From 55ee78d55df69091ad97483e5a963043a6493cdf Mon Sep 17 00:00:00 2001 From: Rushil Umaretiya Date: Thu, 8 Feb 2024 22:03:51 -0500 Subject: [PATCH] finished p3 pset2 --- pset2/pset2.aux | 4 +- pset2/pset2.fdb_latexmk | 10 +- pset2/pset2.log | 20 +-- pset2/pset2.pdf | Bin 157251 -> 171706 bytes pset2/pset2.synctex.gz | Bin 33503 -> 55438 bytes pset2/pset2.tex | 262 +++++++++++++++++++++++++++++++++++++++- 6 files changed, 275 insertions(+), 21 deletions(-) diff --git a/pset2/pset2.aux b/pset2/pset2.aux index d20f8f8..fa9fcd1 100644 --- a/pset2/pset2.aux +++ b/pset2/pset2.aux @@ -16,5 +16,5 @@ \@writefile{toc}{\contentsline {section}{Question 1}{2}{section*.1}\protected@file@percent } \@writefile{toc}{\contentsline {section}{Question 2}{4}{section*.2}\protected@file@percent } \@writefile{toc}{\contentsline {section}{Question 3}{5}{section*.3}\protected@file@percent } -\@writefile{toc}{\contentsline {section}{Question 4}{6}{section*.4}\protected@file@percent } -\gdef \@abspage@last{7} +\@writefile{toc}{\contentsline {section}{Question 4}{7}{section*.4}\protected@file@percent } +\gdef \@abspage@last{10} diff --git a/pset2/pset2.fdb_latexmk b/pset2/pset2.fdb_latexmk index 7f21c44..bb23b37 100644 --- a/pset2/pset2.fdb_latexmk +++ b/pset2/pset2.fdb_latexmk @@ -1,7 +1,7 @@ # Fdb version 4 -["pdflatex"] 1707351160 "/home/rushil/school/econ/pset2/pset2.tex" "pset2.pdf" "pset2" 1707351160 0 +["pdflatex"] 1707447812 "/home/rushil/school/econ/pset2/pset2.tex" "pset2.pdf" "pset2" 1707447813 0 "/etc/texmf/web2c/texmf.cnf" 1693368362 475 c0e671620eb5563b2130f56340a5fde8 "" - "/home/rushil/school/econ/pset2/pset2.tex" 1707351159 12252 52c13df46743968cf554da6e87d75a4f "" + "/home/rushil/school/econ/pset2/pset2.tex" 1707447812 20756 16d1fdf9d66b0f427e651106380abead "" "/usr/share/texlive/texmf-dist/fonts/map/fontname/texfonts.map" 1577235249 3524 cb3e574dea2d1052e39280babc910dc8 "" "/usr/share/texlive/texmf-dist/fonts/tfm/jknappen/ec/tcrm1000.tfm" 1136768653 1536 e07581a4bb3136ece9eeb4c3ffab8233 "" "/usr/share/texlive/texmf-dist/fonts/tfm/public/amsfonts/cmextra/cmex7.tfm" 1246382020 1004 54797486969f23fa377b128694d548df "" @@ -222,9 +222,9 @@ "/usr/share/texmf/web2c/texmf.cnf" 1681034085 39561 34c98e380bf7c7201ee6a7909aff625a "" "/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map" 1693368379 4623455 fa0568a71dd9a288d6c226ee477506c6 "" "/var/lib/texmf/web2c/pdftex/pdflatex.fmt" 1693368408 7880218 5644a8bb2704ddc1060e0c139ce5389a "" - "pset2.aux" 1707351160 926 59637d5d5411bb70bccd7b27c44337da "pdflatex" - "pset2.out" 1707351160 388 d8802db36feabfa2536c2c124f57d049 "pdflatex" - "pset2.tex" 1707351159 12252 52c13df46743968cf554da6e87d75a4f "" + "pset2.aux" 1707447813 927 c879a6028aca07f7662cad73a36bdb19 "pdflatex" + "pset2.out" 1707447813 388 d8802db36feabfa2536c2c124f57d049 "pdflatex" + "pset2.tex" 1707447812 20756 16d1fdf9d66b0f427e651106380abead "" (generated) "pset2.aux" "pset2.log" diff --git a/pset2/pset2.log b/pset2/pset2.log index 205ef67..295f617 100644 --- a/pset2/pset2.log +++ b/pset2/pset2.log @@ -1,4 +1,4 @@ -This is pdfTeX, Version 3.141592653-2.6-1.40.24 (TeX Live 2022/Debian) (preloaded format=pdflatex 2023.8.30) 7 FEB 2024 19:12 +This is pdfTeX, Version 3.141592653-2.6-1.40.24 (TeX Live 2022/Debian) (preloaded format=pdflatex 2023.8.30) 8 FEB 2024 22:03 entering extended mode restricted \write18 enabled. file:line:error style messages enabled. @@ -648,23 +648,23 @@ LaTeX Font Info: Trying to load font information for U+msb on input line 121. 