Alessia has two goods she can spend her income on, skiing and skating, and her total utilities from each are in the table above. The price of each unit of skiing is $10 and the price of each unit of skating is $5. Alessia has $40 to spend. Marginal Utility from Total Quantity Utility of from skiing skiing skiing Total Marginal Marginal Utility from Quantity Utility Utility skiing/Price of skiing Marginal Utility from skating/Price of skating 0 0 1 50 2 90 3 120 4 140 5 150 6 160 7 160 8 155 of skating from skating from skating 0 0 1 70 2 110 3 140 4 160 5 165 6 170 7 170 8 165 a. Calculate and type in marginal utilities and marginal utilities per dollar in the yellow highlighted cells above. b. Find Alessia's affordable bundles of consumption and corresponding marginal utilities per dollar and type in your answers in the green highlighted cells below. Marginal Quantity Quantity Utility from skiing/Price of skiing of of skiing skating 0 8 1 Marginal Utility from skating/Price of skating c. Find the optimal consumption bundle of Alessia and type in the answer in the blanks below. Alessia consumes units of skiing and units of skating.
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To calculate the marginal utility, we need to find the change in total utility when the quantity of skiing or skating increases by 1 unit. For skiing: - Marginal utility from skiing = Total utility from skiing (n) - Total utility from skiing (n-1) - Marginal Show more…
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Akash M.
The utility that Ann receives by consuming food F and clothing C is given by U(F, C) = FC + F. The marginal utilities of food and clothing are MUF = C + 1 and MUC = F. Food costs $1 a unit, and clothing costs $2 a unit. Ann's income is $22. a) Ann is currently spending all of her income. She is buying 8 units of food. How many units of clothing is she consuming? b) Graph her budget line. Place the number of units of clothing on the vertical axis and the number of units of food on the horizontal axis. Plot her current consumption basket. c) Draw the indifference curve associated with a utility level of 36 and the indifference curve associated with a utility level of 72. Are the indifference curves bowed in toward the origin? d) Using a graph (and no algebra), find the utility-maximizing choice of food and clothing. e) Using algebra, find the utility-maximizing choice of food and clothing. f) What is the marginal rate of substitution of food for clothing when utility is maximized? Show this graphically and algebraically. g) Does Ann have a diminishing marginal rate of substitution of food for clothing? Show this graphically and algebraically.
Question 1 A consumer spends all of their money on food and entertainment. The amount of food they consume in a given year is xF , and the amount of entertainment is xE , so that a consumption bundle for the consumer is written as (xF , xE ). They are indifferent between all consumption bundles (xF , xE ) such that xF xE = 2, 000. They are also indifferent between all consumption bundles (xF , xE ) such that xF xE = 4, 000, a different set of bundles. (a) (i) Graph the indifference curves for the consumer that pass through the consumption bundles (50, 40) and (25, 160). (ii) Which of (50, 40) and (25, 160) is preferred by the consumer? How can you tell? (iii) In your graph, shade in area representing the set of bundles weakly preferred to (25, 160), and the area representing the set of bundles to which (50, 40) is weakly preferred. (b) Which of the following are true and which are false for the consumer: (40, 80) ∼ (5, 400), (100, 40) - (10, 200), (50, 80) ≺ (250, 8), (25, 160) - (25, 160)? (c) A shape S in the x1, x2 plane is convex if, whenever X and Y are points contained in S, the whole line between X and Y is contained in S. To practice thinking about this definition, draw the following examples: a filled-in circle is convex, a filled-in square is convex, two disjoint (i.e. not intersecting) filled-in circles are not convex, a hollow circle is not convex, an arc of a hollow circle is not convex. Using this definition, answer the following: Is the set of bundles weakly preferred to (50, 40) convex? What about the set of bundles to which (50, 40) is weakly preferred? (d) What is the marginal rate of substitution between food and entertainment at (50, 40)? What about (25, 160)? (e) Are the two indifference curves you graphed examples of diminishing marginal rates of substitution?
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