Homework #4
problem #14, from Ch. 4, p. 99 of Case/Fair Principles(6th ed.)
a few problems of my own
modifications of problems #5 and 6 from Ch. 6, p. 144 of Parkin Microeconomics (7th ed.)
modifications of problems #5 and 14 from Ch. 5, p. 13233 of Krugm
Homework #2
problems #3 and 8 from Ch. 2, p. 4142 of Case/Fair Principles(6th ed.)
and a few of my own problems
3. Kristin and Anna live in the beach town of Santa Monica. They own a small business in which they
make wristbands and potholders and sell the
Marginal Cost
Marginal cost:
increase in total cost from producing one more unit of output (the
additional cost of inputs required to produce each successive unit of output)
only reflects changes in variable costs
o fixed cost does not increase as output
Homework #1C
1. Find the derivative of each of the following functions:
a. g x
7x 6
b. k y
3y 1
3 23
q
2
c. m q
aw 2
d. h w
e. u z
bw
c
w
5
2. The Total Product of a firm, denoted by TP , depends on the amount of capital and labor that it
employs. Denote
Costs in the Short Run
Fixed cost:
any cost that does not depend on the firms level of output. (The firm
incurs these costs even if it doesnt produce any output).
firms have no control over fixed costs in the short run. (For this
reason, fixed costs are s
Example #1 Total Revenue and Marginal Revenue
Total Revenue, denoted TR , is a function of the quantity of output that a firm produces, denoted Q , and
the price at which the firm sells its output, denoted p . Specifically, Total Revenue is equal to the a
Costs in the Short Run
Fixed cost:
any cost that does not depend on the firms level of output. (The firm
incurs these costs even if it doesnt produce any output).
firms have no control over fixed costs in the short run. (For this
reason, fixed costs are s
the power-function rule
Now if the value of x in the function f x is raised to a power (i.e. it has an exponent), then all we have
to do to find the derivative is roll the exponent over.
To roll the exponent over, multiply the original function by the ori
Lecture 7
Short-Run Costs
and Output Decisions
Eric Doviak
Principles of Microeconomics
Decisions Facing Firms
decisions
1.
2.
3.
Quantity of output to supply
How to produce that output
(which technique to use)
Quantity of each input to
demand
are
based
o
columns because we are looking at large changes in x as opposed to the infinitesimally small changes
described in the notes entitled: Whats the Difference between Marginal Cost and Average Cost?
Why does it make a difference whether we look at small or la
Now Julia graduates college. Since she has graduated, her father no longer gives her an allowance. To
fund her purchases of hamburgers and cocaine, Julia now needs to work.
She gets a job at a bank and receives $5 for each hour that she works. She is expe
Similarly, x 1
x0
x
1
and x 2
x
x1
x
1x
x
1
1
xx
x2
But what about x 0.5 ? Thats the square root of x : x 0.5
By the same logic as before: x 0.5
1
. Ex. 9 0.5
x
.
x . Ex. 16 0.5
1
9
16
4
1
3
a few preliminaries functions
You may have seen something like t
Homework #6
Pam owns a public relations firm that produces flyers, press releases and websites. For simplicity, assume
that she out-sources the printing, so that we can ignore inputs of printing machinery and paper.
Pams firm produces public relations mat
Calculus Tricks
Calculus is not a pre-requisite for this course. However, the foundations of economics are based on
calculus, so what well be discussing over the course of the semester is the intuition behind models
constructed using calculus.
Its not sur
Homework #6
Pam owns a public relations firm that produces flyers, press releases and websites. For simplicity, assume
that she out-sources the printing, so that we can ignore inputs of printing machinery and paper.
Pams firm produces public relations mat
In the graph at right, I have drawn a total cost
curve running from negative one units of output
to four units of output.
Now it should be obvious to you that a firm
would not produce a negative output.
I drew the total cost function from negative one
to
Will you change the allocation of stocks in your portfolio? No, you wont. You cannot earn a higher
return by changing your allocation because the stocks are perfect complements. Any reallocation would
leave you on a lower isoquant your returns would fall.
If the government imposes a 50% tax on the return on
the return to stock B via method #2: the effective price
of stock B rises from $1 to $2 (effectively, a $1 tax per
share) then your isocost line would rotate inward in a
clockwise direction.
Since you h
Plotting the miners marginal product of labor against the amount of hours that he works shows the rate of
output change at each amount of working hours.
tons of coal
hours
0
1
2
3
4
hours
coal
0
1
1.41
1.73
2
coal
hours
1
0.41
0.32
0.27
We dont need to me
Method #2 It is now more costly to hold stock B, so you can think of the tax as increasing the
price of stock B from $1 to $2, while leaving the return unchanged*. The slope of each isocost line
changes. Once again, you end up on a lower isoquant, since y
Eric Doviak
Principles of Microeconomics
Whats the difference between Marginal Cost and Average Cost?
Marginal cost is not the cost of producing the last unit of output. The cost of producing the last unit of
output is the same as the cost of producing th
Eric Doviak
Principles of Microeconomics
Notes on Isoquants, Isocosts and the Memo on Land Value Taxation
In Lecture 6, I used isoquants and isocosts to analyze profit-maximization. This is not strictly correct. The
point of tangency between an isoquant a
6. The Law of Demand says that consumers purchase more of a good when its price is lower and they purchase
less of a good when its price is higher. Can you give that statement a mathematical interpretation? (Hint: Does
price depend on quantity purchased?
Eric Doviak
Principles of Microeconomics
Notes on Isoquants, Isocosts and the Memo on Land Value Taxation
In Lecture 6, I used isoquants and isocosts to analyze profit-maximization. This is not strictly correct. The
point of tangency between an isoquant a
Homework #1B
More Math Review Problems
1. Graph these equations (placing Y on the vertical
axis and X on the horizontal axis):
Y = 2X + 2
Y = 4X + 2
Comparing the two equations, which is different:
the slope or the Y-intercept? How is it different?
Are th
Eric Doviak
Principles of Microeconomics
Notes on Isoquants, Isocosts and the Memo on Land Value Taxation
In Lecture 6, I used isoquants and isocosts to analyze profit-maximization. This is not strictly correct. The
point of tangency between an isoquant a
Homework #1A
problems #13, from Ch. 1, p. 23
of Case/Fair Principles(6th ed.)
1. Graph each of the following sets of numbers. Draw a line through the points and calculate the slope of
each line.
1
X
1
2
3
4
5
2
Y
5
10
15
20
25
X
1
2
3
4
5
3
Y
25
20
15
10
Micro vs. Macro
MICROeconomics
Study of the decision-making
of individuals, households
and firms
Study of distribution of
wealth
MACROeconomics
Study of aggregates
What factors affect:
o Gross Domestic Product?
o the price level?
o the unemployment rate?