Exam 1 W22 answers

Page 2 of 6 Multiple Choice, 12 questions. Choose the best answer. Each correct answer is worth two points. 1. Which of the following statements is FALSE ? a. A rational person will always make the choice that maximizes their total revenue given all the options and information they're aware of. b. The net benefit of an action is the value of its economic benefits minus the value of its economic costs. c. Economics can be defined as the study of unlimited wants vs. scarce resources. d. Accounting costs do not generally measure the full economic cost of a choice. Option (a) is false. A rational person will always make the choice that maximizes their net benefit given all the options and information they're aware of. 2. Maia has $30 to spend on groceries. The price per potato is $2, the price per carrot is $1, and the price per pound of fish is $7. Which of the following bundles is she NOT able to purchase? a. 10 potatoes, 2 carrots, 0 pounds of fish b. 4 potatoes, 2 carrots, 4 pounds of fish c. 5 potatoes, 6 carrots, 2 pounds of fish d. 0 potatoes,15 carrots, 2 pounds of fish The budget constraint is 2 ∗ 𝑃𝑃 + 1 ∗ 𝐶𝐶 + 7 ∗ 𝐹𝐹 ≤ 30 . We need to check all the options and see which one costs more than $30. Verifying the options: a) First option is possible: $ 2 ∗ 10 + $1 ∗ 2 + $7 ∗ 0 = $22 ; b) Second option is also possible: $ 2 ∗ 5 + $1 ∗ 6 + $7 ∗ 2 = $30 ; c) Third option is NOT possible: $ 2 ∗ 4 + $1 ∗ 2 + $7 ∗ 4 = $38 ; d) Last option is possible: $ 2 ∗ 0 + $1 ∗ 15 + $7 ∗ 2 = $29 3. Aurelia loves pears and mangos. Help her find her total spending if she decides to purchase 4 pears and 5 mangos using the table on the right. Choose the correct option. a. $33.50 b. $20.50 c. $15.50 d. We don’t have enough information to find Aurelia’s spending To know total spending, we need to know prices. We have MU/P, so to figure out P, we need to calculate the MU. The easiest way to calculate MU is to find it for the first unit: TU=MU for the first unit. (The rest of the table is irrelevant for the purposes of this question). The marginal utility of the first pear is 15 and the marginal utility of the first mango is 37.5. For the first pear, MU/P = 15/P = 7.5. Therefore P pear = $2 For the first mango, MU/P = 37.5/P = 25. Therefore P mango = $1.5. Aurelia’s total spending for 4 pears and 5 mangos would be $15.5

Page 3 of 6 (=$2*4+$1.5*5). 4. Ellen has a fixed amount of money to spend on pizza and coffee. The diagram to the right represents her budget constraint.. If the price of pizza doubles and the price of coffee triples, what happens to the budget line? a. The new budget constraint is steeper relative to the original constraint b. The new budget constraint is flatter relative to the original constraint c. The new budget constraint is parallel to the original constraint d. The budget constraint does not change Explanation: Since the price of pizza doubles, the y intercept shifts from 8 to 4. The x-intercept shifts from 12 to 4 since the price of coffee triples. Since the fall in x-intercept is larger than the fall in the y-intercept, the new budget constraint will be steeper relative to the original constraint. 5. The figure to the right plots three indifference curves representing Sam’s preferences for Coffee and Croissants. Sam’s preferences obey the two laws of utility. Choose the row that most accurately ranks the three consumption bundles shown, A, B, and C: Most Preferred Moderately Preferred Least Preferred a. A B C b. B C A c. C A B d. C B A Indifference curves have greater utility as you move up and right. The bundle C is on the highest IC, followed by A, and then B. 6. Consider a firm in the short run that can produce any quantity it wants, including fractional amounts. According to economic theory, this optimizing firm a. uses the resources they have and those they can acquire at the market to make as much profit as possible b. chooses their production so that the level of output is where marginal cost equals marginal revenue. c. chooses their production so that the level of output is where marginal profit equals zero. d. does all of the above a,b,c) are all ways of saying the same thing; while you should learn the econ jargon and daunting tables you should