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Market demand for \question{2} -Economists have been interested in markets for illegal and addictive goods for a long time. One question that many economists have asked is whether \textcolor{ForestGreen}{marijuana} and alcohol are substitutes or complements. After Oregon legalized \textcolor{ForestGreen}{marijuana}, Ben began to collect data on the alcohol and \textcolor{ForestGreen}{marijuana} markets to try to answer this question. He found that in August of 2019, the price of an ounce of \textcolor{ForestGreen}{marijuana} fell by 5\%, and that alcohol sales rose by 7\% directly afterwards. +Economists have been interested in markets for illegal and addictive goods for a long time. One question that many economists have asked is whether \textcolor{OliveGreen}{marijuana} and alcohol are substitutes or complements. After Oregon legalized \textcolor{OliveGreen}{marijuana}, Ben began to collect data on the alcohol and \textcolor{OliveGreen}{marijuana} markets to try to answer this question. He found that in August of 2019, the price of an ounce of \textcolor{OliveGreen}{marijuana} fell by 5\%, and that alcohol sales rose by 7\% directly afterwards. \begin{enumerate}[(a)] - \item Calculate the \textcolor{ForestGreen}{marijuana} cross-price elasticity of demand for alcohol. - \item What does Ben's data indicate about the relationship between alcohol and \textcolor{ForestGreen}{marijuana}? + \item Calculate the \textcolor{OliveGreen}{marijuana} cross-price elasticity of demand for alcohol. + \begin{align*} + \text{Cross-Price Elasticity of Demand} &= \frac{\text{Percentage Change in Quantity Demanded of Alcohol}}{\text{Percentage Change in Price of \textcolor{OliveGreen}{marijuana}}}\\ + &= \frac{0.07}{-0.05} = -1.4 + \end{align*} + \item What does Ben's data indicate about the relationship between alcohol and \textcolor{OliveGreen}{marijuana}? + + Ben's data indicates that alcohol and \textcolor{OliveGreen}{marijuana} are complements, as the cross-price elasticity of demand is negative, which means as the price of \textcolor{OliveGreen}{marijuana} falls, and quantity demanded of \textcolor{OliveGreen}{marijuana} rises, the quantity demanded of alcohol also rises. \end{enumerate} \pagebreak @@ -241,9 +247,157 @@ Consider the market for laptops during 2020, after the COVID pandemic began. For \begin{enumerate}[(a)] \item The government provides most U.S. adults with a \$1,200 stimulus check. + + Since the government is providing most U.S. adults with a \$1,200 stimulus check, this will cause the demand curve to shift to the right (up), as people will have more money to spend on laptops. This will cause the equilibrium price to rise, and the equilibrium quantity to rise. + + \begin{tikzpicture} + \begin{axis}[ + title={Market Curve}, + ylabel={Price}, + xlabel={Quantity}, + yticklabel=\empty, + xticklabel=\empty, + xmin=0, xmax=10, + ymin=0, ymax=10, + axis lines=left, + grid=none, + legend pos=outer north east, + ] + + + \addplot[mark=*, color=orange] coordinates {(6,6)}; + \addlegendentry{New Equilibrium} + + + \addplot[domain=0:10, color=black, thick] {x}; + \addlegendentry{Supply} + + \addplot[domain=0:10, color=blue, thick] {-x+10}; + \addlegendentry{Old Demand} + + \addplot[domain=0:10, color=red, thick] {-x+12}; + \addlegendentry{New Demand} + + \addplot[mark=*] coordinates {(5,5)}; + + \end{axis} + \end{tikzpicture} + + \item A global semiconductor shortage causes the price of semiconductors, a crucial component used in laptops, to rise dramatically. + + + Since we see a rise in the price of semiconductors, this will cause the supply curve to shift to the left (up), as the cost of production for laptops will rise. This will cause the equilibrium price to rise, and the equilibrium quantity to fall. + + \begin{tikzpicture} + \begin{axis}[ + title={Market