ECO102 Lecture 02

ECO102 - Week 02.pdf

• Why are some countries growing quickly and other slowly?:
  • Kinda linked to GGR208.
  • Crude Birth Rate has to do with this as well.
  • Industrialized countries are slowing.
• Catchup effect
  • GDP per capita is small in developing countries.
  • They're growing quickly and will catch up.
• Why growing GDP matters?:
  • When a country that isn't growing, the only opportunity to get up is to be rivalrous.
  • In a growing Economy, everyone is better off. People are no longer rivals
• Rule of 72
  • Growing at $3\mathrm{\%}⟹\frac{72}{3}=24$ years.
  • This also indicates Catchup Effect
• 3
  • Suppose that GDP grew by:
    • $\begin{array}{cc}20& 2023\\ 50& 2024\\ \underset{―}{5}& 2025\\ 75\end{array}$
    • Ex: Exp growth
      • $100(1+0.5{)}^2=225.0$
    • $(1.2)(1.5)(1.05)=1.89$
    • We then have an $89\mathrm{\%}$ growth
    • Average annual growth rate
    • $(1+r{)}^3=1.89$
    • $1+r=\sqrt[3]{1.89}$
    • $r=\sqrt[3]{1.89}-1=0.236385589942567$
    • So it's a $23.63\mathrm{\%}$ interest rate per year on average.
    • Geometric Mean
      • Growth rates are ratios and rates, etc.
      • We use geometric means.
• 6
  • Labour Market
    • $$\begin{array}{ccccc}\text{Age}& 15\to 19& 20\to 24& 25\to 54& 55+\\ \text{Popl.}& 2302.9& 2695.4& 16818.1& 12906.5\\ \text{Labour Force}& 978.4& 2021& 14860.8& 4609.4\\ \text{Employment}& 802.8& 1849.4& 14029.8& 4374.3\\ \text{Unemployement}& 175.6& 171.6& 831.0& 235\\ \text{Not in labour force}& 1324.5& 674.4& 1957.3& 8297.2\\ \text{Participation Rate}& 42.5& 74.9& 88.4\\ \text{Employment Rate}& 34.9& & 83.4\\ \text{Unemployment Rate}& 17.9& & 5.6\end{array}$$
    • #tk
  • Participation Rate
    • Around $90\mathrm{\%}$ of people are in the labour force.
    • Only $10\mathrm{\%}$ in the range aren't part of the labour force. Not many.
  • Employment Rate
  • Unemployment Rate
    • In $15\to 19$ there are quite a few people who don't have jobs.
• 7
  • (ECO102 - Week 2, p.4)
  • A population has 50 persons under the age of 15, 150 persons who are aged 15-64 and 50 persons who are 65 years of age or older. 70 persons in this population are employed and 30 persons are unemployed. Calculate a. The Employment Rate x b. The Participation Rate x c. The Unemployment Rate x d. The Dependency Ratio x
  • $\begin{array}{cccc}\text{Age}& 15-& 15\to 64& 65+\\ \text{Popl.}& 50& 150& 50\\ \text{Employed}& 70\\ \text{Unemployed}& 30\end{array}$
  • Dependency Ratio
    • $\frac{50}{250}=0.2$
  • Participation rate
    • $\frac{70+30}{200}=0.5$
  • Employment Rate
    • $\frac{70}{200}=0.35$
  • Unemployment Rate
    • $\frac{30}{70+30}=0.3$
• 8
  • (ECO102 - Week 2, p.4)
  • Decompose GDP into labour market components and provide policy suggestion
  • $\text{POP15}=$ number of people over the age of $15$
  • $\text{E}$ is employed
  • $\text{GDP}=\text{GDP}\left[\frac{\text{POP15}}{\text{POP15}}\right]\left[\frac{\text{LF}}{\text{POP15}}\right]\left[\frac{\text{E}}{\text{E}}\right]\left[\frac{\text{LF}}{\text{LF}}\right]\left[\frac{\text{POP}}{\text{POP}}\right]$
  • $\text{GDP}=\left[\frac{\text{GDP}}{E}\right]\left[\frac{E}{\text{LF}}\right]\left[\frac{\text{POP15}}{\text{POP}}\right]\text{POP}$
    • $\frac{\text{GDP}}{E}$ is Labour Productivity
      • A farmer with more tools is likely to produce more GDP than another.
      • Increase the quality of capital
    • $\frac{\text{POP15}}{\text{POP}}=1-\text{Dependency Ratio}$
      • Anything to reduce this would increase GDP
      • Immigration policy, increase the amount of working age people, without affecting the dependency ratio much.
    • $\frac{\text{E}}{\text{LF}}=\frac{\text{E}}{\text{E}+\text{U}}=1-\frac{\text{U}}{\text{LF}}$
      • To reduce unemployment would increase GDP
    • $\frac{\text{LF}}{\text{POP15}}$
      • Labour force participation rate
      • Make it easy for women to enter the labour force again, increase GDP.
    • $\text{POP}$
      • Rate of Natural Increase but not as a percentage
      • CBR - CDR
      • $\text{Im}-\text{Em}$
        • Need more immigration than emigration
• 9
  • (ECO102 - Week 2, p.5)
  • Spending by Canadian Governments is split between Federal, Provincial, Regional, Local and other governments. In total, around 1.2 trillion dollars and this represents around 40 percent of GDP (Ragan Microeconomics Tables 18-2 and 18-3). Which components of expenditures and transfers are noteworthy?
  • Government spending accounts for $40\mathrm{\%}$ of GDP
    • Healthcare
    • Subsidies
    • EI
    • etc
• 10
  • (ECO102 - Week 2, p.5)
  • Spending on Post-Secondary Education. Ragan notes that revenues of colleges and universities, around 43.4 billion, comes 46% from government, 32% tuition and 21% other. Provide your comments.
  • $\frac{2}{3}$ of tuition is paid by taxpayers.
  • But then you become a taxpayer.
• 12
  • (ECO102 - Week 2, p.5)
  • Ragan suggests that taxes should be assessed on the basis of "equity" and "efficiency". a. What does Ragan suggest about the "ability to pay principle" and the "benefit principal" b. When discussing "efficiency" Ragan (Figures 18-2, 18-3) distinguishes between the "direct burden of a tax" and the "excess burden of a tax". Compute these two quantities for an income tax when t = 2, D = 12 – 2w and S = 2w.
  • Per unit tax has direct burden and excess burden.
  • Efficiency loss is the direct burden of the tax.
  • The government revenue is direct burden.
• 13
  • (ECO102 - Week 2, p.5)
  • Taxes are collected by the federal government (Ottawa) and distributed to the provincial governments. Equalization payments are made to "have not provinces". This might be relevant for the European Union
  • Amount due for a tax bracket
  • $$\text{begin{matrix} text{Bracket} \& text{Rate} \& text{Amount Due} 0to55867 \& 15 \& 8380 55868to 111733 \& 20.5 \& 11452 111734to 173205 \& 26 \& 3449 173206to 246752 \& 29 \& 0 246753+ \& 33 \& 0 }$$
  • They pay 23k on an income of 125, with an average tax rate of $18.6248\mathrm{\%}$
  • Progressive tax rate
• 14

