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# Ch04 - Chapter 4 Consumer Choice The Budget Constraint...

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Chapter 4 Consumer Choice

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The Budget Constraint Suppose a consumer, Eric, purchases only food and clothing. Let x be the number of units of food and y the number of units of clothing per month. The price of a unit of food is P x and the price of a unit of clothing is P y . Assume his income is fixed to I dollars per month. Eric’s total monthly expenditure on food: P x x Eric’s total monthly expenditure on clothing: P y y If he spends all of his income, P x x + P y y = I Budget line: The set of baskets that a consumer can purchase when spending all of her available income.
The Budget Constraint Suppose that Eric has an income of I = \$800, the price of food P x = \$20 per unit, and the price of clothing P y = \$40 per unit. What is Eric’s budget line? Let the horizontal axis measure the units of food and the vertical axis the units of clothing, sketch Eric’s budget line. Consider the following baskets: Basket A: x = 0, y = 20, Basket E: x = 40, y = 0, Basket C: x = 20, y = 10, Basket F : x = 10, y = 10, Basket G: x = 20, y = 15. Which baskets can he buy? Which can not? The Budget constraint: The set of baskets that a consumer can purchase with a limited amount of income. The budget constraint can be expressed as: P x x + P y y ≤ I

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The Budget Constraint
Change in Income If Eric spends all of his income on food, he purchases I/P x units of food: Horizontal intercept = I/P x If Eric spends all of his income on clothing, he purchases I/P y units of clothing: Vertical intercept = I/P y Suppose that Eric’s income goes up to \$1,000 with the prices unchanged. What would be the two intercepts? Sketch Eric’s new budget line. Can Eric buy the basket G now? An increase in income shifts the budget line outward. Budget constraint is relaxed, or, consumer’s purchasing power has increased. An decrease in income shifts the budget line inward. Budget constraint is tightened, or, consumer’s purchasing power has decreased. Prices unchanged, the shifts are in parallel fashion.

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Change in Income
Change in Price How many units of clothing must Eric give up for additional unit of food? Since food is half as expensive as clothing, Eric must give up 1/2 unit of clothing for each additional unit of food: P x /P y = 1/2. For example, if he wants to gain 10 units of food, he must give up 5 units of clothing: ∆x = 10, ∆y = -5. ∆y/ ∆x = -1/2.

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