Curve}, + ylabel={Price}, + xlabel={Quantity}, + yticklabel=\empty, + xticklabel=\empty, + xmin=0, xmax=10, + ymin=0, ymax=10, + axis lines=left, + grid=none, + legend pos=outer north east, + ] + + + \addplot[mark=*, color=orange] coordinates {(4,6)}; + \addlegendentry{New Equilibrium} + + \addplot[domain=0:10, color=blue, thick] {-x+10}; + \addlegendentry{Demand} + + \addplot[domain=0:10, color=black, thick] {x}; + \addlegendentry{Old Supply} + + \addplot[domain=0:10, color=red, thick] {x+2}; + \addlegendentry{New Supply} + + \addplot[mark=*] coordinates {(5,5)}; + + \end{axis} + \end{tikzpicture} \item The government provides most U.S. adults with a \$1,200 stimulus check. At the same time, a global semiconductor shortage causes the price of semiconductors, a crucial component used in laptops, to rise dramatically. + + Since both events are occurring at the same time, the demand curve will shift to the right (up) due to the stimulus check, and the supply curve will shift to the left (up) due to the rise in the price of semiconductors. This will cause the equilibrium price to rise, and an ambiguous effect on the equilibrium quantity. + + \begin{tikzpicture} + \begin{axis}[ + title={Market Curve}, + ylabel={Price}, + xlabel={Quantity}, + yticklabel=\empty, + xticklabel=\empty, + xmin=0, xmax=10, + ymin=0, ymax=10, + axis lines=left, + grid=none, + legend pos=outer north east, + ] + + + \addplot[mark=*, color=orange] coordinates {(5,7)}; + \addlegendentry{New Equilibrium} + + \addplot[domain=0:10, color=blue, thick] {-x+10}; + \addlegendentry{Old Demand} + + \addplot[domain=0:10, color=red, thick] {-x+12}; + \addlegendentry{New Demand} + + \addplot[domain=0:10, color=black, thick] {x}; + \addlegendentry{Old Supply} + + \addplot[domain=0:10, color=green, thick] {x+2}; + \addlegendentry{New Supply} + + \addplot[mark=*] coordinates {(5,5)}; + + \end{axis} + \end{tikzpicture} + \item A large percentage of the U.S. workforce begins to work from home for the duration of the pandemic. At the same time, laptop companies develop new software that lets the machines in their factories make twice as many laptops in a day. + + Since a large percentage of the U.S. workforce begins to work from home, this will cause the demand curve to shift to the right (up), as people will need laptops to work from home. At the same time, the supply curve will shift to the right (down), as the cost of production for laptops will fall. This will cause the equilibrium quantity to rise, and an ambiguous effect on the equilibrium price. + + \begin{tikzpicture} + \begin{axis}[ + title={Market Curve}, + ylabel={Price}, + xlabel={Quantity}, + yticklabel=\empty, + xticklabel=\empty, + xmin=0, xmax=10, + ymin=0, ymax=10, + axis lines=left, + grid=none, + legend pos=outer north east, + ] + + + \addplot[mark=*, color=orange] coordinates {(7,5)}; + \addlegendentry{New Equilibrium} + + \addplot[domain=0:10, color=blue, thick] {-x+10}; + \addlegendentry{Old Demand} + + \addplot[domain=0:10, color=red, thick] {-x+12}; + \addlegendentry{New Demand} + + \addplot[domain=0:10, color=black, thick] {x}; + \addlegendentry{Old Supply} + + \addplot[domain=0:10, color=green, thick] {x-2}; + \addlegendentry{New Supply} + + \addplot[mark=*] coordinates {(5,5)}; + + \end{axis} + \end{tikzpicture} + \end{enumerate} \pagebreak @@ -254,10 +408,109 @@ Consider the market for camp coolers. The market supply of coolersis \(Q_s = 4P\ \begin{enumerate}[(a)] \item Solve for equilibrium price and quantity in the market for camp coolers, and draw a graph illustrating this market. + + \begin{align*} + 4P &= 240 - 4P\\ + 8P &= 240\\ + P &= 30\\ + Q &= 240 - 4(30)\\ + Q &= 120 + \end{align*} + + The equilibrium price of camp coolers is \$30, and the equilibrium quantity