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answerstohomework4summer2014.doc
answerstohomework4summer2014.doc
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answerstohomework4summer2014.doc-Economics 101 Sum...
answerstohomework4summer2014.doc-Economics 101 Summer 2014 Answers to
answerstohomework4summer2014.doc-Ec...
answerstohomework4summer2014.doc-Economics 101 Summer 2014 Answers to
Page 1
Economics 101
Summer 2014
Answers to Homework #4
Due Thursday, June 12, 2014
Directions:
The homework will be collected in a box
before
the lecture. Please place your name
, TA
name
and section number
on top of the homework (legibly). Make sure you write your name as it appears
on your ID so that you can receive the correct grade. Late homework will not be accepted so make plans
ahead of time.
Please show your work.
Good luck!
Please realize that you are essentially creating “your brand” when you submit this homework. Do
you want your homework to convey that you are competent, careful, professional? Or, do you want
to convey the image that you are careless, sloppy, and less than professional. For the rest of your
life you will be creating your brand: please think about what you are saying about yourself when
you do any work for someone else!
1. Suppose you are told that the production function for widgets is given by the following equation where
Q is the quantity of widgets, K is the number of units of capital used in producing widgets, and L is the
number of units of labor used in producing widgets:
Q = 4K
1/2
L
1/2
You are also told that total cost for this firm can be found by using the following equation where TC is
total cost, P
k
is the price per unit of capital, and P
l
is the price per unit of labor:
TC = P
k
K + P
l
L
a. Using this information, fill out the following table depicting the production function and the cost
functions for this firm. Make sure you provide the units of measurement in your answers. If necessary,
round your answers to the nearest hundredth.
L
K
Q
VC
FC
TC
AVC
AFC
ATC
MC
0
25
---
---
---
---
1
25
4
25
$1.25 per
unit of
output
9
25
16
25
$2.00 per
unit of
output
25
25
b. Given the above information, which input is the variable input? Explain why this is your answer.
c. Given the above information, what is the price per unit of capital and what is the price per unit of
labor?
d. Does this firm experience diminishing returns to labor? To answer this question you will find it helpful
to calculate the values for the marginal product of labor, MP
l
. Here’s a table to use in calculating these
values. Make sure you provide the units of measurement in your answers. If necessary, round your
answers to the nearest hundredth.
1
Page 2
L
K
Q
MP
l
0
25
---
1
25
4
25
9
25
16
25
25
25
Answer:
a.
L
K
Q
VC
FC
TC
AVC
AFC
ATC
MC
0
25
0
$0
$50
$50
---
---
---
---
1
25
20
$10
$50
$60
$0.50 per
unit of
output
$2.50 per
unit of
output
$3.00 per
unit of
output
$0.50 per
unit of
output
4
25
40
$40
$50
$90
$1 per unit
of output
$1.25 per
unit of
output
$2.25 per
unit of
output
$1.50 per
unit of
output
9
25
60
$90
$50
$140
$1.50 per
unit of
output
$0.83 per
unit of
output
$2.33 per
unit of
output
$2.50 per
unit of
output
16
25
80
$160
$50
$210
$2.00 per
unit of
output
$0.63 per
unit of
output
$2.63 per
unit of
output
$3.50 per
unit of
output
25
25
100
$250
$50
$300
$2.50 per
unit of
output
$0.50 per
unit of
output
$3.00 per
unit of
output
$4.50 per
unit of
output
b. Labor is the variable input: from the table we can see that the amount of labor varies as the level of
output changes while the level of capital is constant and does not change as the level of output changes.
c. To fill in the table you must figure out the price of labor and the price of capital.
From the table we know that the average variable cost is equal to $2.00 per unit of output and that this
AVC occurs when the firm hires 16 units of labor and produces 80 units of output. Recall that AVC =
VC/Q and in this case VC = P
l
*L. Using this information we have $2.00 per unit of output = P
l
*(16 units
of labor)/(80 units of output) or P
l
= ($2.00 per unit of output)(80 units of output)/(16 units of labor) = $10
per unit of labor. Review this calculation carefully and note in particular how the units of measurement
work out to give you $ per unit of the variable input.
From the table we know that the average fixed cost is equal to $1.25 per unit of output and that this AFC
occurs when the firm hires 25 units of capital and produces 40 units of output. Recall that AFC = FC/Q
and in this case FC = P
k
*K. Using this information we have $1.25 per unit of output = P
k
*(25 units of
capital)/(40 units of output) or P
k
= ($1.25 per unit of output)(40 units of output)/(25 units of capital) = $2
per unit of capital. Review this calculation carefully and note in particular how the units of measurement
work out to give you $ per unit of the fixed input.
d. This firm does experience diminishing marginal returns to labor since as the amount of labor hired
increases, output increases but at a diminishing rate. We can see this by examining the table below that
2
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