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1 The Utility-Maximizing Model Module 11

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Use the utility-maximizing model to explain how consumers choose goods and services. 2 ObjectivesObjectives

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Use the concept of utility to explain how the law of demand results from consumers adjusting their consumption choices to changes in prices. Use the utility-maximizing model to explain how consumers choose goods and services. Use the concept of utility to explain how the law of demand results from consumers adjusting their consumption choices to changes in prices. 3 ObjectivesObjectives

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4 Objective 1 Use the utility-maximizing model to explain how consumers choose goods and services Objective 1 Use the utility-maximizing model to explain how consumers choose goods and services total utilitymarginal utility Be sure to understand the difference between total utility and marginal utility. law of diminishing marginal utility Recall the law of diminishing marginal utility. terminology Also know the terminology of this chapter, for example, terms such as consumption bundle, consumer preferences.

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5 Objective 1 Use the utility-maximizing model to explain how consumers choose goods and services Objective 1 Use the utility-maximizing model to explain how consumers choose goods and services demand curve The goal of the utility-maximizing model is to derive the consumers demand curve. utility maximization Economists assume that consumers try to allocate their limited incomes to maximize their satisfaction, a goal referred to as utility maximization.

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6 Objective 1 Use the utility-maximizing model to explain how consumers choose goods and services Objective 1 Use the utility-maximizing model to explain how consumers choose goods and services optimal The utility-maximizing model is used to determine the optimal amounts of goods and services a consumer will purchase given:

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7 Objective 1 Use the utility-maximizing model to explain how consumers choose goods and services Objective 1 Use the utility-maximizing model to explain how consumers choose goods and services optimal The utility-maximizing model is used to determine the optimal amounts of goods and services a consumer will purchase given: preferences knowledge of consumers preferences

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8 Objective 1 Use the utility-maximizing model to explain how consumers choose goods and services Objective 1 Use the utility-maximizing model to explain how consumers choose goods and services optimal The utility-maximizing model is used to determine the optimal amounts of goods and services a consumer will purchase given: preferences knowledge of consumers preferences prices the prices of the goods and services

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9 Objective 1 Use the utility-maximizing model to explain how consumers choose goods and services Objective 1 Use the utility-maximizing model to explain how consumers choose goods and services optimal The utility-maximizing model is used to determine the optimal amounts of goods and services a consumer will purchase given: preferences knowledge of consumers preferences prices the prices of the goods and services budget the consumers budget constraint

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10 Objective 1 Use the utility-maximizing model to explain how consumers choose goods and services Objective 1 Use the utility-maximizing model to explain how consumers choose goods and services equilibrium bundle budget constraint The consumers equilibrium bundle is a combination of goods and services consumed which gives the consumer the maximum total utility, subject to a budget constraint or an income constraint. The terms equilibrium bundle, optimal bundle and utility-maximizing bundle are used interchangeably.

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11 Suppose a consumer has $I to spend on two goods, X and Y. Let P x = price of good X and P y = price of good Y. Objective 1: Using the utility-maximizing model

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12 Suppose a consumer has $1 to spend on two goods, X and Y. Let P x = price of good X and P y = price of good Y. How will the consumer allocate her $I towards these two goods so that she gets the most satisfaction? Objective 1: Using the utility-maximizing model

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13 Suppose a consumer has $1 to spend on two goods, X and Y. Let P x = price of good X and P y = price of good Y. How will the consumer allocate her $1 towards these two goods so that she gets the most satisfaction? The equilibrium bundle satisfies two conditions: Objective 1: Using the utility-maximizing model

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14 Suppose a consumer has $1 to spend on two goods, X and Y. Let P x = price of good X and P y = price of good Y. How will the consumer allocate her $1 towards these two goods so that she gets the most satisfaction? The equilibrium bundle satisfies two conditions: Condition 1: Income should be allocated so that the last dollar spent on each good yields the same amount of marginal utility. Objective 1: Using the utility-maximizing model

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15 The equilibrium bundle satisfies two conditions: Condition 1: Income should be allocated so that the last dollar spent on each good yields the same amount of marginal utility. In terms of an equation, where MU = marginal utility, and P = price, Objective 1: Using the utility-maximizing model

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16 The equilibrium bundle satisfies two conditions: Condition 1: Income should be allocated so that the last dollar spent on each good yields the same amount of marginal utility. In terms of an equation, where MU = marginal utility, and P = price, Objective 1: Using the utility-maximizing model Marginal utility per dollar spent on good X Marginal utility per dollar spent on good Y

