Micro 1010 Chapter 3

Now suppose that you have a summer job that pays you​ $15 per hour. How would your analysis​ change? With a​ $15-per-hour summer​ job,

the opportunity cost of your time would increase.

If opportunity cost were to suddenly​ increase, total cost would

increase and net benefit would decrease.

In​ general, apartment rental prices ________ as the opportunity cost of commuting​ rises, indicating a strong ________ relationship between rents and commutes.

increase; negative

Maria can purchase shirts for ​$22.00 each. She considers the benefit of one shirt to be ​$45.00​, but with each additional shirt she purchases the benefit decreases by $5. According to the Principle of Optimization at the​ Margin, Maria will purchase ______ shirts. ​(Enter your response as a whole number​.)

5; $45-$22/$5=4.6

A company mines 420,000 tons of coal per year in a rural county. The coal is worth ​$77 per ton. The average price for a​ 2,000-square-foot house with three bedrooms more than 20 km away from the mining site in this county is ​$210,000. The average price for a​ similar, 2,000-square-foot house with three bedrooms within 4 km of the mine is 5 percent lower. Using comparative​ statics, what is the effect of mining on home prices in this​ county? Mining changes the price of a​ 2,000-square-foot home​ (with three​ bedrooms) by ​$ . ​(Round your response to two decimal places and use a negative sign if necessary.​)

$210,000 x 5%= -10,500 $−10,500

You are considering renting a city apartment with​ 1,000 square feet for ​$1,300 per month. The monthly rent on a​ larger, 1,500-square-foot city apartment is ​$1,750. The marginal cost of renting an apartment with 500 additional square feet is ​$_____ per square foot per month. ​(Round your response to two decimal places.​)

(1750-1300)/(1500-1000)= 0.9

Suppose your total benefit from eating slices of pizza​ (value in​ dollars) is 10x−x^2​, where x is the number of slices of pizza. Pizza is sold by the slice and costs ​$2 per​ slice, and so the total cost of pizza is 2x. Using optimization in​ levels, what is the optimal amount of pizza for you to​ eat? Your net benefit is maximized at nothing slices of pizza. ​(Enter your response as an integer.​)

10x-x^2-2x => 8x-x^2 take derivative of both to get 8-2x=0 => Then 8/2=>4=x

You are a professor of economics at a university.​ You've been offered the position of serving as department​ head, which comes with an annual salary that is ​$5,500 higher than your current salary.​ However, the position will require you to work 200 additional hours per year. Suppose the next best use of your time is spending it with your​ family, which has value of ​$20 per hour. What is the difference in the net benefit from becoming the department​ head? The change in net benefit is ​$_____. ​(Enter your response as an integer.​) To​ optimize, you _______become a department head.

20*200=4000 5500-4000=1500 1500; should

Assume that the average price for a​ 2,000-square-foot house in the city is ​$360,000 and the average rent for a​ 2,000-square-foot apartment in the city is ​$1,100 per month. Also assume that the average price for a​ 2,000-square-foot house in the suburbs is ​$250,000​, the average price for a​ 2,000-square-foot house in the county is ​$370,000​, and the average price for a​ 3,000-square-foot house in the suburbs is ​$500,000. Using comparative statics and the information​ above, what is the best estimate of the effect of living in the city​ (relative to living in the​ suburbs) on home​ prices? Living in the city changes home prices by ​$____. ​(Round your response to two decimal places.​)

360,000-250,000=110,000

Your total benefits from spending time with your spouse are shown in the following table. Hours per Day Total Benefit ​Alternatively, you have the option of working as many hours as you​ want, earning ​$11 per hour. Assume this is the next best use of your time. Use the marginal principle to find your optimal number of hours to spend with your spouse per day. The optimal amount of time for you to spend with your spouse is _______hours per day. ​(Enter your response as an integer.​)

4

You have been invited to play a​ 4-hour round of golf that has a value to you of ​$50. The total price to play the round of golf is ​$45. The net benefit of the round of golf is ​$___. ​(Enter your response as an integer.​) Now assume that you have a job that pays you ​$12 per hour. Would you be optimizing to accept the invitation to play​ golf? To​ optimize, you should not______ golf.

5; not play

Research was conducted by professor Jobs to check which one program out of three given programs is the optimal choice for a student. The three options are a 6​ month, a 12​ month, or a 15 month program. Important information considered by the professor in his research is how much a student pays in tuition and fees for a given program within different time spans. The program is​ intensive, so it can be completed faster but at higher costs. The three programs yield the same benefit for the student. The program can be completed in 6​ months, 12​ months, or 15 months. The tuition and fees are​ $38,600, $35,000 and​ $28,600 respectively. Professor Jobs assumes the opportunity cost of time to a student for the program is​ $2,000 per month If professor Jobs assumes the opportunity cost of time to a student for the program is​ $500 per month instead of​ $2,000 per​ month, then the​ $2,000 per month cost curve lies ______the​ $500 per month cost curve. The optimal program for students when the opportunity cost of time for the program is​ $500 per month___________________when compared to the scenario with the opportunity cost of time is​ $2,000 per month.

