{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# answerstohomework2summer2006 - Economics 302 4 Week Summer...

This preview shows pages 1–4. Sign up to view the full content.

Economics 302 4 Week Summer Session 2006 Answers to Homework #2 Due Monday, June 5, 2006 5/31/06 Homework will be graded for content as well as neatness. Sloppy or illegible work will not receive full credit. This homework requires the use of Excel which is a spreadsheet program. 1. Suppose that the production function for an economy is given by Y = F(K, N, A) = AK 1/2 N 1/2 where Y is output, K is capital, N is labor, and A is the level of technology. a. Suppose that the value of A is equal to 1. Fill in the table below based on this information and the given production function. Labor (N) Capital Output MPN MPN Using a Using the Derivative change in output/change in labor 0 25 0 --- ---- 4 25 10 1.25 2.5 9 25 15 0.833333 1 16 25 20 0.625 0.714285714 25 25 25 0.5 0.555555556 36 25 30 0.416667 0.454545455 b. Suppose that the value of A increases to 10. Fill in the table below based on this information and the given production function. Labor (N) Capital Output MPN MPN Using a Using the Derivative change in output/change in labor 0 25 0 --- --- 4 25 100 12.5 25 9 25 150 8.333333 10 16 25 200 6.25 7.142857143 25 25 250 5 5.555555556 36 25 300 4.166667 4.545454545 c. Draw a picture of the two production function relationships you computed in parts (a) and (b) placing output on the vertical axis and labor on the horizontal axis. Verbally explain the effects of a change in technology on the aggregate production function.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
An increase in the level of technology enables the economy to produce a higher level of real GDP for every positive level of labor usage. This is illustrated when you graph these two aggregate production functions since for a given level of labor the level of real GDP is greater with the enhanced technology. d. In the tables you computed the MPN using a derivative and the MPN using a formula for discrete data (the change in output/the change in labor). Provide an explanation for why these two measures would not be equivalent and use a graphical explanation to explore what would make these two measures numerically closer to one another. The gist here is that the derivative uses continuous data while the formula uses discrete data. The formula provides an approximation while the calculus is precise. The two methods will approach one another the smaller the changes in the level of labor used in the formula: for example, if labor was initially 4 units and then we used the formula to calculate the MPN for labor equal to 5 units we would get a closer approximation than if we used 4 units of labor versus 9 units of labor. (You might actually check this out.) 2. Suppose that the production function for an economy is given by Y = F(K, N, A) = K 1/2 N 1/2 A where Y is output, K is capital, N is labor, and A is the level of technology.
a.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern