Consumer Theory and Budget Constraints
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Questions and Answers

What does the budget line represent in a microeconomic context?

  • The set of bundles that cost less than m
  • The maximum consumption of good 1 only
  • The set of bundles that cost exactly m (correct)
  • The minimum consumption necessary to meet m

What does the slope of the budget line indicate?

  • The overall market demand for good 1
  • The opportunity cost of consuming good 1 in terms of good 2 (correct)
  • The vertical distance between goods 1 and 2
  • The total consumption of both goods

How can the two intercepts of the budget line be determined?

  • By setting p1 equal to m
  • By averaging the prices of both goods
  • By substituting x1 and x2 values into the budget equation
  • By determining the maximum quantities of each good based on prices (correct)

How is the rate of substitution between good 1 and good 2 expressed mathematically?

<p>By using the slope of the line as ∆x2/∆x1 (B)</p> Signup and view all the answers

When a consumer increases their consumption of good 1, what must occur to maintain the budget constraint?

<p>The amount consumed of good 2 must decrease (B)</p> Signup and view all the answers

What does the budget constraint equation represent?

<p>The maximum expenditure on goods compared to available income (D)</p> Signup and view all the answers

In the context of the budget constraint, if p1 increases, what happens to the budget set?

<p>The budget set shrinks (D)</p> Signup and view all the answers

How is good 2 defined in the two-good model?

<p>As a composite good representing all other goods (B)</p> Signup and view all the answers

If a consumer's income (m) increases, what is the immediate effect on the budget constraint?

<p>The budget constraint line shifts outward (B)</p> Signup and view all the answers

Which statement about the budget constraint is true?

<p>It determines the affordability of goods based on income (A)</p> Signup and view all the answers

In the equation $p_1x_1 + p_2x_2 \leq m$, what does the term $p_2x_2$ represent?

<p>The spending on good 2 (A)</p> Signup and view all the answers

Which of the following would decrease the set of affordable consumption bundles?

<p>An increase in the price of good 1 (A)</p> Signup and view all the answers

If a consumer spends all their income on good 1, what can be inferred about their consumption of good 2?

<p>They cannot afford good 2 (A)</p> Signup and view all the answers

What does the budget constraint formula represent?

<p>The total expenditure on goods must equal the consumer's income. (C)</p> Signup and view all the answers

How does increasing the income (m) affect the budget line?

<p>It leads to a parallel outward shift of the budget line. (D)</p> Signup and view all the answers

What would happen if the price of good 1 (p1) increases?

<p>The budget line becomes steeper. (C)</p> Signup and view all the answers

When a consumer's consumption of good 1 (x1) is less than or equal to x̄1, what is the slope of the budget line?

<p>−(p1 / p2) (C)</p> Signup and view all the answers

What does it mean to assign one price a value of 1 in economic theory?

<p>It defines a numeraire, simplifying the measurement of other prices. (A)</p> Signup and view all the answers

In terms of budget lines, how does multiplying all prices by a factor t affect the budget line?

<p>It does not change the position of the budget line. (C)</p> Signup and view all the answers

What is represented by the vertical intercept of the budget line?

<p>The maximum amount of good 2 that can be consumed when good 1 is not purchased. (B)</p> Signup and view all the answers

What does the term 'budget set' refer to?

<p>All combinations of goods that do not exceed the budget constraint. (D)</p> Signup and view all the answers

What happens to the budget line if price 2 increases more than price 1?

<p>The budget line becomes flatter. (A)</p> Signup and view all the answers

What is the formula for the budget line if good 2 is pegged as the numeraire?

<p>p1 x1 + p2 x2 = p2 (B)</p> Signup and view all the answers

How does a quantity tax affect the price of good 1?

<p>It increases by the amount t. (C)</p> Signup and view all the answers

If an ad valorem subsidy is applied, how is the price of good 1 affected?

<p>It decreases to (1 - σ)p1. (D)</p> Signup and view all the answers

When price 2 is set to 1, what do p1 and income m represent?

<p>Relative price of good 1 and relative income. (D)</p> Signup and view all the answers

What is the result of a value tax (ad valorem tax) on the budget line?

<p>The budget line becomes steeper. (A)</p> Signup and view all the answers

How does a quantity subsidy influence the budget line?

<p>It makes the budget line flatter by decreasing the price of good 1. (C)</p> Signup and view all the answers

What is the effect on the budget line if price 2 increases less than price 1?

<p>The budget line steepens. (D)</p> Signup and view all the answers

What happens to the budget line when income increases from m to m0, where m0 > m?

<p>The budget line shifts outward. (D)</p> Signup and view all the answers

When the price of good 1 increases while holding the price of good 2 and income fixed, what is expected to happen to the slope of the budget line?

<p>The slope becomes steeper. (D)</p> Signup and view all the answers

If both prices (p1 and p2) increase by a factor of t where t > 1, what effect does this have on the budget line?

