Math Problem Statement
Solution
The linear regression models for price-supply and price-demand data are as follows:
-
Price-Supply Model:
where is supply (in billions of bushels) and is price (in dollars). -
Price-Demand Model:
where is demand (in billions of bushels) and is price (in dollars).
Equilibrium:
The equilibrium occurs when supply equals demand. The equilibrium supply and demand are approximately 7.68 billion bushels, and the equilibrium price is about $2.38 per bushel.
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Here are 5 related questions to expand on this:
- How is linear regression used to model price-supply and price-demand relationships?
- What does the slope of the price-supply line signify?
- How does the intercept affect the interpretation of both models?
- How could changes in supply and demand factors shift the equilibrium price?
- What real-world factors might affect the accuracy of these regression models?
Tip: In economics, equilibrium prices adjust when either the supply or demand curve shifts due to factors like technological advancements or changes in consumer preferences.
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Math Problem Analysis
Mathematical Concepts
Linear Regression
Slope-Intercept Form
Equilibrium in Economics
Formulas
y = mx + b
Equilibrium condition: Supply = Demand
Theorems
Linear Regression (Least Squares Method)
Suitable Grade Level
Grades 10-12
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