HW 5
Sienna gets a total of 20 utils per week from her consumption of pizza and a total of 40 utils per week from her consumption of yogurt. The price of pizza is $1 per slice, the price of yogurt is $1 per cup, and she consumes 10 slices of pizza and 20 cups of yogurt each week. Which of the following statements is correct regarding Sienna's current consumption of pizza and yogurt?
We cannot determine if Sienna is maximizing her total utility with the information provided. Explanation: We must apply the rational spending rule to find out if Sienna's current combination of pizza and yogurt is optimal. To do this, we need to know the marginal utility per dollar that Sienna receives from each good; in other words, how much utility she gained from the last dollar spent on pizza and from the last dollar spent on yogurt. However, the information given only enables us to conclude that Sienna's average utility per dollar is the same for both pizza and yogurt. We do not have enough information to know whether her marginal utility per dollar is the same for both goods.
For the demand curve shown, find the total amount of consumer surplus that results in the gasoline market if gasoline sells for $2 per gallon. The horizontal axis labeled quantity of 1,000s of gallons per year ranges from 10 to 120 in increments of 10. The vertical axis labeled price in dollar per gallon ranges from 0 to 12 in increments of 1. A line begins at the point (0, 10) goes down to the right, and ends at the point (100, 0). The point (80, 2) is marked out on the line. Instructions: Enter your response as a whole number. Consumer surplus: $___________ per year.
$320,000 Explanation: 1/2 (base) × (height) = 1/2(80,000 gallons/year) × ($8/gal) = $320,000 per year The horizontal axis labeled 1,000s of gallons per year ranges from 0 to 100 in increments of 100. Point 80 is marked out on the horizontal axis. The vertical axis labeled price in dollar per gallon ranges from 0 to 10 in increments of 10. Point 2 is marked out on the vertical axis. A line begins at the point (0, 10) goes down to the right, and ends at the point (100, 0). A dotted horizontal line goes left from the point (80, 2) till the vertical axis. A dotted vertical line goes down from the point (80, 2) to the horizontal axis. The area above the dotted horizontal line and below the line is shaded and labeled consumer surplus = $ 320,000 per year.
Kai's current marginal utility from consuming orange juice is 75 utils per ounce and her marginal utility from consuming coffee is 50 utils per ounce. If orange juice costs 25 cents per ounce and coffee costs 20 cents per ounce, is Kai maximizing her total utility from the two beverages? Instructions: Enter your responses as whole numbers. At her current level of consumption, Kai is receiving: ______ utils per dollar spent on orange juice. At her current level of consumption, Kai is receiving: ______ utils per dollar spent on coffee. Therefore, Kai _________ maximizing her total utility because MUoj/Poj is ___________ MUc/Pc.
300; 250; is not; not equal Explanation: At her current level of consumption, Kai receives (75 utils per ounce)/($0.25 per ounce) = 300 utils per dollar spent on orange juice, and she receives (50 utils per ounce)/($0.20 per ounce) = 250 utils per dollar spent on coffee. Since the two are not equal, she is not maximizing her utility. Given that she receives more utils per dollar spent on orange juice than on coffee, she should spend more on orange juice and less on coffee.
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 equal to her marginal utility from the 4th apple she buys. Explanation: According to the rational spending rule, at a consumer's optimal consumption bundle, the ratio of marginal utility to price must be the same for all goods. Thus, if peaches and apples both cost $1 each, then if Fiona is maximizing her utility, her marginal utility from the 16th peach she buys must be equal to her marginal utility from the 4th apple she buys.
Which of the following factors would impact a buyer's reservation price for a given good or service? Instructions: In order to receive full credit, you must make a selection for each option. For correct answer(s), click the box once to place a check mark. For incorrect answer(s), click the option twice to empty the box. check all that apply The cost of producing the item, Peer influence, The price of a good
Peer influence; The price of a good Explanation Peer influence provides an example of how social forces often influence demand; it is often the most important single determinant of demand. A change in the price moves the consumer along the demand curve and does not affect reservation price. A change in cost is a supply-side influence that will shift supply and not affect reservation price.
Suppose you and your friend go out for dinner. Your friend orders a cheeseburger and fries. When your food first arrives, you ask your friend if you can have one of his fries. He looks at you like you are crazy and says, "No!" Then a few minutes later, after you both have started eating, you ask again, and your friend reluctantly says, "Sure. Go ahead." An economist's explanation for your friend's change of heart is most likely to be that:
Your friend's marginal utility from eating additional fries declines as he eats more of them, so he's more likely to share with you after he's eaten a few. Explanation: An economist would argue that as your friend eats more fries, his marginal utility from eating additional fries decreases because of diminishing marginal utility. This implies that he will be more willing to share his fries with you after he has already eaten a few.