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17 Condition 2: The consumer must spend the total income allocated to the consumption of goods and services. Objective 1: Using the utility-maximizing model

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18 Condition 2: The consumer must spend the total income allocated to the consumption of goods and services. In terms of an equation: Where = Price of good X × Quantity of good X = expenditure on good X, and = Price of good Y × Quantity of good Y = expenditure on good Y Objective 1: Using the utility-maximizing model

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19 The table below shows Kayla's utility from soup and sandwiches. Cups of Soup Total Utility Number of Sandwiches Total Utility 1 40145 2 60275 3 723102 4 824120 5 885135 6 906145 Objective 1: Using the utility-maximizing model … an example

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20 The table below shows Kayla's utility from soup and sandwiches. The price of a cup of soup is $2 and the price of a sandwich is $3. Cups of Soup Total Utility Number of Sandwiches Total Utility 1 40145 2 60275 3 723102 4 824120 5 885135 6 906145 Objective 1: Using the utility-maximizing model … an example

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21 The table below shows Kayla's utility from soup and sandwiches. The price of a cup of soup is $2 and the price of a sandwich is $3. Kayla has $18 to spend on these two goods. Cups of Soup Total Utility Number of Sandwiches Total Utility 1 40145 2 60275 3 723102 4 824120 5 885135 6 906145 Objective 1: Using the utility-maximizing model … an example

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22 Step 1: Step 1: Calculate the marginal utility per dollar spent on each good using the formula: marginal utility per dollar = marginal utility ÷ price of the good Note: Note: To apply this step you must have marginal utility figures and the price of the product. If you are given total utility figures, you will have to calculate the marginal utility before using the equation above. Objective 1: … applying the utility- maximizing conditions

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23 1 40 40÷2=20145 45÷3=15 2 602020÷2=102753030÷3=10 3 721263102279 4 821054120186 5 88635135155 6 90216145103.33 Step 1: Step 1: Calculate the marginal utility per dollar spent on each good using the formula: marginal utility per dollar = marginal utility ÷ price of the good Begin by calculating Marginal Utility. (1) Cups of soup (2) Total Utility (3) Marginal Utility (4) Marginal Utility per dollar MU/Psoup (5) Number of Sandwiches (6) Total Utility (7) Marginal Utility (8) Marginal Utility per dollar MU/Psandwich Price of Soup = $2 per cupPrice of Sandwich = $3 per cup

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24 1 40 40÷2=20145 45÷3=15 2 602020÷2=102753030÷3=10 3 721263102279 4 821054120186 5 88635135155 6 90216145103.33 Step 1: Step 1: Calculate the marginal utility per dollar spent on each good using the formula: marginal utility per dollar = marginal utility ÷ price of the good Begin by calculating Marginal Utility. Next, calculate Marginal Utility per dollar using the equation above. (1) Cups of soup (2) Total Utility (3) Marginal Utility (4) Marginal Utility per dollar MU/Psoup (5) Number of Sandwiches (6) Total Utility (7) Marginal Utility (8) Marginal Utility per dollar MU/Psandwich Price of Soup = $2 per cupPrice of Sandwich = $3 per cup

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25 Step 2: Step 2: Identify the combinations of the goods that satisfy the marginal utility per dollar rule: Objective 1: Applying the utility-maximizing conditions (1) Cups of soup (4) Marginal Utility per dollar MU/P soup (5) Number of Sandwiches (8) Marginal Utility per dollar MU/P sandwich 1 40÷2=20145÷3=15 220÷2=10230÷3=10 3639 4546 5355 6163.33

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26 The marginal utility per dollar rule holds for these three combinations: 2 cups of soup and 2 sandwiches 3 cups of soup and 4 sandwiches 4 cups of soup and 5 sandwiches Objective 1: Applying the utility-maximizing conditions (1) Cups of soup (4) Marginal Utility per dollar MU/P soup (5) Number of Sandwiches (8) Marginal Utility per dollar MU/P sandwich 140÷2=20145÷3=15 220÷2=10230÷3=10 3639 4546 5355 6163.33

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27 Which of the three bundles is the optimal bundle? Objective 1: Applying the utility-maximizing conditions

