# econ assignment

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ECONOMICS 100A: INTERMEDIATE MACROECONOMICS

Summer Session I 2021

PROBLEM SET 3

Due Wednesday July 14th by midnight

1. Pindyck and Rubinfeld, Chapter 6

2.

Suppose a chair manufacturer is producing in the short run (with its existing plant and equipment). The manufacturer has observed the following levels of production corresponding to different numbers of workers:

 Number of Workers Number of Chairs 1 10 2 18 3 24 4 28 5 30 6 28 7 25

a.
Calculate the marginal and average product of labor for this production function.

b.
Does this production function exhibit diminishing returns to labor? Explain.

c.
Explain intuitively what might cause the marginal product of labor to become negative.

3.

Fill in the gaps in the table below.

 Quantity of Variable Input Total Output Marginal Product of Variable Input Average Product of Variable Input 0 0 — — 1 225 2 300 3 300 4 1140 5 225 6 225

4.

or letters to potential voters in a reelection campaign. Describe the production function for campaign votes. How might information about this function (such as the shape of the isoquants) help the campaign manager to plan strategy?

5.

For each of the following examples, draw a representative isoquant. What can you say about the marginal rate of technical substitution in each case?

a.
A firm can hire only full-time employees to produce its output, or it can hire some combination of full-time and part-time employees. For each full-time worker let go,
the firm must hire an increasing number of temporary employees to maintain the same level of output.

b.
A firm finds that it can always trade two units of labor for one unit of capital and still keep output constant.

c.
A firm requires exactly two full-time workers to operate each piece of machinery in the factory.

6.

A firm has a production process in which the inputs to production are perfectly substitutable in the long run. Can you tell whether the marginal rate of technical substitution is high or low, or is further information necessary? Discuss.

7.

The marginal product of labor in the production of computer chips is 50 chips per hour. The marginal rate of technical substitution of hours of labor for hours of machine capital is 1/4. What is the marginal product of capital?

8.

Do the following functions exhibit increasing, constant, or decreasing returns to scale? What happens to the marginal product of each individual factor as that factor is increased and the other factor held constant?

a.

32

qLK

=+

b.

1

2

(22)

qLK

=+

c.

2

3

qLK

=

d.

11

22

qLK

=

e.

1

2

44

qLK

=+

9.

The production function for the personal computers of DISK, Inc., is given by

q

 10

K

0.5

L

0.5, where

q

is the number of computers produced per day,

K

is hours of machine time, and

L

is hours of labor input. DISK’s competitor, FLOPPY, Inc., is using the production function

q

 10

K

0.6

L

0.4.

a.
If both companies use the same amounts of capital and labor, which will generate more output?

b.
Assume that capital is limited to 9 machine hours, but labor is unlimited in supply. In which company is the marginal product of labor greater? Explain.

10.

In Example 6.4, wheat is produced according to the production function

q

 100(

K

0.8

L

0.2).

a.
Beginning with a capital input of 4 and a labor input of 49, show that the marginal product of labor and the marginal product of capital are both decreasing.

b.
Does this production function exhibit increasing, decreasing, or constant returns to scale?

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