The buyers' side of the market for amusement park tickets consists of two consumers whose demand curves are shown in the diagram below. a. Graph the market demand curve for this market. Instructions: Use the tool provided to plot the market demand curve for prices: $36, $24 and $0 (three points total). Instructions: Enter your response as a whole number. b. Calculate the total consumer surplus in the amusement park market if tickets sell for $12 each. $________ per year.
a. (0,36), (16,24), (144,0) b. $672 Explanation a. The market demand curve (right panel) is the horizontal summation of the two individual demand curves (left and center panels). Graph to the left. The horizontal axis labeled tickets per year ranges from 0 to 96 in an increment of 96. The vertical axis labeled price in dollars per ticket ranges from 0 to 24 in increments of 12. A line begins at the point (0, 24) goes down to the right and ends at the point (96, 0). Graph in the center. The horizontal axis labeled tickets per year ranges from 0 to 48 in an increment of 48. The point 16 is also marked out on the horizontal axis. The vertical axis labeled price in dollars per ticket ranges from 0 to 36 in increments of 12. A line begins at the point (0, 36) goes down to the right and ends at the point (48, 0). A vertical dotted line going up from the point (16, 0) meets the line at the point (16, 24). Graph to the right. The horizontal axis labeled tickets per year ranges from 0 to 144 in an increment of 144. The points 16 and 80 are also marked out on the horizontal axis. The vertical axis labeled price in dollars per ticket ranges from 0 to 36 in increments of 12. A line begins at the point (0, 36) goes down to the right till the point (16, 24) then goes further down and right and ends at the point (144, 0). A vertical dotted line going up from the point (80, 0) meets the line at the point (80, 12). The area below the original line for all values equal and above $24 per ticket forms a triangle and is shaded in blue color. The area below the original line for all values between $12 and $24 is divided into 2 sections. The portion less than 16 tickets per year forms a rectangular area and is colored in pink color. The portion more than 16 and less than 80 tickets per year forms a triangle and is colored in grey color. b. Total consumer surplus is the sum of the three shaded areas: Area of small triangle = 1/2(base) × (height) = 1/2(16 tickets/year) × ($12/ticket) = $96 per year Area of rectangle = (base) × (height) = (16 tickets/year) × ($12/ticket) = $192 per year Area of large triangle = 1/2(base) × (height) = 1/2(64 tickets/year) × ($12/ticket) = $384 per year Total consumer surplus is thus $672/year ($96 + $192 + $384).
Zander has a weekly allowance of $24, all of which he spends on pizza and movie rentals, whose prices are $6 per slice and $3 per rental, respectively. We can assume that pizza slices and movie rentals are available only in whole-number amounts. Instructions: Enter your responses as whole numbers. a. For the given levels of pizza consumption, calculate how many rentals Zander can afford with his remaining income. Pizza: 0,1,2,3,4 Rentals: ____________ b. Using the utility values in the table below, how many pizza slices and how many movie rentals should Zander consume each week to maximize his total utility? Pizza slices per week: 0,1,2,3,4,5,6,7,8 Utils/week from pizza: 20,36,48, 58, 66, 72, 76, 78 Movie rentals per week: 0,1,2,3,4,5,6,7,8 Utils/week from rentals: 0,40,46,50,54,56,57,57,57 Pizza slices to be consumed per week: Movie rentals to be consumed per week:
a. Rentals: 8,6,4,2,0 b. 3;2 Explanation: a. The affordable combinations and their corresponding utilities are listed in the table below: Combinations of pizza and movie rentals that cost $24 per week: 0 pizzas, 8 rentals; 1 pizza, 6 rentals; 2 pizzas, 4 rentals; 3 pizzas, 2 rentals; 4 pizzas, 0 rentals Total utility: 0 + 57 = 57; 20 + 57 = 77; 36 + 54 = 90; 48 + 46 = 94; 58 + 0 = 58 b. The rational spending rule states that the marginal utility for the last pizza divided by the price of pizza should be equal to the marginal utility for the last rental divided by the price of rentals. The information on marginal utility divided by price is summarized in the table below: Pizza slice per week: 0,1,2,3,4,5,6,7,8 Utils/week from pizza: 0,20,36,48,58,66,72,76,78 Marginal utility from pizza:-,20,16,12,10 MU/Price:-,3.33,2.66,2,1.67 Movie rentals per week: 0,1,2,3,4,5,6,7,8 Utils/week from rentals:0,40,46,50,54,56,57,57,57 Marginal utility from rentals:-,40,6,4,4,2,1,0,0 MU/Price: -,13.33,2,1.33,1.33,0.67,0.33,0,0 Since the marginal utility per dollar (marginal utility divided by price) for the 3rd pizza (12/$6 = 2) is equal to the marginal utility per dollar of the 2nd rental (6/$3 = 2), we know that the optimal combination is 3 pizzas per week and 2 movie rentals. This finding can be confirmed by computing the total utility for each combination of pizza and rentals computed in part a.
Any consumer trying to decide whether to buy a given good or service will base the decision on his or her reservation price and the existing market price. When making this decision, the buyer's reservation price measures the The market price measures the The consumer will purchase the good or service only if the buyer's reservation price is
marginal benefit: the value of the resources used in production.marginal benefit: the highest price that a buyer is willing to pay for a product; marginal cost: the amount that buyer will actually have to pay; equal to or higher than the market price. Explanation: The highest price that a consumer is willing to pay for a product is known as the reservation price. Market price is the price that is actually paid by the consumer. Consumers will not purchase any product if their reservation price is lower than the market price. Therefore, the consumers will only purchase a product if their reservation price is higher than, or equal to, the market price.
You are having lunch at an all-you-can-eat buffet. If you are rational, what should be your marginal utility from the last morsel of food you swallow?Marginal utility from the last morsel of food you swallow should be
zero Explanation: The marginal cost of an additional morsel of food is zero at an all-you-can-eat buffet. Thus, applying the rational spending rule, a rational person will continue eating until the marginal utility of the last morsel falls to zero.
