Book cover for Microeconomics

Microeconomics

Jeffrey M. Perloff

ISBN #9781292056531

7th Edition

753 Questions

Group icon
19,304 Students Helped

Homework Questions

Right arrow
Summary
Learning Objectives
Key Concepts
Example Problems
Explanations
Common Mistakes

Summary

The section explores how consumer choices are modeled using indifference curves and budget constraints. It demonstrates that changes in the price of a good (while holding income and other prices constant) rotate the budget line, leading to different optimal consumption bundles, which in turn trace out a demand curve. Additionally, when consumers face perfect substitutes, as in Mahdu's case with Coke and Pepsi, corner solutions often appear. The text also illustrates that changes in income shift the entire demand curve, emphasizing the difference between movement along the curve and a shift of the curve. These concepts are crucial for understanding consumer behavior and the foundations of demand theory in economics.

Learning Objectives

1

Explain how changes in the price of a good affect consumer choices using indifference curves and budget constraints.

2

Derive an individual demand curve from the price-consumption curve, illustrating the Law of Demand.

3

Analyze consumer behavior in scenarios involving perfect substitutes, as demonstrated by Mahdu's Coke and Pepsi example.

4

Examine how variations in income (holding prices constant) shift the demand curve.

5

Apply these concepts to real-world examples, such as tobacco pricing and consumer budget adjustments.

Key Concepts

CONCEPT

DEFINITION

Indifference Curve

A graph showing combinations of two goods between which a consumer is indifferent, meaning each combination provides the same level of satisfaction.

Budget Constraint

A line that represents all possible combinations of two goods that a consumer can afford given their income and the prices of the goods.

Price-Consumption Curve

The curve traced out by the optimal consumption bundles as the price of one good changes while income and other prices remain constant.

Demand Curve

A graph showing the relationship between the price of a good and the quantity demanded by consumers, typically downward sloping as predicted by the Law of Demand.

Perfect Substitutes

Goods that a consumer considers identical in terms of satisfaction, leading to situations where the consumer will switch entirely from one to the other based on relative prices.

Income Effect

The change in the quantity demanded of a good resulting from a change in the consumer's income, holding prices constant, which shifts the demand curve.

Example Problems

Example 1

Draw diagrams similar to Figure 5.1 showing that the price-consumption curve can be horizontal or downward sloping.

Example 2

In Figure $5.1,$ how does Mimi's utility at $E_{1}$ on $D^{1}$ compare to that at $E_{2}$ ? As we move down from the highest point on an individual's downward-sloping demand curve, must the individual's utility rise?

Example 3

Derive and plot Olivia's demand curve for pie if she eats pie only à la mode and does not eat either pie or ice cream alone (pie and ice cream are perfect complements). (Hint: See Solved Problem $5.1 .)$

Example 4

Manufactured diamonds have become as big and virtually indistinguishable from the best natural diamonds. In $2013,$ manufactured diamonds retailed for between $20 \%$ and $30 \%$ less than mined diamonds. Suppose consumers change from believing that manufactured diamonds, $M$, were imperfect substitutes for natural diamonds, $N$, to perfect substitutes, so that their utility function becomes $U(M, N)=M+N .$ What effect will that have on the demand for manufactured diamonds? Derive the new demand curve for manufactured diamonds and draw it.

Example 5

How would your answer to Question 1.4 change if $U=\ln (M+N),$ so that consumers have diminishing marginal utility of diamonds?

Scroll left
Scroll right

Step-by-Step Explanations

QUESTION

How does a change in the price of beer alter Mimi's consumption bundle and ultimately derive her demand curve for beer?

STEP-BY-STEP ANSWER:

Step 1: Establish the initial budget constraint (L1) with beer priced at $12 per unit, wine at $35 per unit, and an annual budget of $419. Identify the optimal bundle where the indifference curve (I1) is tangent to L1 (Bundle e1: 26.7 gallons of beer and 2.8 gallons of wine).
Step 2: Lower the price of beer to $6 per unit, which rotates the budget line outward to L2. This increases the maximum amount of beer Mimi can buy, while the vertical intercept (wine) remains unchanged. Determine the new optimal bundle at the tangency point (Bundle e2: 44.5 gallons of beer and 4.3 gallons of wine).
Step 3: Further reduce the price of beer to $4 per unit to obtain budget line L3, resulting in an even flatter line. Identify the new optimal bundle (Bundle e3: 58.9 gallons of beer and 5.2 gallons of wine).
Step 4: Plot these optimal bundles on a graph to trace Mimi's price-consumption curve, and then record the corresponding quantity of beer demanded at each price on the horizontal axis to form her demand curve, which is downward sloping as predicted by the Law of Demand.
Final Answer: Mimi’s demand curve for beer is derived by observing the increasing quantity of beer demanded at lower prices, reflecting a downward sloping relationship between price and quantity demanded.

Deriving Mimi's Demand Curve for Beer

QUESTION

How can Mahdu’s demand curve for Coke be derived when Coke and Pepsi are perfect substitutes?

STEP-BY-STEP ANSWER:

Step 1: Recognize that Mahdu’s indifference curves have a slope of -1 because he views Coke and Pepsi as perfect substitutes, meaning he is indifferent between them.
Step 2: With the price of Pepsi held constant at p*, analyze different scenarios by varying the price of Coke (p). If p > p*, the budget line is steeper, and Mahdu maximizes utility by purchasing only Pepsi (resulting in a corner solution with zero units of Coke).
Step 3: When the price of Coke falls below the price of Pepsi (p < p*), the budget line becomes flatter, and Mahdu maximizes his utility by spending his entire budget on Coke, yielding q = Y/p units of Coke.
Step 4: In the special case where p = p*, the slope of the budget line matches the indifference curves, and Mahdu is indifferent among all combinations of Coke and Pepsi that exhaust his budget, with the total quantity purchasable being Y/p*.
Final Answer: Mahdu’s demand curve for Coke is derived by showing that when Coke is more expensive than Pepsi he buys none; when it is cheaper he buys only Coke (with quantity determined by Y/p), and when prices are equal he is indifferent over a range of combinations, reflecting the unique consumer choice under perfect substitutes.

Deriving Mahdu's Demand Curve for Coke

Scroll left
Scroll right

Common Mistakes

  • Confusing movement along a demand curve (substitution effect) with a shift of the demand curve (income effect).
  • Overlooking the importance of the tangency condition between the indifference curve and the budget line when determining the optimal bundle.
  • Misunderstanding that a change in the price of one good rotates the budget line rather than merely shifting it parallel.
  • Neglecting the role of corner solutions in cases involving perfect substitutes, where consumption may jump from one good to another based on slight price differences.