ECON-2120 Lecture Notes - Lecture 5: Marginal Product, Production Function, Macroeconomics

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peachmoose534

13 Mar 2019

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Before i get into discussing gdp, factors of production, and so-called aggregate production functions , i want to expose you to the concept of a production function and illustrate the property of diminishing marginal productivity. If a variable y is a function of another variable x, this means that the value that. Y takes on depends on the value of x. We can express a function in the following way: For example, suppose that y is your grade on our exam in 2 weeks and that x is the amount of time that you spend studying for the exam. In this case, we expect (or at least hope) that the more you study, the higher your grade will be. So, the higher the value of x, the higher the value of y will be. If we wanted to, we could add more variables to the function.

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By studying, Will can produce a higher grade, Gw, on an upcomingeconomics exam. His production function depends on the number ofhours he studies marginal analysis problems, A, and the number ofhours he studies supply and demand problems, R. Specifically, Gw =2.5(A)^(0.36)B^(0.64). His roommate David's grade productionfunction is Gd=2.5A^(0.25)B^(0.75).

a. What is Will's marginal productivity from studying supply anddemand problems? What is David's?

b. What is Will's marginal rate of technical substitution (MRTS)between studying the two types of problems? What is Davids?

c. Is it possible that Will and David have different marginalproductivity functions but the same marginal rate of technicalsubstitution functions? Explain.

I GIVE FULL KARMA!

rubyfly170

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 doesnâtstudy 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 doesnâtstudy 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.

chocolatemosquito651

Question:

Is it true that in a short-run production process, the marginal cost curve eventually slopes upward because firms have to pay workers a higher wage rate as they produce more output? Explain your answer.

Answer:

The marginal product of labor is the increase in output resulting from a one-unit increase in the amount of labor employed. In my own opinion, the statement can be true in the sense that, as the firm produces more and more the cost of production has to come down first; that becomes constant or minimum and then starts to increase. The marginal cost is also a U-shaped curve that first falls then reaches a minimum and starts rising. The reason for rising marginal costs in the short term will only be an increase in the wages as the only factor which is variable in the short-run is labor whereas all factors are kept fixed, so the fixed costs will keep coming down. If you increase labor, you are going to suffer from diminishing marginal returns. And in the long-run, one will suffer diminishing returns from both input factors, labor, and capital.

The short-run cost relationship between the marginal product of labor and the marginal cost, the labor is variable. We have already established that there are diminishing marginal returns because the labor decreases. To increase output in the short-run, a firm must increase the amount used of a variable input. The marginal product reduces, not because consecutive workers are lesser, but because more workers are being used relative to the amount of equipment that is available, what they have left to work with. An example; if a clinic has only one dentist on duty and several assistants are available and we have a lot of patients waiting to see that doctor, the number of patients served by this office cannot increase without limit. The excess assistants will not be able to increase the number of patients in the office, not because they are not reliable or good enough, but because they cannot perform the doctor's job, and there is only one doctor in the office.

https://www.quora.com/Why-does-the-marginal-cost-curve-slope-upwards

I need a peer reply for this.

amethystwhale496

ECON-2120 Lecture Notes - Lecture 5: Marginal Product, Production Function, Macroeconomics

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