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?
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 B
Suppose the firm wants to spend exactly $100. With labor on the horizontal axis and capital on the vertical axis, find the equation of the isocost line (in a graphable form), and graph it.
Question 6
For each of the following production functions, identify whether the production process exhibits constant returns to scale, increasing returns to scale, or decreasing returns to scale. Be sure to show your work!
Question 7
Jerry’s Berries is a small farm that has the following production function for strawberries using combinations of labor and land :
The marginal products (of labor, ; and land, are:
Put labor, on the horizontal axis and land, on the vertical axis.
Part B
Suppose the farm is currently using 4 units of labor and 1 unit of land. How much output (tons of strawberries) is the farm producing?
Part C
From its current production, how much more output would the farm get by utilizing 1 more unit of labor? What about 1 more unit of land (instead of labor)?
Part D
From its current production, how many units of land would the farm be willing to forgo in order to use one more unit of labor and still produce the same output as before? How many units of labor would the farm be willing to forgo in order to use one more unit of land and still produce the same output as before?
Question 8
Your firm builds aircraft engines using both labor (L) and power tools (K). The production function for aircraft engines is
Part A
Can you completely mechanize the production of aircraft engines (i.e. produce using all capital, no labor)?
Part B
Suppose you currently have 100 power tools. In the short run, you cannot buy or sell power tools. Derive your short run production function.
Part C
Find the (i) total product of labor, (ii) average product of labor, and (iii) marginal product of labor for using 0, 1, 2, 3, 4, and 5 workers. [Hint: make a table!] Round to the nearest engine. Does labor experience diminishing returns?
Question 9
Dunder Mifflin paper company produces reams of paper each week according to the production function:
They have determined that they need to ship 1,000 reams of paper this week to Scranton, PA. Using capital costs 10.
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 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 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:
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?