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28 Which of the three bundles is the optimal bundle? Step 3: Step 3: Identify the optimal bundle by applying Condition 2: that Kaylas expenditure on the two goods must exhaust her budget of $18. Objective 1: Applying the utility-maximizing conditions

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29 Which of the three bundles is the optimal bundle? Step 3: Step 3: Identify the optimal bundle by applying the condition 2: that Kaylas expenditure on the two goods must exhaust her budget of $18. 2 cups of soup and 2 sandwiches will cost her $10 ($2×2 cups of soup + $3×2 sandwiches) Objective 1: Applying the utility-maximizing conditions

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30 Which of the three bundles is the optimal bundle? Step 3: Step 3: Identify the optimal bundle by applying the condition 2: that Kaylas expenditure on the two goods must exhaust her budget of $18. 2 cups of soup and 2 sandwiches will cost her $10 ($2×2 cups of soup + $3×2 sandwiches) 3 cups of soup and 4 sandwiches will cost her $18 ($2×3 cups of soup + $3×4 sandwiches) Objective 1: Applying the utility-maximizing conditions

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31 Which of the three bundles is the optimal bundle? Step 3: Step 3: Identify the optimal bundle by applying the condition 2: that Kaylas expenditure on the two goods must exhaust her budget of $18. 2 cups of soup and 2 sandwiches will cost her $10 ($2×2 cups of soup + $3×2 sandwiches) 3 cups of soup and 4 sandwiches will cost her $18 ($2×3 cups of soup + $3×4 sandwiches) 4 cups of soup and 5 sandwiches will cost her $23 ($2×4 cups of soup + $3×5 sandwiches) Objective 1: Applying the utility-maximizing conditions

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32 Which of the three bundles is the optimal bundle? Step 3: Step 3: Identify the optimal bundle by applying the condition 2: that Kaylas expenditure on the two goods must exhaust her budget of $18. 2 cups of soup and 2 sandwiches will cost her $10 ($2×2 cups of soup + $3×2 sandwiches) 3 cups of soup and 4 sandwiches will cost her $18 ($2×3 cups of soup + $3×4 sandwiches) 4 cups of soup and 5 sandwiches will cost her $23 ($2×4 cups of soup + $3×5 sandwiches) equilibrium bundle Kaylas equilibrium bundle is 3 cups of soup and 4 sandwiches. Objective 1: Applying the utility-maximizing conditions

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33 The utility maximizing model applies a key economic principle: optimal decisions are made at the margin. Objective 1: … the utility-maximizing model

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34 The utility maximizing model applies a key economic principle: optimal decisions are made at the margin. Examine the marginal utility per dollar rule again: Objective 1: … the utility-maximizing model Marginal utility per dollar spent on good X Marginal utility per dollar spent on good Y

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35 The utility maximizing model applies a key economic principle: optimal decisions are made at the margin. Examine the marginal utility per dollar rule again: Rearrange to get Objective 1: … the utility-maximizing model ratio of marginalutilities ratio of prices

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36 Examine the marginal utility per dollar rule: Rearrange to get relative prices ratio of prices is also called relative prices Objective 1: … the utility-maximizing model What is the meaning of relative prices? Suppose, where X=soup and Y=sandwich, then Kayla must give up 2/3 of a sandwich (Y) for I more cup of soup (X). opportunity cost The relative price is the opportunity cost of consuming 1 more market dictated rate of exchange unit of X or the market dictated rate of exchange between good X and good Y.

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37 Examine the marginal utility per dollar rule: Rearrange to get relative prices ratio of prices is also called relative prices Ratio of marginal utilities marginal also called the marginal rate of substitution Objective 1: … the utility-maximizing model What is the ratio of marginal utilities? marginal rate The ratio of marginal utilities is also called the marginal rate of substitution of substitution. It shows the rate at which the consumer is willing to give up some of good Y (sandwich) for an additional unit of good X (soup). In subjective other words, it is a measure of the consumers subjective or personal personal rate of exchange.

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38 Examine the marginal utility per dollar rule: Rearrange to get relative prices ratio of prices is also called relative prices ratio of marginal utilities marginal also called the marginal rate of substitution Objective 1: … the utility-maximizing model In equilibrium, the consumers subjective rate of exchange (ratio of marginal utilities) equals the rate of exchange required by the market (ratio of prices).

