Asked by Himani Patel on Apr 24, 2024
Verified
The demand function for orange juice is q 269 9p and the supply function is q 9 4p, where q is the number of units sold per year and p is the price per unit, expressed in dollars.The government decides to support the price of orange juice at a price floor of $24 per unit by buying orange juice and destroying all that it has purchased.How many units must the government destroy per year?
A) 52
B) 56
C) 25
D) 61
E) 57
Price Floor
A government- or group-imposed price control or limit on how low a price can be charged for a product, good, commodity, or service.
Supply Function
A mathematical relation showing the amount of goods a supplier is willing and able to provide to the market at various prices, holding all other factors constant.
Demand Function
A demand function quantifies the relationship between the price of a good and the quantity demanded by consumers, holding other factors constant.
- Understand how supply and demand functions determine the equilibrium price and quantity in a market.
- Analyze the impact of government interventions such as price floors, taxes, and price ceilings on market equilibrium.
Verified Answer
SA
Samer AlanbakiMay 02, 2024
Final Answer :
A
Explanation :
To find the quantity the government must destroy, first, we calculate the quantity supplied and demanded at the price floor of $24. For the demand function, q = 269 - 9p, substituting p = 24 gives q = 269 - 9(24) = 269 - 216 = 53. For the supply function, q = 9 + 4p, substituting p = 24 gives q = 9 + 4(24) = 9 + 96 = 105. The government must destroy the difference between the quantity supplied and demanded, which is 105 - 53 = 52 units.
Learning Objectives
- Understand how supply and demand functions determine the equilibrium price and quantity in a market.
- Analyze the impact of government interventions such as price floors, taxes, and price ceilings on market equilibrium.