6months x 2000= 12000 +38600=50600 12months x2000=24000+35000=59000 15montherx2000=30000+28600=58600 above switches to 15 month program Program 1 is the best program for the student with an opportunity cost of time of​ $2,000 per month. This program has the lowest total cost by taking into account both direct cost of tuition and fees and indirect time costs of the program.​ Therefore, Program 1 is the optimal choice for student. To​ optimize, it is necessary to convert all of the costs and benefits into common units. The time cost of a program is calculated by using the​ student's opportunity cost of​ time, which is​ $500 per month. Programs Program time span​ (months) Time cost of a program Tuition and fees Total​ cost: Time cost of a programplus+Tuition and fees 1 6 months 6 times $ 500 equals $ 3 comma 0006×$500=$3,000 ​$38,600 $ 3 comma 000 plus $ 38 comma 600 equals $ 41 comma 600$3,000+$38,600=$41,600 2 12 months 12 times $ 500 equals $ 6 comma 00012×$500=$6,000 ​$35,000 $ 6 comma 000 plus $ 35 comma 000 equals $ 41 comma 000$6,000+$35,000=$41,000 3 15 months 15 times $ 500 equals $ 7 comma 50015×$500=$7,500 ​$28,600 $ 7 comma 500 plus $ 28 comma 600 equals $ 36 comma 100$7,500+$28,600=$36,100 The​ $500 curve has lower time costs for each​ program, so the total​ cost, which takes into account both the direct cost of tuition and fees and the indirect cost of​ time, is lower for all programs compared to the time cost for each program with an opportunity cost of​ $2,000 per month.​ Therefore, the​ $2,000 per month cost curve lies above the​ $500 per month cost curve. Program 3 is the best program for the student with an opportunity cost of time of​ $500 per month.​ Therefore, the optimal program for students with an opportunity cost of​ $500 per month switched to 15 month program when compared to the scenario with the opportunity cost of​ $2,000 per month.

Which one of the following is common between optimization using total value and optimization using marginal​ analysis? A.It is a​ cost-benefit analysis technique for optimization. B.It calculates the change in total value and chooses the option with the highest total value as a best feasible option. C.It calculates the extra cost generated by moving from one feasible alternative to the next feasible alternative. D.It excludes the information that is not relevant to the decision.

A.It is a​ cost-benefit analysis technique for optimization. There are two​ cost-benefit analysis techniques for optimization. The first technique simply calculates the total value of each feasible option and then picks the option with the greatest total value. The second technique is marginal analysis and reminds you to exclude information that is not relevant to your decision. The marginal cost is the extra cost generated by moving from one feasible alternative to the next feasible alternative. It focuses on the differences among the feasible options and chooses the option with the highest total value as a best feasible option.

Which of the following statements regarding marginal analysis are​ true? ​(Check all that apply.​) A.It is often faster to implement than optimization using total value. B.It always picks out a different optimum than the minimization of the total cost. C.It focuses on the difference between one feasible alternative and the next feasible alternative. D.It excludes information that is relevant to the​ individual's decision.

A.It is often faster to implement than optimization using total value. C.It focuses on the difference between one feasible alternative and the next feasible alternative.

Marginal analysis always picks out the same optimum as minimization of total cost.

Always; the same

Suppose there are four products that Samuel can purchase. Samuel obtains a discount on each of the products. The total benefit obtained by Samuel through discounts is calculated by finding out the difference in the actual price of the product and the discounted price of the product. This is shown on the Y axis of the graph. The X axis of the graph represents the products which Samuel can purchase. In this​ case, Samuel will purchase product ____ as an optimal product.

Answer: Samuel will purchase product 2 as an optimal product. Samuel will purchase that product which will maximize his total benefit. That is, the optimal product is the product which gives him the highest Total benefit. In the graph when Samuel buys product 1, he gets a total benefit of 4. When he buys product 2, he gets a total benefit of 5. When he buys product 3, the total benefit he gets is 2. And when he buys product 4, his total benefit is 3. Therefore, he gets the maximum Total benefit of 5 when he buys product 2. Thus the answer is: product 2.

Which of the following statements regarding marginal analysis is​ true? A.If total cost is​ falling, marginal cost could be zero. B.If total cost is​ rising, marginal cost could be falling. C.If total cost is​ rising, marginal cost must be rising. D.If total cost is​ falling, marginal cost must be positive.

B.If total cost is​ rising, marginal cost could be falling.

Since optimization is used to analyze​ people's choices and help them improve the outcomes of their​ choices, its A. normative only. B.both normative and positive. C.positive only. D.neither because it describes preferences but not how to improve themdescribes preferences but not how to improve them

B.both normative and positive.