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39 Objective 2 Use the concept of utility to explain how the law of demand results … Objective 2 Use the concept of utility to explain how the law of demand results … An individuals utility-maximizing choices lead to a demand curve. Recall, that the demand curve shows the quantities demanded at alternative prices The utility-maximizing consumer adjusts her consumption choices to changes in prices.

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40 To derive Kaylas demand for sandwiches curve, we must change the price of sandwiches and observe what happens to her quantity demanded of sandwiches, holding all else constant. Objective 2 Use the utility maximizing model to derive a demand curve Objective 2 Use the utility maximizing model to derive a demand curve

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41 To derive Kaylas demand for sandwiches curve, we must change the price of sandwiches and observe what happens to her quantity demanded of sandwiches, holding all else constant. We already have one price-quantity combination: At a price of $3, Kaylas optimal quantity was 4 sandwiches. Objective 2 Use the utility maximizing model to derive a demand curve Objective 2 Use the utility maximizing model to derive a demand curve

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42 To construct a demand curve we need at least one other price-quantity combination. Objective 2: … deriving a demand curve.

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43 To construct a demand curve we need at least one other price-quantity combination. Suppose the price of sandwiches rises to $4.00. How would Kaylas quantity demanded of sandwiches change? Objective 2: … deriving a demand curve.

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44 To construct a demand curve we need at least one other price-quantity combination. Suppose the price of sandwiches rises to $4.00. How would Kaylas quantity demanded of sandwiches change? Since the price of one good has changed we have to recalculate the marginal utility per dollar for that good. Objective 2: … deriving a demand curve.

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45 Step 1: Step 1: Calculate the marginal utility per dollar spent on each good using the formula: marginal utility per dollar = marginal utility ÷ price of the good Price of Soup = $2 per cupPrice of Sandwich = $4 per cup (1) Cups of soup (2) Total Utility (3) Marginal Utility (4) Marginal Utility per dollar MU/P soup (5) Number of Sandwiches (6) Total Utility (7) Marginal Utility (8) Marginal Utility per dollar MU/P sandwich 140 40÷2=20145 45÷4=11.25 2602020÷2=102753030÷4=7.5 3721263102276.75 4821054120184.50 588635135153.75 690216145102.5 Objective 2: … deriving a demand curve.

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46 How to determine the optimal combination of soup and sandwiches in the case where the rule of equal marginal utility per dollar does not hold? Objective 2: … deriving a demand curve.

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47 How to determine the optimal combination of soup and sandwiches in the case where the rule of equal marginal utility per dollar does not hold? Apply the principle of marginal analysis. Ask the question: what is the first item Kayla should buy? Objective 2: … deriving a demand curve.

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48 How to determine the optimal combination of soup and sandwiches in the case where the rule of equal marginal utility per dollar does not hold? Apply the principle of marginal analysis. Ask the question: what is the first item Kayla should buy? (1) Cups of soup (4) Marginal Utility per dollar MU/P soup (5) Number of sandwiches (8) Marginal Utility per dollar MU/P sandwich 140÷2=20145÷4=10.8 220÷2=10230÷4=7.5 3636.75 4544.50 5353.75 6162.5 Objective 2: … deriving a demand curve

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49 Obviously, the item that gives her the highest marginal utility per dollar spent. What is the 2 nd item? … and so forth until her budget is exhausted. Goods consumed Budget = $18 1 st cup of soup$18-$2 =$16 1 st sandwich$16-$4 =$12 2 nd cup of soup$12-$2 =$10 2 nd sandwich$10-$4=$6 3 rd sandwich$6-$4 =$2 3 rd cup of soup$2-$2 =$0 (1) Cups of soup (4) Marginal Utility per dollar MU/Psoup (5) Number of Sandwiches (8) Marginal Utility per dollar MU/Psandwich 1 40÷2 = 20145÷4 = 10.8 2 20÷2 = 10230÷4 = 7.5 3 636.75 4 544.50 5 353.75 6162.5 Objective 2: … deriving a demand curve

