Due by 11:59 PM Friday October 14 via by Blackboard Assignments

# 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 continue to 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”)?