Page 5 of 6 Firms maximize profits, not marginal profits. Profits are maximized when marginal profit=0. In the short run, a firm will stay open if it can pay all of its variable costs and at least a little bit of its fixed cost. Profits will be negative if price < ATC but the firm will not close as long as it can pay all variable costs and at least some fixed costs. Profits are maximized when MR = MC. If MR > MC then the firm should produce at least a little bit more to keep making more profits. 10. The table to the right has information about production costs in a factory that produces footballs. The factory is in the short run and has fixed costs. Which of the following statements about the factory’s costs are FALSE ? a. The average variable cost of producing 8 footballs is 0.625 b. The total cost is zero when the firm hires zero workers. c. The marginal cost of increasing football production from 8 to 16 footballs is 0.625 d. If the price of a football is $4 and the factory produces 8 footballs, the factory will earn a profit of $12. The average variable cost of producing 8 footballs is VC/Q = 5/8 = .625. The marginal cost of increasing football production from 8 to 16 footballs is ∆TC/∆Q= ∆VC/∆Q = 5/8 = .625. (∆FC=0). Profit = price * quantity – total cost = $4*8 – (5+15) = $32 – 20 = $12. We know that the firm has a fixed cost of 15, and so total cost is always positive – total cost is at least 15, regardless of production choice 11. Which of the following statements about supply and demand is FALSE ? a. Supply and Demand is a useful model of production for any number of firms participating in a market. b. The Supply and Demand framework suggests that market forces will lead to the efficient quantity of goods provided. c. In equilibrium, consumers who value the goods the most will consume them. d. In equilibrium, producers with the lowest marginal cost will produce. A crucial assumption in supply and demand is that markets are competitive. Therefore, no firm should have a large market share. 12. The market for whole milk is competitive and initially at its equilibrium price and quantity, with a price of $3 per gallon. One Monday, in hopes of helping families struggling to afford groceries, the government mandates the price to temporarily be $1.50 per gallon for that one day. Which of the following is certainly a TRUE statement? a. The price of milk will fall further in later days. b. On Monday, the market will not clear. c. On Monday, there will be an excess supply of whole milk. d. All consumers who want milk on Monday will be able to purchase it. Number of workers Quantity of footballs produced Variable cost Fixed cost 1 8 5 15 2 16 10 15 3 22 15 15 4 26 20 15

Page 6 of 6 $3 is the equilibrium price, so $1.50 is below the equilibrium. The forces of excess supply and demand will mean that if the price is different from equilibrium, we will return to equilibrium. In this case, there will be an excess demand. Excess demands tend to push the price up, not down. If there is an excess demand, the market does not clear (that is, Qd ≠ Qs). This is equivalent to saying that some people want milk but are not able to purchase it This page intentionally left blank (available as scratch paper)

Page 3 of 6 Name: _________________________________________ 2. (7 points total) Roger is a first-year student at the University of Michigan. He trains for soccer and studies for Econ 101. Outside of sleeping and doing chores, he has 16 hours to split between these activities. One session of soccer practice takes 2 hours, and each session with his Econ study group takes 3 hours. The table to the right shows his total utility gained from each activity a. (1 pt) Write Roger’s budget constraint. Let S be Roger’s quantity of soccer training sessions and E be his number of Econ study groups. Rather than spending money, he “spends” time. Each S takes 2 hours and each E takes 3 hours, and he has 16 hours to allocate. His budget constraint of time is therefore. 2 ∗ 𝑆𝑆 + 3 ∗ 𝐸𝐸 = 16 b. (3 pts) Fill in the table below, calculating the MU and MU/Hour of each activity based on the information given above. Quantit y of soccer training s MU of soccer MU/hour of soccer Quantity of Econ 101 study group meetings MU of Econ studyin g MU/hour of Econ studying 0 - - 0 - - 1 200 100 1 160 53.3 2 100 50 2 150 50 3 90 45 3 90 30 4 80 40 4 45 15 5 70 35 5 30 10 6 60 30 6 3 1 7 50 25 7 0 0 Quantity of soccer training Total Utility from soccer trainings Quantity of Econ 101 study group meetings Total Utility from Econ 101 study group meetings 0 0 0 0 1 200 1 160 2 300 2 310 3 390 3 400 4 470 4 445 5 540 5 475 6 600 6 478 7 650 7 478

Page 4 of 6 Name: _________________________________________ c. (2 pts) Roger maximizes his utility by splitting the remaining part of his day between soccer trainings and study group meetings. What are his optimal quantities of soccer trainings and study group meetings? Show your work! Follow the rule of picking the highest MU/P of the remaining goods available. Roger has a constraint of 16 hours a day. ● First choice, he chooses to play soccer (100>53.3), he spends 2 hours (14 hours left). ● Second choice, he chooses to study (53.3>50), he spends 3 hours (11 hours left). ● Third choice, he chooses to play soccer and to study (to do both, 50 in both and has the same quantity of training and study group visits), he spends 5 hours in both (6 hours left). ● Fourth choice, he chooses to play soccer (45>30), he spends 2 hours (4 hours left). ● Fifth choice, he plays soccer again (40>30), he spends 2 hours (2 hours left). ● His last choice, he plays soccer again (35>30), he spends 2 hours (0 hours left). Roger’s optimal quantities of soccer trainings and study group visits are: 5 soccer trainings and 2 study group meetings. d. (1 pt) How many total utils does Roger obtain from his optimal consumption bundle? Roger will obtain from his optimal consumption bundle 540 utils from playing soccer and 310 utils from going to the study group meetings, that will amount to 850. 3. (9 points total) A profit-maximizing book printing company has an Average Variable Cost curve, an Average Total Cost curve and a Marginal Cost curve. The price is $5 per book, and the firm must decide how many books to produce. a. (2 pts) If the firm prints 30 books, then profits are $60. What is the Average Total Cost (ATC) of printing 30 books? Profit = total revenue – total costs, which can be re-written as profit = (p-ATC)*Q, or in this case 60 = (5 – ATC)*30. Solve for ATC to get ATC = p – (profit/Q) = $5 – ($60/30) = $3 b. (2 pts) Given what we know from part (a), if the book printing company’s fixed cost is $45, then what is the Average Variable Cost (AVC) of producing 30 books? There are lots of ways to solve this! One goes as follows: ATC = Total cost /Q = (VC+FC)/Q. Total Cost = ATC*Q = $3*30 = $90. Since fixed cost is $45 that leaves $45 in variable costs when Q = 30.. AVC = VC/Q = $45/30 = about $1.50

Page 6 of 6 Name: _________________________________________ e. (2 pts) If the price is $2.50 per book (as in part d above), would the company print books or choose to shut down? Explain. The books printing company remains open if price > AVC. When quantity=20 books, AVC= $2.25 so the company would remain open even though profits are negative. The company stays open because the revenue from 20 books is sufficient for pay the variable costs and pay b 4. (4 points total). There are two goods, X and Y. Gail has an income of $24. The price of Y is P Y = $3. a. (3 pts) In the same graph, plot a graph of utility maximizing consumption choice where i. The price of X is P X = $4, resulting in an optimal quantity of Q X = 4. ii. The price of X falls to P X = $2. Show how utility-maximizing quantity of X changes when its price falls (no exact Q number is required here, just an indication of the direction of change). Label all intercepts as accurately as possible! A clearly labeled graph requires no additional explanation. All the references to “utility maximization” means that we need to see a graph that contains utility, and that utility as at the optimum possible – a tangency between the budget constraint and an indifference curve. b. (1 pt) In your own words, explain how your graph from part (a) relates to the Demand curve. This is the exact process we use to get (“derive”) the individual demand curve! All else equal, we are finding out the best possible Q at every possible P for that person. As P goes down Q goes up. It’s the consumer willingness to buy a good given its price.