# Consider a firm that has the following relationship between labor and

## Name ______________________________________ last 4 PSU ID ________________

### ECON 104 HOMEWORK #5 (100 points total)

Instructions: Please show all work or points will be taken off. Good luck!

1. Initial Conditions (25 points total)
Consider a firm that has the following relationship between labor and output, i.e., a production function.  Along this production function, we hold land, capital (K) and technology (total factor productivity) fixed.  Fill in the following table (5 points).

TABLE 1

L

Q

MPL

MRP

Marginal Profit

### Total Profit

0

0

0

1

8

2

20

3

28

4

35

5

41

6

45

The current wage is \$150 and the price of output (Q) = \$20.[1]

1. (5 points for i through iv)

i.        The profit maximizing output is _______.

ii.      The profit maximizing level of labor input is ________ workers.

iii.    The maximum profit for this firm is  __________.

iv.    What is the marginal revenue product of the 6th worker? ___________

b.      (10 points for correct and completely labeled diagram with points A, B, C, D) Draw the production function associated with the table above.  Note, labor (L) is the variable on the horizontal axis and output (Q) is the variable on the vertical axis and locate this initial point as point A.

c.       (5 points) Now draw the W / MRP labor market diagram (associated with Table 1 above) as we did in lecture being sure to be clear on the areas that represent labor costs, MRP, and the marginal profit or loss – use the “smoothed out version” rather than the barchart version (use different colors if at all possible). You will need to draw a total of three of these ‘initial conditions W / MRP labor market’ diagrams (point A).

Be sure to watch the Homework 5 Explanation video in the Homework 5 folder in ANGEL for some guidance on the rest of the Homework Assignment.

We are now going to consider 3 different scenarios.  We treat each scenario as independent events. You will start off with a new W / MRP labor market diagram for each scenario with these same initial conditions.  Specifically, we start at point A and then depict and explain what happens when we go from scenario to scenario, much like we did in the lectures.   That is, once we evaluate each scenario, we return back to the original conditions and then consider the next scenario.

1. Scenario # 1: (25 points total).Suppose that due to favorable economic conditions, the price that this firm can sell its product for rises to \$22. Fill in the following table. Solve for the new profit  maximizing output and profit (5 points).

TABLE 2

L

Q

MPL

MRP

Marginal Profit

### Total Profit

0

0

0

1

8

2

20

3

28

4

35

5

41

6

45

The current wage is \$150 and the price of output (Q) = \$22.

a.       (5 points for i through iii)

i.      The profit maximizing output is _______.

ii.      The profit maximizing level of labor input is ________ workers.

iii.      The maximum profit for this firm is  __________.

b.      Locate this change in conditions as point B on the production function you drew in part 1b above.

c.       (10 points for correct and completely labeled diagram with points A, B, C, and D) Now construct a supply curve as we did in lecture with point A representing the original price – output combination and point B representing the price – output combination after the change in economic conditions (after price rises to \$22).[2]  Make sure you label the graph completely including what we hold constant along the supply curve. Note, you will be adding points C and D to this diagram.

Given the change in prices, identify point B on your W / MRP labor market diagram that you drew in part 1c.  Be sure to completely label your diagram as we do in the lectures.

d.      (5 points) Explain exactly why the firm changes their behavior (hint, it might help to consider what the difference would be if they did not change their behavior).

1. Scenario # 2 (20 points total) We return to the original conditions and now we let wages change.  In particular, let an increase in labor supply lowers the wage that the firm needs to pay to \$130.  Fill in the table below (5 points).

TABLE 3

L

Q

MPL

MRP

Marginal Profit

### Total Profit

0

0

0

1

8

2

20

3

28

4

35

5

41

6

45

The current wage is \$130 and the price of output (Q) = \$20.

a.       (5 points for i though iii)

i.      The profit maximizing output is _______.

ii.      The profit maximizing level of labor input is ________ workers.

iii.      The maximum profit for this firm is  __________.

b.      Locate this change in conditions as point C on the production function you drew in part 2b above.

c.       (5 points) Explain exactly why the firm changes their behavior (hint, it might help to consider what the difference would be if they did not change their behavior).

d.      (5 points) Re – draw the W / MRP labor market diagram depicting initial conditions (i.e., point A) and now add the new conditions given the lower wage as point C.

Now add point C to your supply curve diagram (don’t draw a new diagram) that you drew in part 2b),  being sure to label diagram completely.

4.      Scenario # 3: (30 points total)
In this final scenario, we return to our original conditions and consider a positive productivity shock, just like we did in the lectures.  In particular, let the MPL of each worker rise by two, due to  an increase in total factor productivity (denoted A), relative to the initial conditions. Fill in the following table (5 points) and answer the following questions.

TABLE 4

L

Q

MPL

MRP

Marginal Profit

### Total Profit

0

0

0

1

2

3

4

5

6

The current wage is \$150 and the price of output (Q) = \$20.

a.       (5 points i through iii)

i.      The profit maximizing output is _______.

ii.      The profit maximizing level of labor input is ________ workers.

iii.      The maximum profit for this firm is  __________.

b.      Locate this change in conditions as point D on the production function diagram you drew in part 1b).

c.       (5 points) Explain exactly why the firm changes their behavior (hint, it might help to consider what the difference would be in terms of profit if they did not change their behavior).

d.      (5 points) Re – draw the W / MRP labor market diagram depicting initial conditions (i.e., point A) and now add the new conditions given the increase in productivity as point D.

Now add point D to your supply curve diagram (don’t draw a new diagram) that your drew in part 1b),  being sure to label diagram completely.

e.       (10 points)  Suppose the workers bargain for and get a raise so that nominal wages rise to \$170.  Re-calculate the maximum profits that this firm can achieve given he increase in productivity and nominal wages and compare to the original profits.  Also compare the level of labor, real wages, and output given these two changes relative to the original conditions.  Are these results consistent with the New Economy, why or why not?

[1] Note, we are assuming, as we did the lectures, that the firm is small relative to the market so that the firm is a price taker in the marketplace and the labor market. Put differently, the firm can sell as much as they want at the market (given)  price (P = \$20) and hire all the labor it wants at the given wage (W = \$150).

[2] We follow the lecture by identifying two points (A and B) and then connect the dots with a ruler implying a linear supply curve.  Even though this is probably not the case, the idea is to understand exactly why the supply curve slopes upward and not to worry about whether the slope is constant or not.

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