Subpart (a):
Utility maximizing output.
Subpart (a):
Explanation of Solution
According to the maximization of the utility method, the
The utility maximizing combination of goods can be calculated at the point where the last dollar spent on each commodity yields the same level of utility. Thus, the marginal utility per dollar spent on each commodity can be calculated using the following formula as follows:
To calculate the marginal utility (MU) per dollar for the first unit of good A, substitute the respective values in equation (1).
Table -1 shows the value of marginal utility per dollar for the different goods and their prices that are obtained by using equation (1).
Table -1
MU per dollar unit 1 | MU per dollar unit 2 | MU per dollar unit 3 | MU per dollar unit 4 | MU per dollar unit 5 | MU per dollar unit 6 | MU per dollar unit 7 | MU per dollar unit 8 | |
Good A | 4.00 | 3.00 | 2.50 | 2.00 | 1.50 | 1.00 | 0.83 | 0.67 |
Good B | 4.00 | 2.50 | 2.00 | 1.50 | 1.17 | 0.83 | 0.33 | 0.17 |
Good C | 3.75 | 3.00 | 2.00 | 1.75 | 1.25 | 1.00 | 0.88 | 0.75 |
Good D | 1.5. | 1.25 | 1.00 | 0.75 | 0.54 | 0.29 | 0.17 | 0.08 |
savings | 5.00 | 4.00 | 3.00 | 2.00 | 1.00 | 0.50 | 0.25 | 0.13 |
Since, the marginal utility of a dollar is 5 for 1 unit of saving, he will go for it. Then, he will go for the consumption of Good A, B and another unit of savings which gives 4 utils of marginal utility per dollar. Then, the consumption of the first unit of good C will take place which gives 3.75 utils of marginal utility per dollar. Then, he will go for the 2nd unit of Good A and C along with the third unit of saving which provides 3 utils of marginal utility per dollar. Then, he will consume the 3rd unit of Good A and 2nd unit of Good B for marginal utility per dollar worth 2.50 utils. Finally, the 4th unit of Good A and savings along with 3rd unit of Good B and C which gives 2 utils of marginal utility per dollar is consumed. As a result, his total budget would exhaust and cease his consumption, where his utility would be at the maximum.
The utility maximizing output combination is the combination where the marginal utility per dollar spent on each commodity is equal. Analyzing the table, we can see that 4 units of good A and D, 3 units of Good B and C and 4 units of savings will provide an individual with the marginal utility per dollar worth 2 utils. Since, no unit of good D provides marginal utility per dollar worth 2 utils, no unit of good D will be consumed.
Concept introduction:
Utility: It can be explained as the benefit or the satisfaction which is derived from the consumption of a good or service by the consumer.
Marginal utility: It is the extra satisfaction that a consumer derives from the consumption of an additional unit of the specific good or service.
Utility maximizing combination: The utility maximizing combination is such that the last rupee spent on each commodity should yield the same level of an additional utility or the marginal utility spent on each commodity should be equal.
Utility per dollar spent: It is the utility of one dollar spent on the unit. It can be calculated by dividing the marginal utility with the initial price.
Subpart (b):
Utility maximizing output.
Subpart (b):
Explanation of Solution
According to the marginal utility per dollar, the consumer consumes the goods and services until when it gives the equal marginal utility per dollar which are worth 2 utils. It is at 4 units of savings, the marginal utility per dollar equals to 2 units and thus, the consumer will choose to save $4.
Concept introduction:
Utility: It can be explained as the benefit or the satisfaction which is derived from the consumption of a good or service by the consumer.
Marginal utility: It is the extra satisfaction that a consumer derives from the consumption of an additional unit of the specific good or service.
Utility maximizing combination: The utility maximizing combination is such that the last rupee spent on each commodity should yield the same level of an additional utility or the marginal utility spent on each commodity should be equal.
Utility per dollar spent: It is the utility of one dollar spent on the unit. It can be calculated by dividing the marginal utility with the initial price.
Subpart (c):
Utility maximizing output.
Subpart (c):
Explanation of Solution
The utility maximizing combination is 4Units of Good A, 3 units of Good B, 3 units of Good C, 0 unit of Good D and 4 Unit of savings. With this combination, the total budget of the consumer gets exhausted. This can be verified by substituting the values as follows:
Since the total budget is $106 which is equal to the cost of the utility maximizing combination, the total budget gets exhausted with this combination of goods and savings.
Concept introduction:
Utility: It can be explained as the benefit or the satisfaction which is derived from the consumption of a good or service by the consumer.
Marginal utility: It is the extra satisfaction that a consumer derives from the consumption of an additional unit of the specific good or service.
Utility maximizing combination: The utility maximizing combination is such that the last rupee spent on each commodity should yield the same level of an additional utility or the marginal utility spent on each commodity should be equal.
Utility per dollar spent: It is the utility of one dollar spent on the unit. It can be calculated by dividing the marginal utility with the initial price.
Want to see more full solutions like this?