  • The laffer curve

  • (ECO102 - Week 2, p.5)

  • The Laffer Curve (Figure 18-4). Will increasing a tax always result in more tax revenues? Graph the Laffer Curve when D = 12 – 2p and S = 2p

  • $R=y$

  • $t=x$

  • Reduction in tax rate would increase revenue.

       \begin{document}
    	 \begin{tikzpicture}[scale=1.2]
    	   % Draw the axes for Tax Rate and Tax Revenue
    	   \draw[thick, ->] (0,0) -- (7,0) node[right] {Tax Rate ($t$)};
    	   \draw[thick, ->] (0,0) -- (0,10) node[above] {Tax Revenue ($R$)};
    
    	   % Draw the Laffer Curve using the derived function R = 6t - t^2
    	   % The domain is set from 0 to 6 as revenue becomes zero at t=6
    	   \draw[very thick, color=blue, domain=0:6, samples=100] plot (\x, {6*\x - \x*\x});
    
    	   % Mark the peak of the curve (the optimal tax rate)
    	   % Vertex is at t=3, R=9
    	   \draw[dashed, color=gray] (3,0) -- (3,9);
    	   \draw[dashed, color=gray] (0,9) -- (3,9);
    	   \filldraw[color=black] (3,9) circle (1.5pt);
    
    	   % Add labels for the optimal point and the curve
    	   \node[below] at (3,0) {$t^* = 3$};
    	   \node[left] at (0,9) {$R_{max} = 9$};
    	   \node[color=blue, right] at (4.5,7) {Laffer Curve};
    
