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).

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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

a. (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 __________.

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).

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.

2

2. 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

2

3

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.

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).

4

3. 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.

5

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.

6

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.

7

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?

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