If the government imposes a price ceiling of 4 units on the market described by functions Q_d = 90 - 10P and Q_s = 10 + 6P, what will be the market outcome?
Understand the Problem
The question is asking to analyze the market outcome resulting from a price ceiling set by the government. This involves finding the quantities demanded and supplied at the imposed price and determining if there is excess demand, excess supply, or if the market remains in equilibrium.
Answer
There is a shortage in the market.
Answer for screen readers
There is a shortage in the market when the quantity demanded is greater than the quantity supplied at the price ceiling.
Steps to Solve
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Identify the price ceiling Determine the price ceiling imposed by the government and note its value. This will be the maximum price that can be charged for a good or service in the market.
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Determine the quantity demanded at the price ceiling Using the demand equation or graph, find the quantity demanded by substituting the price ceiling value into the demand function. This gives the total amount consumers want to buy at that price.
For example, if the demand function is $Q_d = 100 - 2P$ and the price ceiling is $P = 30$, calculate:
$$ Q_d = 100 - 2(30) = 40 $$
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Determine the quantity supplied at the price ceiling Using the supply equation or graph, find the quantity supplied by substituting the price ceiling value into the supply function. This provides the total amount producers are willing to sell at that price.
For example, if the supply function is $Q_s = 20 + 3P$ and the price ceiling is $P = 30$, calculate:
$$ Q_s = 20 + 3(30) = 110 $$
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Compare the quantity demanded and supplied Now, compare the quantity demanded ($Q_d$) and the quantity supplied ($Q_s$) at the price ceiling:
- If $Q_d > Q_s$, there is excess demand (shortage).
- If $Q_d < Q_s$, there is excess supply (surplus).
- If $Q_d = Q_s$, the market is in equilibrium.
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Conclusion on market outcome Based on the comparison, conclude whether there is a shortage, surplus, or equilibrium status in the market under the price ceiling.
There is a shortage in the market when the quantity demanded is greater than the quantity supplied at the price ceiling.
More Information
When a price ceiling is implemented, it often leads to a situation where the quantity demanded exceeds the quantity supplied, resulting in a shortage. This means not all consumers can purchase the good at the set price, which can lead to long lines, black markets, or other inefficiencies in the market.
Tips
- Failing to substitute the price ceiling correctly into both the demand and supply equations.
- Misinterpreting the results; remembering that a price ceiling can lead to a shortage if demand exceeds supply is crucial.
- Not clearly defining the demand and supply equations prior to solving the problem.
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