mirror of
https://github.com/Rushilwiz/econ101.git
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222 lines
7.4 KiB
TeX
222 lines
7.4 KiB
TeX
\documentclass{article}
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\usepackage{fancyhdr}
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\usepackage{extramarks}
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\usepackage{amsmath}
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\usepackage{amsthm}
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\usepackage{amsfonts}
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\usepackage{tikz}
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\usepackage[plain]{algorithm}
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\usepackage{algpseudocode}
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\usepackage[shortlabels]{enumitem}
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\usepackage{mathtools}
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\usepackage{amssymb}
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\usetikzlibrary{automata,positioning}
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%
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% Basic Document Settings
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%
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\topmargin=-0.45in
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\evensidemargin=0in
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\oddsidemargin=0in
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\textwidth=6.5in
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\textheight=9.0in
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\headsep=0.25in
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\linespread{1.1}
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\pagestyle{fancy}
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\lhead{\hmwkAuthorName}
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\chead{\hmwkClassTime (\hmwkClassInstructor): \hmwkTitle}
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\lfoot{\lastxmark}
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\cfoot{\thepage}
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\renewcommand\headrulewidth{0.4pt}
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\renewcommand\footrulewidth{0.4pt}
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\setlength\parindent{0pt}
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%
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% Create Problem Sections
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%
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\newcommand{\enterProblemHeader}[1]{
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\nobreak\extramarks{}{Problem \arabic{#1} continued on next page\ldots}\nobreak{}
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\nobreak\extramarks{Problem \arabic{#1} (continued)}{Problem \arabic{#1} continued on next page\ldots}\nobreak{}
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}
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\newcommand{\exitProblemHeader}[1]{
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\nobreak\extramarks{Problem \arabic{#1} (continued)}{Problem \arabic{#1} continued on next page\ldots}\nobreak{}
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\stepcounter{#1}
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\nobreak\extramarks{Problem \arabic{#1}}{}\nobreak{}
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}
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\setcounter{secnumdepth}{0}
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\newcounter{partCounter}
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\newcounter{homeworkProblemCounter}
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\setcounter{homeworkProblemCounter}{1}
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\nobreak\extramarks{Problem \arabic{homeworkProblemCounter}}{}\nobreak{}
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\newcommand{\hmwkTitle}{Problem Set 1}
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\newcommand{\hmwkDueDate}{January 26th, 2024}
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\newcommand{\hmwkClass}{Introduction to Economics}
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\newcommand{\hmwkClassTime}{ECON 101}
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\newcommand{\hmwkClassInstructor}{Robert McDonough}
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\newcommand{\hmwkAuthorName}{\textbf{Rushil Umaretiya}}
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%
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% Title Page
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%
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\title{
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\vspace{2in}
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\textmd{\textbf{\hmwkClass:\ \hmwkTitle}}\\
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\normalsize\vspace{0.1in}\small{\textbf{Due\ on\ \hmwkDueDate\ at 11:59pm}}\\
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\normalsize\text{Tuesday/Thursday 3:30-4:45, Genome Sciences 100}\\
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\vspace{0.1in}\large{\textit{\hmwkClassInstructor\ - \hmwkClassTime}}
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\vspace{3in}
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}
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\author{\hmwkAuthorName\\\small{rumareti@unc.edu}}
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\date{}
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\renewcommand{\part}[1]{\textbf{\large Part \Alph{partCounter}}\stepcounter{partCounter}\\}
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%
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% Various Helper Commands
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%
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% Useful for algorithms
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\newcommand{\alg}[1]{\textsc{\bfseries \footnotesize #1}}
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% For derivatives
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\newcommand{\deriv}[1]{\frac{\mathrm{d}}{\mathrm{d}x} (#1)}
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% For partial derivatives
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\newcommand{\pderiv}[2]{\frac{\partial}{\partial #1} (#2)}
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% Integral dx
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\newcommand{\dx}{\mathrm{d}x}
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% Alias for the Solution section header
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\newcommand{\solution}{\textbf{\large Solution}}
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\newcommand{\question}[1]{\pagebreak\section{Question #1}}
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% Probability commands: Expectation, Variance, Covariance, Bias
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\newcommand{\E}{\mathrm{E}}
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\newcommand{\Var}{\mathrm{Var}}
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\newcommand{\Cov}{\mathrm{Cov}}
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\newcommand{\Bias}{\mathrm{Bias}}
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\begin{document}
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\maketitle
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\question{1}
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We apply the cost-benefit principle every day. As students, the choice to attend UNC involved big costs and (hopefully) benefits.
