. A value greater than 1 indicates elastic demand; consumers are highly responsive to price changes. A value less than 1 signifies inelastic demand; consumers are not as swayed by price fluctuations. And if it equals exactly 1, economists call it unit elastic demand.

Elasticity of Supply

Opposite to demand, the elasticity of supply gauges how sensitive the quantity supplied is to a change in price. It answers this question: when the price of a product increases, do producers supply a lot more, or does their supply reaction lag behind?

The elasticity of supply, represented by \( E_{s} \) , is figured out similarly to demand elasticity, by dividing the percentage change in quantity supplied by the percentage change in price. Here's an interesting point: supply is elastic when the value of \( E_{s} \) is greater than 1, implying producers are quick to boost output as prices go up. Conversely, when \( E_{s} \) is below 1, the supply is considered inelastic because producers aren't as reactive to price changes. If precisely 1, it's unit elastic, indicating a proportional response to price shifts.

Market Equilibrium

Market equilibrium is a key moment when forces of supply and demand are in perfect harmony; a product's supply matches its demand. Think of it as a dance where both partners move in sync. In terms of price and quantity, this balance is where the curve of demand intersects with the curve of supply.

Here's the catch: equilibrium is a moving target. If, let's say, a new fad or a sudden shortage jolts the market, equilibrium shifts. The price and quantity at which buyers and sellers agree to transact undergoes a change. In our chocolate example, if suddenly everyone wanted one and the store had only a limited supply, the price might go up until demand and supply reach a new equilibrium point.

Price Determination

Price determination is like finding the sweet spot in the market, the price that balances buyers' willingness and ability to buy with sellers' willingness and ability to sell. This sweet spot is struck at the equilibrium price, also known as the market-clearing price. It's where the quantity demanded meets the quantity supplied – no shortages or excesses.

How does price get determined though? It's essentially a tug-of-war between consumer demand and producer supply. When demand surges, prices tend to climb until the market settles at a new equilibrium. Inversely, if supply overtakes demand, prices typically slide. All these shifts occur until the market reaches equilibrium, and that's how we regularly experience price determination in action across different markets.