Marginal analysis is a​ cost-benefit calculation that A.analyzes the marginal revenue at points on the demand curve. B.focuses on the similarities between one feasonable alternative and the next feasible alternative. C.analyzes the marginal costs at points on the demand curve. D.focuses on the differences between one feasonable alternative and the next feasible alternative.

D.focuses on the differences between one feasonable alternative and the next feasible alternative.

You and your​ friend, Jim, have just moved out of your dorm and into a new apartment. Both of you decide that you need to get a couch. Jim thinks you should get a new one from a furniture store nearby. You feel​ that, given your​ budget, it is best to buy a used one. Your other options are to buy one online or get a couch​ custom-made at the same furniture store. How would you arrive at an optimal solution​ here? Assume that your opportunity cost of time is​ $5 per hour. You and Jim would need to consider​ ___________. A.the indirect costs of traveling to the furniture store and the opportunity cost of your time required to shop. B.only the marginal benefit of each couch. C.the direct costs of the price of each couch and the cost of having each couch moved to your apartment. D.the direct costs and the indirect opportunity cost of your time required to shop. E.only the price of each couch.

D.the direct costs and the indirect opportunity cost of your time required to shop.

Suppose apartments are in four​ locations: Location​ A, Location​ B, Location​ C, and Location D. Location A is in the​ city, where your job is. Location B is 10 minutes farther from your job than Location A. Location C is 10 minutes farther from your job than Location​ B, and Location D is 10 minutes farther than Location C. In​ turn, similar apartments in Location B rent for ​$115115 less per month than apartments in Location​ A, apartments in Location C rent for ​$115115 less than in Location​ B, and apartments in Location D rent for ​$115115 less than in Location C. Suppose the value of your time is ​$2020 per hour and you work 21 days per​ month, with each day requiring a​ round-trip commute from your apartment to work. For​ simplicity, assume rent and the opportunity cost of your time commuting to work are the only factors influencing the location in which to rent an apartment. You should rent an apartment in_______________. Suppose you currently rent an apartment in Location Upper C Location C. By moving to​ optimize, you change your net benefit by ​$______. ​(Enter your response as an integer.​)

Location A.: 50

Which of the following statements regarding the principle of optimization is​ true? ​(Check all that apply.​) A. It applies only in the case of monetary and financial matters. B. It is the unifying principle that connects various seemingly unrelated decisions. C. It means always choosing the best feasible option. D. It takes into account and evaluates multiple​ trade-offs. In which of the following situations is optimization a good description of​ behavior? A.Tia is a very fun loving person. She chooses to go on a vacation with friends instead of volunteering at NGO as a vacation is more enjoyable. Your answer is correct. B.Kat, the MIT business management​ graduate, starts his first business and incurs huge financial losses despite graduating from MIT. C.Rita watches movies late at night. The next​ day, she wakes up late causing her to be late to her exam. D.John is careless and irresponsible causing him to make a lot of mistakes in his work.

Part 1 D and B; part 2 A.Tia is a very fun loving person. She chooses to go on a vacation with friends instead of volunteering at NGO as a vacation is more enjoyable. Optimization means picking the best feasible​ option, given the available information. Economists believe that optimization​ describes, or at least​ approximates, many of the choices economic agents make.​ However, economists​ don't take optimization for granted. Several special situations are associated with behavior that is not optimal. For​ example, when people have​ self-control problemslong dash—like being careless and irresponsible or not being punctuallong dash—optimization is not a good description of behavior as in the case of John and Rita. People also tend to fail as optimizers when they are new to a task as in the case of Kat.​ Consequently, optimization is a better description of choices when people have lot of experience. Tia has two feasible options to choose​ from: to go on a vacation or volunteering at an NGO. As she is a very fun loving​ person, she chooses the option that is more enjoyable for her.​ Therefore, in her case optimization is a good description of the behavior.

You have the option to play tennis or a round of golf​ (but not​ both). The tennis match requires you to take 2 hours off from work and the round of golf requires you to take 4 hours off from work. Playing tennis has value to you equal to ​$70​, while golf has value to you equal to ​$95. Tennis courts are publicly available at no​ cost, but golf costs ​$30 per round. Suppose your wage from working is ​$10 per hour. The net benefit from playing tennis is ​$50 and the net benefit from playing golf is ​$25. ​(Enter your responses as integers.​) ​Therefore, you should play tennis.

Tennis=> 2 hours x 10 per hour=$20 $70-$20= $50 Golf=> 4hours x 10 per hour=$40 $95-$30-$40=$25 You should play tennis because it has a higher value to you.

When John determines what choice of walking shoes will give him the best bang for his buck​, he is using optimization based on total value . When Janet looks at the additional value of purchasing a new laptop to the cost as compared to keeping her old​ one, she is using optimization based on marginal analysis .

Total value; Marginal analysis

When optimizing for total​ value, opportunity cost must be added to total cost. Assuming equal ​benefits, the lowest cost option is the optimal choice.

added to; equal

When you optimize in __________ you evaluate the change in utility that would result from selecting one option over another option. differences levels benefits

differences