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50 Obviously, the item that gives her the highest marginal utility per dollar spent. What is the 2 nd item? … and so forth until her budget is exhausted. Goods consumed Budget = $18 1 st cup of soup$18-$2 =$16 1 st sandwich$16-$4 =$12 2 nd cup of soup$12-$2 =$10 2 nd sandwich$10-$4=$6 3 rd sandwich$6-$4 =$2 3 rd cup of soup$2-$2 =$0 utility maximizing bundle Her utility maximizing bundle is 3 cups of soup and 3 sandwiches. (1) Cups of soup (4) Marginal Utility per dollar MU/Psoup (5) Number of Sandwiches (8) Marginal Utility per dollar MU/Psandwich 1 40÷2 = 20145÷4 = 10.8 2 20÷2 = 10230÷4 = 7.5 3 636.75 4 544.50 5 353.75 6 162.5 Objective 2: … deriving a demand curve

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51 Now that we have two price-quantity combination points on Kaylas demand for sandwiches curve we can trace her demand curve. Objective 2: … deriving a demand curve

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52 Now that we have two price-quantity combination points on Kaylas demand for sandwiches curve we can trace her demand curve. Objective 2: … deriving a demand curve

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53 Now that we have two price-quantity combination points on Kaylas demand for sandwiches curve we can trace her demand curve. law of demand. The resulting demand curve is downward- sloping. It obeys the law of demand. Objective 2: … deriving a demand curve

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54 demand curve. utility-maximizing quantity The utility-maximizing choices lead to a demand curve. Each price-quantity combination on a demand curve is a utility-maximizing quantity, given the price. Key Points

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55 Key Points demand curve. utility-maximizing quantity The utility-maximizing choices lead to a demand curve. Each price-quantity combination on a demand curve is a utility-maximizing quantity, given the price. law of demand If people seek to maximize utility, then the law of demand follows.

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56 Key Points substitution When price changes, there a substitution effect income and an income effect on the quantity of the good demanded. substitution effect The substitution effect of a price change is the change in quantity demanded that results from a change in price, making the good more of less expensive relative to other goods (that can substitute for it), holding purchasing power constant. income effect The income effect of a price change is the change in quantity demanded that results from the effect of the price change on the consumers purchasing power, all else constant.

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57 Key Points substitution When price changes, there a substitution effect and income an income effect on the quantity of sandwiches demanded. This movement along the curve is caused by a change in the price of sandwiches and is made up of two effects.

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58 Initially, when the price of soup = $2 and the price of sandwich = $3, Kaylas equilibrium bundle was 3 cups of soup and 4 sandwiches. Objective 2: … how a consumer adjusts to a price change

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59 Initially, when the price of soup = $2 and the price of sandwich = $3, Kaylas equilibrium bundle was 3 cups of soup and 4 sandwiches. The ratio of marginal utility to price was the same for soup and for sandwiches. Objective 2: … how a consumer adjusts to a price change

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60 Initially, when the price of soup = $2 and the price of sandwich = $3, Kaylas equilibrium bundle was 3 cups of soup and 4 sandwiches. The ratio of marginal utility to price was the same for soup and for sandwiches. When a consumer is in equilibrium, she is maximizing utility. Objective 2: … how a consumer adjusts to a price change

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61 When the price of sandwiches rises to $4, the ratios of marginal utility to price no longer hold with equality. Objective 2: … how a consumer adjusts to a price change

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62 A dollar spent on soup gives Kayla more utility than a dollar spent on sandwiches Objective 2: … how a consumer adjusts to a price change When the price of sandwiches rises to $4, the ratios of marginal utility to price no longer hold with equality. We now have:

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63 equilibrium, To restore equilibrium, Kayla buys more soup and fewer sandwiches, subject to her budget constraint. A dollar spent on soup gives Kayla more utility than a dollar spent on sandwiches Objective 2: … how a consumer adjusts to a price change

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64 equilibrium, To restore equilibrium, Kayla buys more soup and fewer sandwiches, subject to her budget constraint. In my example, given her budget, Kayla buys fewer sandwiches but is not able to increase her soup consumption. A dollar spent on soup gives Kayla more utility than a dollar spent on sandwiches Objective 2: … how a consumer adjusts to a price change

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65 equilibrium, To restore equilibrium, Kayla buys more soup and fewer sandwiches, subject to her budget constraint. In my example, given her budget, Kayla buys fewer sandwiches but is not able to increase her soup consumption. law of demand. Note that when the price of sandwiches rises, quantity demanded falls – a result consistent with the law of demand. Objective 2: … how a consumer adjusts to a price change A dollar spent on soup gives Kayla more utility than a dollar spent on sandwiches

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66 The Utility-Maximizing Model End of Module 11 Song:Material Girl Album:Like a Virgin Artist:Madonna

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