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- Suppose that each week Fiona buys 16 peaches and 4 apples at her local farmer's market. Both kinds of fruit cost $1 each. From this we can infer that: If Fiona is maximizing her utility, then her marginal utility from the 16th peach she buys must be greater than her marginal utility from the 4th apple she buys. Fiona is not maximizing her utility. If Fiona is maximizing her utility, then her marginal utility from the 16th peach she buys must be equal to her marginal utility from the 4th apple she buys. The law of diminishing marginal utility does not hold for Fiona.Penelope utility function is U (a, b) = a+ 10b−b2, where a is the amount of applesconsumed and b is the amount of bananas consumed. He has $100 income. Theprice of apple is $0.5 per lb. Price of banana’s though increases with its purchase.Specifically, buying, b pounds of bananas will cost Pedro b2.a. What is Penelopes optimal consumption?b. Now, he suddenly acquires an extra $100 income. How this will changehis allocation?A consumer finds only three products, X, Y, and Z, are for sale. The amount of utility which their consumption will yield is shown in the table below. Assume that the prices of X, Y, and Z are $10, $2, and $8, respectively, and that the consumer has an income of $74 to spend. Product X Product Y Product Z Quantity Utility Marginal Utility per $ Quantity Utility Marginal Utility per $ Quantity Utility Marginal Utility per $ 1 42 NA 1 14 NA 1 32 NA 2 82 4 2 26 6 2 60 3.5 3 118 3.6 3 36 5 3 84 3 4 148 3 4 44 4 4 100 2 5 170 2.2 5 50 3 5 110 1.25 6 182 1.2 6 54 2 6 116 0.75 7 182 _0 7 56.4 _1.2 7 120 _0.5_ Why would the consumer not be maximizing utility by purchasing 2 units of X, 4 units of Y, and 1 unit of Z?
- A consumer finds only three products, X, Y, and Z, are for sale. The amount of utility which their consumption will yield is shown in the table below. Assume that the prices of X, Y, and Z are $10, $2, and $8, respectively, and that the consumer has an income of $74 to spend. Product X Product Y Product Z Quantity Utility Marginal Utility per $ Quantity Utility Marginal Utility per $ Quantity Utility Marginal Utility per $ 1 42 NA 1 14 NA 1 32 ___NA__ 2 82 4 2 26 6 2 60 __3.5_ 3 118 3.6 3 36 5 3 84 __3___ 4 148 3 4 44 4 4 100 __2___ 5 170 2.2 5 50 3 5 110 _1.25___ 6 182 1.2 6 54 2 6 116 _0.75__ 7 182 0 7 56.4 1.2 7 120 _0.5_ How many units of X, Y, and Z will the consumer buy when maximizing utility and spending all…Suppose that Elif spends her income on shoes and outfits. The price of a shoe is 100/unit and the price of an outfit is 200/unit. Q shoes outfits total utility marginal util. MU/Ps total utility marginal util. MU/Po 1 1000 1800 2 1700 3000 3 2000 4000 4 2200 4600 15) What is the quantity of shoes and outfits that maximizes Elif’s utility? a) 3 shoes and 3 outfits b) 4 shoes and 2 outfits c) 3 shoes and 4 outfits d) 4 shoes and 3 outfits 16) Suppose the price of an outfit increases to 500. What is the new utility maximizing quantity of shoes and outfits for Elif? a) 3 shoes and 4 outfits b) 3 shoes and 2 outfits c) 3 shoes and 1 outfits d) 4 shoes and 3 outfitsYou are choosing between two goods, X and Y, and your marginal utility from each is shown in the following table. Units of X MUx Units of Y MUy 1 10 1 8 2 8 2 7 3 6 3 6 4 4 4 5 5 3 5 4 6 2 6 3 Instructions: Enter your answers as a whole number. a. If your income is $9 and the prices of X and Y are $2 and $1, respectively, what quantities of each will you purchase to maximize utility? 2 units of X and 5 units of Y b. What total utility will you realize? 48 utils c. Assume that, other things remaining unchanged, the price of X falls to $1. What quantities of X and Y will you now purchase? 3 units of X and 3 units of Y d. Using the two prices and quantities for X, complete the table to derive the demand schedule (a table showing prices and quantities demanded) for X. Instructions: Start with the highest price first Price of X Quantity Demanded of X $ $
- Penelope utility function is U (a, b) = a+ 10b−b2, where a is the amount of applesconsumed and b is the amount of bananas consumed. He has $100 income. Theprice of apple is $0.5 per lb. Price of banana’s though increases with its purchase.Specifically, buying, b pounds of bananas will cost Pedro b2.a. What is Penelope optimal consumption?b. Now, he suddenly acquires an extra $100 income. How this will changehis allocation?Columns 1 through 4 of the accompanying table show the marginal utility, measured in utils, that Ricardo would get by purchasing various amounts of products A, B, C, and D. Column 5 shows the marginal utility Ricardo gets from saving. Assume that the prices of A, B, C, and D are $18, $6, $4, and $24, respectively, and that Ricardo has an income of $105. What quantities of A, B, C, and D will Ricardo purchase in maximizing his utility? How many dollars will Ricardo choose to save? Check your answers by substituting them into the algebraic statement of the utility‑maximizing rule. In other words, show it works when using this rule.Columns 1 through 4 in the following table show the marginal utility, measured in utils, that Ricardo would get by purchasing various amounts of products A, B, C, and D. Column 5 shows the marginal utility Ricardo gets from saving. Assume that the prices of A, B, C, and D are, respectively, $18, $6, $4, and $24 and that Ricardo has an income of $106. a. What quantities of A, B, C, and D will Ricardo purchase in maximizing his utility? b. How many dollars will Ricardo choose to save? c. Check your answers by substituting them into the algebraic statement of the utility-maximizing rule.
- Mylie’s total utility from singing the same song over and over is 50 utils after one repetition, 90 utils after two repetitions, 70 utils after three repetitions, 20 utils after four repetitions, −50 utils after five repetitions, and −200 utils after six repetitions. Write down her marginal utility for each repetition. Once Mylie’s total utility begins to decrease, does each additional singing of the song hurt more than the previous one or less than the previous one?A student has a monthly budget of $120 to spend on eitherburritos, which cost $6 each, or sodas, which cost $4 each.1. What is the largest number of burritos that the studentcould afford to purchase in one month?2. What is the largest number of sodas the student couldafford to purchase in one month?3. Draw the student's budget constraint. Put burritos on thex-axis and sodas on the y-axis.Graded Assignment due Monday4. Which combinations of burritos and sodas are unaffordable--those tothe left of the line in the graph or those above the line in the graph? Why?5. Which combinations would leave some budget unspent - those to theleft of the line in the above graph or those to the right of the line in theabove graph?6. What is the equation for the student's budget constraint? In yourequation, use Q1 as the variable to represent the quantity of burritos andQ2 to represent the quantity of sodas.7. What is the opportunity cost of a burrito?8. What is the opportunity cost of a soda?9. The local…Jack derives utility from Hokey course (H) and Chess course (C) as given by the following utility function:U (H, C) = √HCThe average price for the hokey course is 20 dollars and for chess course16 dollars. Moreover, Jack has a budgetof 80 dollars. c) Find the income level which is necessary to make Jack reach the same utility level as before theprice change.d) Compute the quantities demanded with the new prices and the income you found in section c.e) Compute the quantities demanded with the new prices and the original budget of 800 dollars.