of camp coolers sold is 120. + + \begin{tikzpicture} + \begin{axis}[ + title={Market Curve}, + ylabel={Price}, + xlabel={Quantity}, + xmin=0, xmax=240, + ymin=0, ymax=60, + axis lines=left, + grid=none, + legend pos=outer north east, + ] + + \addplot[domain=0:240, color=blue, thick] {x/4}; + \addlegendentry{Supply} + + \addplot[domain=0:240, color=red, thick] {60-x/4}; + \addlegendentry{Demand} + + \addplot[mark=*, color=black] coordinates {(120,30)} node[right, pos=3] {(120,\$30)}; + \addlegendentry{Equilibrium} + \end{axis} + \end{tikzpicture} + \item The government imposes a \$5 tax on those selling camp coolers. How will this change the supply function for coolers? (Hint: you may want to rearrange the supply function so that it is in the form “P=...”, like the example from our slides) + + \begin{align*} + P &= \frac{Q^s}{4}\\ + P &= \frac{Q^s_{tax}}{4} + 5 + \end{align*} + + This will cause the supply function to shift to the left (up) by \$5 since the cost to produce coolers has increased by \$5. + \pagebreak \item Solve for the new equilibrium price and quantity sold after the tax is implemented. + + \begin{align*} + \frac{Q_{tax}}{4} + 5 &= 60 - \frac{Q_{tax}}{4}\\ + \frac{Q_{tax}}{4} + \frac{Q_{tax}}{4} &= 60 - 5\\ + \frac{Q_{tax}}{2} &= 55\\ + Q_{tax} &= 110\\ + P_{tax} &= \frac{130}{4} - 5\\ + P_{tax} &= 32.5 + \end{align*} + + The new equilibrium price of camp coolers is \$32.5, and the new equilibrium quantity of camp coolers sold is 110. + \item Modify your graph from part (a) to show the impact of the tax. + + \begin{tikzpicture} + \begin{axis}[ + title={Market Curve}, + ylabel={Price}, + xlabel={Quantity}, + xmin=0, xmax=240, + ymin=0, ymax=60, + axis lines=left, + grid=none, + legend pos=outer north east, + ] + + \addplot[domain=0:240, color=blue, thick] {x/4}; + \addlegendentry{Supply} + + \addplot[domain=0:240, color=red, thick] {60-x/4}; + \addlegendentry{Demand} + + \addplot[mark=*, color=black] coordinates {(120,30)} node[right, pos=3] {(120,\$30)}; + \addlegendentry{Equilibrium} + + \addplot[domain=0:240, color=green, thick] {x/4 + 5}; + \addlegendentry{New Supply} + + \addplot[mark=*, color=orange] coordinates {(110,32.5)} node[left, pos=3] {(110,\$32.5)}; + \addlegendentry{New Equilibrium} + \end{axis} + + \end{tikzpicture} + \pagebreak \item Calculate how much revenue the government earns from the tax, and the deadweight loss caused by the tax. + + \begin{align*} + \text{Revenue} &= \text{Tax} \times \text{Quantity}\\ + \text{Revenue} &= \$5 \times 110\\ + \text{Revenue} &= \$550 + \end{align*} + \begin{align*} + \text{Deadweight Loss} &= \frac{1}{2} \times \text{Tax} \times \text{Change in Quantity}\\ + \text{Deadweight Loss} &= \frac{1}{2} \times \$5 \times (120 - 110)\\ + \text{Deadweight Loss} &= \frac{1}{2} \times \$5 \times 10\\ + \text{Deadweight Loss} &= \frac{1}{2} \times \$50\\ + \text{Deadweight Loss} &= \$25 + \end{align*} + \end{enumerate} \pagebreak @@ -269,7 +522,8 @@ For this question, consider the market for gasoline in North Carolina. Suppose t \end{align*} \begin{enumerate}[(a)] - \item Use these supply and demand functions to calculate the market equilibrium for gasoline in Oregon. + \item Use these supply and demand functions to calculate the market equilibrium for gasoline in Oregon. + \item Calculate producer and consumer surplus in the market for gasoline in North Carolina. For the rest of this question, assume also that each gallon of gasoline creates an external cost of \$0.50, due to increased healthcare costs for those individuals who breath in engine exhaust. Note that as a result, the social supply function for gasoline in North Carolina would be: \begin{align*} S_{social}(p) = 30,000p - 15,000