<p>The budget line shifts inward. (A)</p> Signup and view all the answers

What is the effect on the budget line when both prices and income decrease?

<p>The budget line shifts inward. (D)</p> Signup and view all the answers

When price p1 increases to p10, which equation represents the new budget line?

<p>x2 = m/p2 - p1 x1 (D)</p> Signup and view all the answers

What happens to the intercepts of the budget line when income decreases?

<p>The intercepts decrease. (C)</p> Signup and view all the answers

If both prices and income simultaneously increase, what will be the overall impact on the budget line?

<p>It will shift inward regardless of the amount of increase. (C)</p> Signup and view all the answers

In the equation of a budget line, which of the following best describes the meaning of 'mp2'?

<p>Maximum affordable quantity of good 2. (D)</p> Signup and view all the answers

If the budget constraint is represented by the equation $x2 = mp2 - p2 x1$, which variable shows the quantity consumed of good 1?

<p>x1 (C)</p> Signup and view all the answers

From the changes in budget constraints, what is indicated by the notation 't < 1'?

<p>The budget line shifts outward. (C)</p> Signup and view all the answers

Flashcards

Budget Constraint

The limit on the amount of goods a consumer can purchase given their income and prices.

Consumption Bundle (X)

The combination of goods a consumer chooses to buy, represented by X = (x1, x2) where x1 is the amount of good 1 and x2 is the amount of good 2.

Budget Constraint Equation

p1x1 + p2x2 ≤ m, where p1 is the price of good 1, x1 is the amount of good 1, p2 is the price of good 2, x2 is the amount of good 2, and m is income. The equation states that the total amount spent on goods cannot exceed income.

Budget Set

The collection of all possible consumption bundles a consumer can afford given their income and prices.

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Budget Line

The line that represents all the consumption bundles a consumer can buy if they spend all their income. It's defined by p1x1 + p2x2 = m.

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Slope of the Budget Line

  • (p1/p2), where p1 is the price of good 1 and p2 is the price of good 2. The slope shows the rate at which the consumer can substitute good 1 for good 2.
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Opportunity Cost

The value of the best alternative forgone. The slope of the budget line represents the opportunity cost of consuming good 1, showing how much of good 2 must be sacrificed to get one more unit of good 1.

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Vertical Intercept of the Budget Line

(m/p2), where m is income and p2 is the price of good 2. It represents the maximum amount of good 2 the consumer can buy if they spend all their income on only good 2.

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Horizontal Intercept of the Budget Line

(m/p1), where m is income and p1 is the price of good 1. It represents the maximum amount of good 1 the consumer can buy if they spend all their income on only good 1.

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Shifting the Budget Line: Income Increase

An increase in income shifts the budget line outward, parallel to the original budget line. The consumer can now afford more of both goods.

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Shifting the Budget Line: Income Decrease

A decrease in income shifts the budget line inward, parallel to the original budget line. The consumer can now afford less of both goods.

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Shifting the Budget Line: Price of Good 1 Increase

An increase in the price of good 1 makes the budget line steeper. The consumer can afford less of good 1 but the same amount of good 2.

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Shifting the Budget Line: Price of Good 1 Decrease

A decrease in the price of good 1 makes the budget line flatter. The consumer can afford more of good 1 but the same amount of good 2.

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Shifting the Budget Line: Price of Both Goods Increase (Proportional)

If both prices increase proportionally, the budget line shifts inward. The consumer can afford less of both goods.

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Shifting the Budget Line: Price of Both Goods Increase (Non-Proportional)

If both prices increase but one increases more than the other, the budget line rotates. The slope of the budget line changes, reflecting the relative change in prices.

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Shifting the Budget Line: Price of Both Goods Decrease (Proportional)

If both prices decrease proportionally, the budget line shifts outward. The consumer can afford more of both goods.

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Numeraire

The good whose price is set to 1, allowing all other prices and income to be expressed relative to its price. It's used to simplify the budget constraint.

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Quantity Tax

A fixed amount paid per unit of a good consumed. It effectively increases the price of the good.

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Value Tax (Ad Valorem Tax)

A tax based on the value of a good. Usually expressed as a percentage of the price. Increases the price of the good.

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Quantity Subsidy

A fixed amount given to the consumer for each unit of a good they purchase. This effectively decreases the price of the good.

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Value (Ad Valorem) Subsidy

A subsidy based on the value of a good, usually expressed as a percentage of the price. This decreases the price of the good.

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Rationing

A limit on the amount of a good a consumer can purchase. This is represented by a kink in the budget line.

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What is the relationship between the slope of the budget line and the opportunity cost of consuming good 1?

The slope of the budget line represents the opportunity cost of consuming good 1. This is because the slope shows the rate at which the consumer must give up good 2 to get one more unit of good 1.

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How does a change in income affect the budget constraint?

A change in income shifts the budget line parallel to the original budget line. An increase in income shifts it outward, allowing the consumer to afford more. A decrease in income shifts it inward, limiting the consumer's affordability.

