# Problem Set 3

• Section 1 (M/W): Due by 11:59 PM Sunday, Mar 14, 2021
• Section 2 (Tu/Th): Due by 11:59 PM Sunday, Mar 21, 2021

by PDF upload in Blackboard Assignments

Please type your answers to the following questions in a document and save as a PDFIn MS Word, or Pages, or most word processing software, File -> Save As -> PDF, or File -> Export -> PDF.

to upload on Blackboard under Assignments. You may handwrite answers if you will be able to scan/photograph & convert them to a single PDF, if they are easily readable, but this is not preferred. See my guide to making a PDF - an essential skill in the modern world. If you are handwriting answers, you may print the pdf above and write on it, or just write on a piece of paper (we only need your answers).

For the few questions that ask you to draw a graph, try to do so on your computer (use MS Paint, the drawing tools in MS Word or MS Powerpoint, plot points in MS Excel, drawing/notetaking apps, etc.), and save it as an image to include on your homework document. Again, they need not be perfect or to scale, just show that you understand the broad idea. Being able to understand and sketch the graphs is still a very important and useful skill! If all else fails, I will be lenient in grading graph questions if you are unable to technologically include a graph.

You may work together (and I highly encourage that) but you must turn in your own answers. Your TA, under my supervision, will grade homeworks 70% for completion, and for the remaining 30%, and one question will be graded for accuracy - so it is best that you try every problem, even if you are unsure how to complete it accurately.

## Concepts and Critical Thinking

Please answer the following questions briefly (1-3 sentences). Use examples as necessary. Be sure to label graphs fully, if appropriate.

### Question 1

Describe, in your own words, what the marginal rate of technical substitution means. How is it different from the slope of the isocost line?

### Question 2

Describe, in your own words, what is true at the least-cost input combination (the optimum) for a firm. Why is it the optimum? What does the equality of the slope of the isoquant curve and the slope of the isocost line mean, in English?

### Question 3

Explain the difference between the short run and the long run in production.

### Question 4

Describe, in your own words, what the law of diminishing marginal returns means. How can firms increase output?

## Problems

Show all work for calculations. You may lose points, even if correct, for missing work. Be sure to label graphs fully, if appropriate.

### Question 5

Suppose a firm can hire labor at $5/hour and rent capital for$20 per hour.

#### Part A

Write an equation for the total cost of the firm.

#### Part A

What is the cost-minimizing combination of labor and capital that will yield 1,000 reams of paper? Round each to the nearest whole number.

#### Part B

What is the total cost of using this combination of inputs?

#### Part C

Now suppose that they need to double their output this week, and need to produce 2,000 reams of paper. How does their optimal combination of inputs change?Hint: neither the equation for MRTS nor any prices are changing!

#### Part D

What is the total cost of this new level of output?

#### Part E

Suppose management at Dunder Mifflin develops a new program that magically makes everyone at the firm more productive, such that the firm’s new production function becomes: \begin{align*}q &=20 l^{0.5} k^{0.5}\\ MP_l& = 10l^{-0.5}k^{0.5}\\ MP_k& = 10l^{0.5}k^{-0.5}\\ \end{align*}

Still needing to supply 2,000 reams of paper this week at the same input prices, what is their new optimal combination of labor and capital?

#### Part F

How much does this combination cost? What does this show you about technological improvement (or “total factor productivity”)?