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ECON 2 Midterm: Economics 210A UCSB Midterm12

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turquoisegnu128
31 Jan 2019
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UCSB
Department
Economics
Course
ECON 2
Professor
All

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ECON 2 Full Course Notes
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Document Summary

If not, provide a counterexample. (in all answers where you provide a counterexample, you must show that your example is really a counterexample. ) De ne the function f with domain + (the positive real numbers. ) such that f (x) = x2. We show two things: this function is quasi-concave. 1 to see this, note that f is a strictly increasing function on +. Therefore if f (y) f (x), it must be that y x and hence for any t [0, 1], ty + (1 t)x x. F is an increasing function, it follows that f (ty + (1 t)x) f (x). To see this, note that f (2) = 4 and f (0) = 0, but. 2: = f (1) = 1 . If f is concave, its domain is a convex set a. For all x and y in a, and t between 0 and 1, if f (tx + (1 t)y) tf (x) + (1 t)f (y).

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Related Questions

A question about utility maximization.

Nancy Lerner is trying to decide how to allocate her time instudying for her Economics course.There are two examinationsin this course. Her overall score for the course will be theminimum of her scores on the two examinations.She has decided todevote a total of 1,200 minutes to studying for these twoexams, and she wants to get as high an overall score aspossible. She knows that on the first examination if she doesn’tstudy at all, she will get a score of zero on it. For every 10minutes that she spends studying for the first examination,she will increase her score by one point.If she doesn’tstudy at all for the second examination she will get a zero onit. For every 20 minutes she spends studying for the secondexamination, she will increase her score by one point.

What is Nancy's utility maximizing scores for exam 1 and exam 2?What is her maximum utility? Find how much time she must spend oneach exam to maximize her overal score?

I am able to determine that Nancy's budget line here would be 10X +20Y = 1200, where X = exam 1 score, Y = exam 2 score, however, I amhaving trouble determining the utility maximization since I can'tfigure out how to determine her utility function, U(X, Y), fromthere I can use the Lagrangian method to determine how to maximizeher utility. It could be that I am going about this the wrong waythough. Any help would be appreciated.

Thank you.

Need assistance with these problems!


1. The following is a linear programming formulation of a labor planning problem. There are four overlapping shifts, and management must decide how many employees to schedule to start work on each shift. The objective is to minimize the total number of employees required while the constraints stipulate how many employees are required at each time of day. The variables X1 - X4 represent the number of employees starting work on each shift (shift 1 through shift 4).
Minimize X1 + X2 + X3 + X4
Subject to: X1 + X4%u2265 12 (shift 1)
X1 + X2%u2265 15 (shift 2)
X2 + X3%u2265 16 (shift 3)
X3 + X4%u2265 14 (shift 4)
all variables %u2265 0

Find the optimal solution using QM.
How many workers would be assigned to shift 1? (Points : 3) 12
13
0
none of the above

2. When appropriate, the optimal solution to a maximization linear programming problem can be found by graphing the feasible region and: (Points : 3)
finding the profit at every corner point of the feasible region to see which one gives the highest value.
moving the isoprofit lines towards the origin in a parallel fashion until the last point in the feasible region is encountered.
locating the point that is highest on the graph.
none of the above.
all of the above.


3. Multiple optimal solutions can occur when the objective function is __________ a constraint line. (Points : 3)
unequal to
equal to
linear to
parallel to


4. When applying linear programming to diet problems, the objective function is usually designed to: (Points : 3)
maximize profits from blends of nutrients.
maximize ingredient blends.
minimize production losses.
maximize the number of products to be produced.
minimize the costs of nutrient blends.


5. For a maximization problem, assume that a constraint is binding. If the original amount of a resource is 4 lbs., and the range of feasibility (sensitivity range) for this constraint is from 3 lbs. to 6 lbs., increasing the amount of this resource by 1 lb. will result in the: (Points : 3)
same product mix, different total profit.
different product mix, same total profit as before.
same product mix, same total profit.
different product mix, different total profit.


6. The corner point solution method: (Points : 3)
will yield different results from the isoprofit line solution method.
requires that the profit from all corners of the feasible region be compared.
will provide one, and only one, optimum.
requires that all corners created by all constraints be compared.
will not provide a solution at an intersection or corner where a non-negativity constraint is involved.


7. Consider the following linear programming problem.
Maximize 4X + 10Y
Subject to: 3X + 4Y %u2264 480 and 4X + 2Y %u2264 3 360
all variables %u2265 0
The feasible corner points are (48,84), (0,120), (0,0), (90,0).

What is the maximum possible value for the objective function? (Points : 3)
1032
1200
360
none of the above


8. When using Excel's Solver to input and solve a linear programming problem, it is essential that one perform an additional task before submitting the formulation. That important additional function is: (Points : 3)
guessing the values of the variables.
putting in a value for the objective function.
choosing the options for assuming both a linear model and non-negative variables.
resetting the parameters.
none of the above.


9. Consider the following linear programming problem.
Maximize 5X + 6Y
Subject to: 4X + 2Y %u2264 420 and 1X + 2Y %u2264 120
all variables %u2265 0

Which of the following points (X,Y) is not feasible? (Points : 3)
(50,40)
(20,50)
(60,30)
none of the above


10. ____________ is used to analyze changes in model parameters. (Points : 3)
Optimal solution
Feasible solution
Sensitivity analysis
None of the above

View the video transcript below and share your thoughts on the economic concepts that you believe are applicable.

Question# 1. Provide a rationale on whether or not a firm has to possess market power in order to raise prices.

How to Raise Prices Without Losing Customers

JJ RAMBERG, anchor:

With gas prices soaring and the economy tightening, you may think it’s not possible to charge your customers more. But, it turns out you can successfully raise prices without driving those customers away. Bob Prosen runs the consulting company, Prosen Center for Business. He’s helped business leaders rapidly increase performance, productivity and profits, and he’s also author of the book, “Kiss Theory Goodbye: Five Proven Ways to Get Extraordinary Results in Any Company.” Bob, welcome.

Mr. BOB PROSEN: Thank you.

RAMBERG: So, if you’re going to raise prices on your customers, one of the things you say is don’t surprise them. So, how do you give them warning?

Mr. PROSEN: Well, our customers are very important to us, lets not surprise them. Let’s let them know in advance that prices will increase. But, it’s important to explain to them in their language as to why prices are increasing. For instance, if its fuel surcharges, they’ll understand that. But its important we put it in their language so that they, in turn, can pass that along and plan for it in their own business.

RAMBERG: So, a lot of times when people are paying more, they expect to get more. So, you should communicate increased value I assume. But is saying, um--gas prices are going up for me, is that uh--the same as saying, you’re going to get more for your money?

Mr. PROSEN: No, definitely it’s not. In fact, the equation for value is benefits plus price. So, if prices are going to go up we have to have increased benefits for our customers. So, we can do things like under promise and over deliver. Give them a little bit more. Understand their customer’s customer. So that when we provide our services to them, they’re customized for our customers. They see more value, we understand their business, and therefore they’ll be more appreciative of what we do and less sensitive to price increases.

RAMBERG: That seems to--to follow into your next point, or go right into your next point, which is, track the quality of your products.

Mr. PROSEN: This is absolutely critical, and we can track the quality of our products many ways. Customers call us, complaints, warranty, rework. If we’ll deal with that, capture that, and inside of “Kiss Theory Goodbye” I teach business people how to reduce these problem occurrences and increase the quality of their product. You do it for two reasons: One, customers like us a lot more when things work the way they’re supposed to; and our cost structure goes down therefore maybe we don’t have to increase our prices as much and we can be more competitive.

RAMBERG: And then, also, relationships matter.

Mr. PROSEN: Oh this…

RAMBERG: So, if you have a good relationship, you can do more within that relationship.

Mr. PROSEN: Oh, definitely. People like to do business with people they like. So, lets make sure we stay in touch with our clients. Customize what we touch them with. You know, for instance, when I travel and I deal with business people, I always carry thank you notes in my briefcase. When I’m finished, I send them a note. It’s a rarity these days to even get a thank you note.

RAMBERG: Yeah, it absolutely is. So, about how much can you raise prices by? Can you suddenly figure out that your costs are gone up so much because of energy prices, or food prices, or gas prices, whatever it is, um--and raise it by 50%? Should you do it incrementally? Should you do it all at once? How does it work?

Mr. PROSEN: Yeah, that’s a great question. It depends on what industry you’re in. It depends on what you customers are doing. It depends on a number of things that determine how much, and when, and the frequency of our ability to raise prices. Therefore, what I always recommend to business leaders is work on your cost structure; make sure you’re efficient and effective. Keep your costs as low as you can. Therefore, you can be more competitive on your pricing. Sometimes, you have to pass along the price. Other times, try to absorb what you can through improved efficiencies.

RAMBERG: Should you be looking at your competitors and how much they’re charging?

Mr. PROSEN: Yes, you should absolutely be looking at your competitors. We always want to know what they’re charging. And by the way, we want to differentiate our products and services from our competitors. And, if we can prove a higher value by dealing with us versus our competitor we should be able to articulate that, and we do it based on facts because we know what’s going on in the industry.

RAMBERG: Alright, Bob I know a lot of people are thinking about raising prices so thanks for giving them some tips on how to actually do it.

Mr. PROSEN: My pleasure.