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How does a change in the price of good 1 affect the budget constraint?

A change in the price of good 1 changes the slope of the budget line. An increase in the price makes the line steeper, reducing the affordability of good 1. A decrease in the price makes the line flatter, increasing the affordability of good 1.

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Why is the Numeraire concept helpful?

The Numeraire simplifies the budget constraint by setting the price of one good to 1, allowing all other prices and income to be expressed relative to it. This makes the relationship between prices and income easier to understand.

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Study Notes

Consumer Theory

  • Consumers choose the best bundle of goods they can afford
  • The “best” bundle is the focus of the next chapter
  • The “can afford” is the budget constraint

The Budget Constraint

  • The consumer's consumption bundle of goods is X = (x1, x2)
    • x1 is the amount of good 1 consumed
    • x2 is the amount of good 2 consumed
  • Prices are (p1, p2)
    • p1 is the price of good 1
    • p2 is the price of good 2
  • The consumer's income is m
  • The budget constraint equation is: p1x1 + p2x2 ≤ m
    • p1x1 represents the amount of money spent on good 1
    • p2x2 represents the amount of money spent on good 2
    • This means the total amount of money spent on both goods must be less than or equal to the consumer's total income
  • The budget set is the set of all affordable consumption bundles at prices (p1, p2) and income m

The Budget Line

  • The budget line is the set of all consumption bundles that cost exactly m
  • The formula for the budget line is p1x1 + p2x2 = m
  • Rearranging it gives: x2 = (m/p2) - (p1/p2)x1
    • This formula shows the relationship between the amount of good 1 and good 2 that the consumer can purchase
  • The slope of the budget line is - (p1/p2)
  • The vertical intercept is (m/p2)
  • The horizontal intercept is (m/p1)

Economic Interpretation of the Slope

  • The slope of the budget line represents the opportunity cost of consuming good 1
  • The opportunity cost is the rate at which the market is willing to substitute good 1 for good 2
  • The opportunity cost means if the consumer wants to consume one more unit of good 1, how much of good 2 must they give up to stay within their budget?

Changes in the Budget Constraint

  • Changes in Income*
  • A change in income, from m to m0 will result in a parallel shift of the budget line
  • If m0 is greater than m then the shift will be outward, meaning the consumer can afford more of both goods
  • If m0 is less than m then the shift will be inward, meaning the consumer can afford less of both goods
  • Changes in Price of Good 1*
  • Increasing p1 to p10 will result in a change in the slope of the budget line
  • The slope of the budget line will become steeper
  • The vertical intercept will stay the same, but the horizontal intercept will change
  • This is because the consumer can afford less of good 1 at the higher price
  • Changes in the Price of Both Goods*
  • Multiplying p1 and p2 by t is the same as dividing income by t
  • If t is greater than 1 then the budget line will shift inward, meaning the consumer can afford less
  • If t is less than 1 then the budget line will shift outward, meaning the consumer can afford more
  • Changes in Both Price and Income*
  • If both prices increase and income decreases, then the budget line will shift inward as the consumer can afford less overall
  • If price 2 increases more than price 1, then the budget line will become flatter
  • If price 2 increases less than price 1, then the budget line will become steeper

The Numeraire

  • The budget line is defined by two prices and one income, but one of these variables is redundant
  • You can set one of the prices to a fixed value and measure the other price and income relative to that
  • Choosing p2 = 1 makes good 2 the Numeraire
  • This means the price of good 1 (p1) is now relative to the price of good 2 (which is 1 dollar)
  • The income (m) is now also relative to the price of good 2

Taxes, Subsidies and Rationing

  • Taxes*
  • Quantity tax: A fixed amount is paid for each unit of good 1 consumed
  • This increase the price of good 1 by the amount of the tax
  • Value tax (ad valorem tax): A tax on the value of good 1
  • This is usually in percentage terms
  • This increases the price of good 1 by a percentage of the original price
  • Subsidies*
  • Quantity subsidy: A fixed amount is given to the consumer for each unit of good 1 consumed
  • This decreases the price of good 1 by the amount of the subsidy
  • Ad valorem subsidy: A subsidy based on the price of the good
  • This is also usually in percentage terms
  • This decreases the price of good 1 by a percentage of the original price

Rationing

  • Rationing is when the amount of a good that can be consumed is limited
  • This is represented by a kink in the budget line

Summary

  • The budget constraint is a key concept in consumer theory and allows for a graphical representation of what consumers can afford given their income and prices
  • The slope of the budget line represents the opportunity cost of consuming good 1
  • Changes in income, prices or rationing all impact the budget constraint and the consumer's ability to choose different bundles of goods

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Chapter 2: Budget Constraint PDF

Description

This quiz focuses on the concepts of consumer theory, particularly the budget constraint and how it affects consumer choices. It covers the definitions and equations relevant to understanding how consumers decide on the optimal bundle of goods they can afford. Test your knowledge on the budget line and consumption choices in relation to income and prices.

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