Chapter 7 Solutions
ECONOMICS - UPDATED
- 22. Peanut butter (PB) sells for 10 dollars per pound and Oysters (O) sell for 50 dollars perpound. Suppose Pat buys 5 pounds of peanut butter and one pound of oysters each month.With this consumption bundle, his MRSP B,O = 3. Which of the following is true (assumingPat’s preferences satisfy all the basic assumptions of consumer theory)?(a) Pat could increase his utility by buying more oysters and less peanut butter.(b) Pat could increase his utility by buying more peanut butter and less oysters.(c) Pat could increase his utility by buying more peanut butter and more oysters.(d) Pat could increase his utility by buying less peanut butter and less oysters.arrow_forwardSuppose that Omar’s marginal utility for cups of coffee is constant at 1.5 utils per cup no matter how many cups he drinks. On the other hand, his marginal utility per doughnut is 10 for the first doughnut he eats, 9 for the second he eats, 8 for the third he eats, and so on (that is, declining by 1 util per additional doughnut). In addition, suppose that coffee costs $1 per cup, doughnuts cost $1 each, and Omar has a budget that he can spend only on doughnuts, coffee, or both. How big would that budget have to be before he would spend a dollar buying a first cup of coffee?arrow_forward11) Suppose there are two goods, X and Y, with X measured on the horizontal axis and Y measured onthe vertical axis. Which of the following statements about a budget line relating the two goods is correct? The budget line shows all the possible combinations of X and Y a consumer can buy given the level of income and prices. The budget line shows all the possible combinations of X and Y a consumer can buy given the level of income, prices, and borrowings. The budget line shows the most preferred combinations of X and Y a consumer can buy given the level of income and prices. The budget line shows the least-cost combinations of X and Y a consumer will buy given the level of income and prices.arrow_forward
- True or false with reasoning: 1) _______When we claim that utility can be ordinally measured, we assume that the consumer is able to measure the total and marginal utility received when one extra unit of a commodity is consumed. 2)_______If MRS between two goods is constant, then having more of one good without having more of the other does not increase utility. 3)_______Marginal Utility increases until total utility is at a maximum and then marginal utility decreases.arrow_forwardJohn likes Coca-Cola. After consuming one Coke, John has a total utility of 10 utils. After two Cokes, he has a total utility of 25 utils. After three Cokes, he has a total utility of 50 utils. Does John show diminishing marginal utility for Coke, or does he show increasing marginal utility for Coke? Supposethat John has $3 in his pocket. If Cokes cost $1 each and John is willing to spend one of his dollars on purchasing a first can of Coke, would he spend his second dollar on a Coke, too? What about the third dollar? If John’s marginal utility for Coke keeps on increasing no matter how many Cokes he drinks, would it be fair to say that he is addicted to Coke?arrow_forwardPetra has $480 to spend on DVDs and books. Abook costs $24 and a DVD costs $15. [LO 7.2]a. Write an equation for the budget constraint.Let x 5 books. Let y 5 DVDs.b. Use your equation to determine how manybooks Petra can buy if she buys 8 DVDs.arrow_forward
- 12)Suppose a consumer has $100 to spend on two goods, shoes and shirts. If the price of a pair of shoes is $20 per pair and the price of a shirt is $15 each, which of the following combinations is unaffordable to the consumer? A) 0 pairs of shoes and 0 shirts B) 2 pairs of shoes and 4 shirts C) 5 pairs of shoes and 0 shirts D) 0 pairs of shoes and 7 shirts E) 2 pairs of shoes and 3 shirtsarrow_forwardTitle Suppose that Lynn enjoys coconut oil in her coffee. She has very particular preferences, and she mus Description Suppose that Lynn enjoys coconut oil in her coffee. She has very particular preferences, and she must have exactly two spoonfuls of coconut oil for each cup of coffee. Let C be the number of cups of coffee, and O be the number of spoonfuls of coconut oil. Also, let PC be the price of a cup of coffee. Suppose Lynn has $12 to spend on coffee and coconut oil. Also, the price of coconut oil is $.50 per spoonful.a) Graph Lynnâs Price Consumption Curve for prices, PC = $1, PC = $2, and PC = $3. Please put the number of cups of coffee on the horizontal axis, and the number of spoonfuls of coconut oil on the vertical axis. Be sure to label your graph carefully and accurately.b) Graph Lynnâs demand curve for coffee. You may assume that both coconut oil and coffee are continuous variables so she can consume any amount of coffee and coconut oil that she could afford.…arrow_forwardYou 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 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? ______units of X and ______units of Y b. What total utility will you realize? ______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? _____units of X and ______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 $ $arrow_forward
- An individual's utility function is given by: U (q1 , q2) = q11/2 . q2 Suppose we know that the individual is maximizing their utility by consuming 9 units of good #1 (q1=9) and six units of good #2 (q2=6). If the current price for good #1 is $1 (p1=1), what must be the price of good #2 (p2) and what must be the individual's current income (y) available to spend on the two goods? a.) p2 = b.) y=arrow_forwardA consumer’s budget set for two goods (X and Y) is 600 ≥ 3X + 6Y. (LO2) a. Illustrate the budget set in a diagram. b. Does the budget set change if the prices of both goods double and the consumer’s income also doubles? Explain. c. Given the equation for the budget set, can you determine the prices of the two goods? The consumer’s income? Explain.arrow_forward5) A consumer of two goods, good 1 and good 2, has a utility function u (X1, X2) = x1 0,6. X2 0,4, where x denotes units of good 1 and X2 units of good 2. The price of good 1 is 5 euros And the price of good 2 is 3 euros per unit and the consumer’s income is 150 euros. Suppose that only the price of good 1 changes and that the new price is p, ‘ = 2. Then the demand function of good 1 that is derived from the utility function is Choose one: A) X1= 0.6m/p1 B) X1= 6m/p1 C) X1= 4m/p1 D) X1= 0.4m/p1 E) Not definedarrow_forward
- Principles of MicroeconomicsEconomicsISBN:9781305156050Author:N. Gregory MankiwPublisher:Cengage Learning