Math Problem Statement

The table contains price-supply data and price-demand data for corn. Find a linear regression model for the price-supply data where x is supply (in billions of bushels) and y is price (in dollars). Do the same for the price-demand data. Find the equilibrium price for corn.

Solution

The linear regression models for price-supply and price-demand data are as follows:

  1. Price-Supply Model:
    y=0.22x+0.66y = 0.22x + 0.66
    where xx is supply (in billions of bushels) and yy is price (in dollars).

  2. Price-Demand Model:
    y=0.14x+3.48y = -0.14x + 3.48
    where xx is demand (in billions of bushels) and yy 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:

  1. How is linear regression used to model price-supply and price-demand relationships?
  2. What does the slope of the price-supply line signify?
  3. How does the intercept affect the interpretation of both models?
  4. How could changes in supply and demand factors shift the equilibrium price?
  5. 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