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\begin{enumerate}[(a)]
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\item Attending UNC involves large out-of-pocket costs, which are listed
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on UNC's student aid website:
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https://studentaid.unc.edu/current/costs/.
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Using this site, find the total yearly cost of attending UNC as an
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in-state student.
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\item What is the North Carolina state minimum wage? Use the state minimum wage to calculate the foregone wages that you lose by attending UNC for the year.
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\item Not all costs are measured in dollars! Describe some of the nonmonetary costs of spending a year at UNC.
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\item At UNC, most students graduate after 8 semesters (4 years). Setting aside the non-monetary costs, use the numbers you found
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above to calculate the opportunity cost of earning your degree. Ignore the possibility of student loans and aid, and pretend that
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you are paying out of pocket.
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\item Explain the cost-benefit principle in a sentence or two. Incorporating the numbers you found above, then explain your decision
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to attend UNC this year using the cost-benefit principle.
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\end{enumerate}
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\question{2} Your car needs gas before you can go to work this morning. You
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decide to go to the gas station that is out of the way, but where gas
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is \$0.10/gallon cheaper than the gas station on the way to work. This
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gets you into work 10 minutes later than going to the other gas station.
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If your wage is \$20/hour and you have to purchase 20 gallons of gas,
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was this worth it? Why or why not?
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\question{3} Tanner and Jasmine are each capable of producing two services: walking dogs or cooking meals. Tanner can cook a meal for 6 people in
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an hour, or walk 1 dog in an hour. Jasmine can cook a meal for 2
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person in an hour, or walk 3 dogs in an hour. They each have 4 hours
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available to use to cook meals or walk dogs.
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\begin{enumerate}[(a)]
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\item Draw a production possibilities frontier showing Tanner's capacity to cook meals or walk dogs, then add another PPF showing
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Jasmine's ability to cook meals or walk dogs.
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\item Label (including numbers) a point on Tanner's PPF that he could
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produce at without trading. Do the same for a point on Jasmine's
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PPF
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\item Who has the comparative advantage in cooking meals? Who
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has the comparative advantage in walking dogs? Explain both
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answers.
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\item Tanner and Jasmine decide to specialize in producing one thing,
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then trade. What will Tanner choose to produce and what will
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Jasmine choose to produce. Explain your answer.
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\item What can we say about the price that Tanner and Jasmine would
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both be willing pay to trade meals and dog walks?
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\item Suppose that before trading, Tanner and Jasmine each spent two
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hours walking dogs and two hours cooking meals. What are the
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gains to specialization and trade in this situation? Provide an
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example for how the gains from trade could be distributed so
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that Tanner and Jasmine each have more of each service than
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before.
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\item In your example for how the gains of trade could be distributed,
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how much of each good are Tanner and Jasmine trading to one
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another? Do these ”terms of trade” make sense, given what you
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wrote in part (e)?
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\end{enumerate}
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\question{4}
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Consider the market for a new physical copy of our textbook, \emph{Principles of Economics by Stevenson and Wolfers}. The instructors teaching large classes of ECON 101 at UNC all use this textbook. For each
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of the following situations, decide if demand will shift, if supply will
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shift, or if neither will shift. Then, draw a graph clearly illustrating
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how supply or demand will shift.
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\begin{enumerate}[(a)]
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\item The price of textbook ink increases.
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\item UNC mandates that all arts and science majors must take ECON
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101.
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\item The price of the textbook rises.
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\item The price of used copies of the old edition of the textbook decrease.
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\end{enumerate}
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\question{5}
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Consider the daily market for a cup of coffee in Chapel Hill. Market
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demand for coffee is given by the equation \(P = 80 - \frac{1}{2}Q_d\), and market
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supply of coffee is given by \(P = \frac{Q_s}{38}\).
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\begin{enumerate}[(a)]
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\item If the price of coffee is \$0, how many cups would buyers want to
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consume? How many cups would sellers want to sell?
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\item Calculate the price at which buyers would not want to buy any
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coffee (i.e., \(Q_d = 0\)).
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\item Calculate the equilibrium price of coffee and the quantity of coffee
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cups sold in Chapel Hill every day.
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\item Draw a properly labeled diagram for the market for coffee in
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Chapel Hill.
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\end{enumerate}
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\end{document} |