    	   % Labelling the regions
    	   \node[font=\small, align=center] at (1.5,4) {Revenue\\Increasing};
    	   \node[font=\small, align=center] at (4.5,4) {Revenue\\Decreasing};
    
    	 \end{tikzpicture}
       \end{document}
    

  • $p=p_s+t$

  • So Demand $D=12-2p_s-2t$

  • $S=D$

    • $2p_s=12-2p_s-2t$
    • $p_s=3-\frac{1}{2}t$
    • $q=2p_s=6-t$
    • $R=tq=6t-t^2$
    • So keep tax rate at $3$ will maximize revenue.
• 15
  • (ECO102 - Week 2, p.5)
  • Discuss the mechanics behind a Universal Basic Income
  • Poverty Trap
  • If someone receives $12k$ in social assistance.
  • If they get a job, they lose the unemployment insurance.
  • Entry level jobs like door-dash, etc would give you $8k$ instead.
  • Solution is Universal Basic Income
  • Suppose everyone is given $10k$. Suppose tax rate is $0.4$
  • If your income is below a threshold of $25000$ then the government gives you money.
  • Disparity between the two lines with different slopes both crossing at $x=25000$ is government giving you money or taking money.
  • Two lines, y-intercept on the first starts at $10000$ and the second starts at $0$ where both lines cross at $x=25000$.
  • Reduce the scale of everything to be from 0 to 1000 on x and 0 to 1000 on y

    \begin{document}
      \begin{tikzpicture}[x=0.01cm, y=0.01cm]
    	% Draw the axes with a small buffer for labels
    	\draw[thick, ->] (0,0) -- (1100,0) node[right] {Gross Income};
    	\draw[thick, ->] (0,0) -- (0,1100) node[above] {Disposable Income};
    
    	% Draw grid lines for better readability
    	\draw[help lines, color=gray!30, step=100] (0,0) (1000,1000);
    
    	% Line 1: Gross Income (y = x)
    	\draw[very thick, color=blue] (0,0) -- (1000,1000) node[above right] {Gross Income ($y=x$)};
    
    	% Line 2: Net Income (y = 0.6x + 200)
    	% Intercept k = 200, Slope = 0.6
    	\draw[very thick, color=red] (0,200) -- (1000,800) node[right] {Net Income ($y=0.6x + k$)};
    
    	% Intersection point (Threshold)
    	\filldraw[color=black] (500,500) circle (3pt);
    	\draw[dashed, thin] (500,500) -- (500,0) node[below] {Threshold (500)};
    	\draw[dashed, thin] (500,500) -- (0,500) node[left] {500};
    
    	% Label the y-intercept k
    	\node[left, color=red, font=\bfseries] at (0,200) {k (200)};
    
    	% Shading/Indicating the regions
    	% Subsidy region (Government gives money)
    	\draw[<->, color=green!60!black, thick] (200,200) -- (200,320) node[midway, right, font=\small] {Subsidy};
    
    	% Tax region (Government takes money)
    	\draw[<->, color=orange!80!black, thick] (800,800) -- (800,680) node[midway, right, font=\small] {Tax Paid};
    
    	% Labels for clarity
    	\node[anchor=south west, color=green!40!black] at (50,300) {Govt. Gives};
    	\node[anchor=north east, color=orange!60!black] at (950,700) {Govt. Takes};
    
      \end{tikzpicture}
    \end{document}
    

• 16
  • (ECO102 - Week 2, p.5)
  • Discuss and illustrate the government budget constraint. (Ragan Macro Figure 16-3). Compute the level of GDP that results in a balanced budget if T = 10, G = 40 and t = 0.10
  • $T=10$ is an indirect tax, because amount paid is not related to income. Like HST
  • $t=0.1$ as tax rate
  • $G=40$ is government spending. Unemployment insurance, public worker salary.
  • $B=T+tY-G$
  • Government's revenue is $T+tY$
  • $Y$ is income
  • If government budget balance is $-$, then you might be in a deficit, otherwise in a surplus.
  • Create an x y graph with a line with a y intercept at -30, two lines on x at 100 and 400 indicating 100 as deficit and 400 as surplus

    \begin{document}
      \begin{tikzpicture}[>=stealth, x=0.018cm, y=0.12cm]
        % Axes
        % Horizontal axis scaled to fit 500 units into a viewable width
        \draw[->] (-50, 0) -- (550, 0) node[right] {Income ($Y$)};
        % