Question

Suppose equilibrium price in a market is \(\$ 5,\) and then a price ceiling of \(\$ 3\) is imposed. Assume (as in the chapter) that those who value the product the most are able to buy whatever quantity is available, and there is no black market. a. If supply is completely price inelastic between \(\$ 3\) and \(\$ 5,\) is there a dead weight loss? Briefly, why or why not? b. If demand is completely price inelastic between \(\$ 3\) and \(\$ 5,\) is there a dead weight loss? Briefly, why or why not?

Short answer

a. No, there is no deadweight loss when supply is completely price inelastic between \$3 and \$5 since the imposition of a price ceiling does not prevent any transactions that would have otherwise occurred. b. Similarly, there is no dead weight loss when demand is completely price inelastic between \$3 and \$5 because the imposition of a price ceiling doesn't prevent any transactions that would have been made otherwise.

Step-by-step solution

Analyze the impact of a price ceiling on a market with completely price inelastic supply

A price ceiling of \$3 is imposed on a market where supply is completely price inelastic between \$3 and \$5. This means that the quantity supplied remains the same irrespective of any price changes in this interval. It means that producers are willing and able to supply the same quantity at \$3 as they were at \$5. Consequently, the imposition of a price ceiling does not create a shortage and does not lead to a deadweight loss because it does not prevent any transactions that would otherwise occur.

Analyze the impact of a price ceiling on a market with completely price inelastic demand.

Here, a price ceiling of \$3 is also imposed, but now demand is completely price inelastic between \$3 and \$5. This means that the quantity demanded does not change with changes in price within this interval. This translates to consumers being willing to buy the same quantity of goods at \$3 as they were at \$5. Therefore, imposing a price ceiling does not create a surplus and does not lead to a deadweight loss as it does not prevent any transactions that would have been made otherwise.

Key concepts

Price Inelastic Supply

Price inelastic supply describes a situation where the quantity of a good that producers are willing to supply does not change, even when its price changes. This is an extreme scenario which assumes that factors such as costs of production or producer surplus are not affecting supply. For instance, if the supply of a product is completely price inelastic between \( \$3 \) and \( \$5 \), producers supply the same amount of their product regardless of whether they are able to sell it at \( \$5 \) or if they are forced by a price ceiling to sell it at \( \$3 \). This can occur in markets where producers might not be able to quickly adjust production due to long-term contracts, high fixed costs, or regulations.

For students, it’s essential to recognize that in a market where supply is completely price inelastic, imposed price ceilings, like the one in the exercise at \( \$3 \), do not create a shortage of the product, nor do they cause a deadweight loss. This is because the number of transactions in the market remains the same—the quantity supplied is unchanged.

Price Inelastic Demand

The concept of price inelastic demand refers to a market condition where the quantity demanded by consumers does not change in response to a price change. This implies a vertical demand curve where, regardless of the price increase or decrease, consumers still purchase the same amount of goods. If demand for a product is completely price inelastic within the price interval of \( \$3 \) and \( \$5 \), consumers will purchase the exact same amount of this good whether the price is at the higher end or if it hits the price ceiling of \( \$3 \).

Particularly when studying the effects of a price ceiling in an exercise, students should understand that in such markets, a set price limit lower than the equilibrium will not change the quantity demanded or generate a surplus of goods. As with price inelastic supply, deadweight loss does not occur under these specific circumstances because the amount of products exchanged in the market does not alter.

Deadweight Loss

Deadweight loss in economics signifies a loss of economic efficiency that can occur when equilibrium in a market is not achieved or something prevents the market from reaching equilibrium. This loss is the gap between the maximum total welfare that could be achieved in an unregulated market and the welfare that is actually achieved under market distortions, such as taxes, subsidies, or price controls.

In the context of the exercise, if a price ceiling leads to fewer transactions than would occur at the equilibrium price, it usually results in a deadweight loss, as the mutual benefits of trades that do not happen are lost to both consumers and producers. However, when dealing with completely price inelastic supply or demand, no such deadweight loss occurs with the imposition of a price ceiling, since the quantity of goods traded remains constant despite the price change. Thus, the total welfare under the price ceiling is the same as it would be without it.

Equilibrium Price

Equilibrium price is the price at which the quantity of a good demanded by buyers equals the quantity supplied by sellers, leading to a balance in the market. At this price, the market clears, meaning there is no surplus or shortage of goods, and the market reaches a state of economic efficiency. The equilibrium price is determined by the intersection of the supply and demand curves for a given product.

When students examine problems involving price controls, such as price ceilings, it's crucial to understand that these mandates can cause the market price to deviate from equilibrium. When a price ceiling is set below the equilibrium price, it can lead to shortages and inefficiencies, except in situations with completely price inelastic supply or demand, examples of which are outlined in the given exercise. Here, despite the price ceiling of \( \$3 \) being below the equilibrium price of \( \$5 \), the quantity of goods traded in the market remains unchanged in scenarios where supply or demand is price inelastic.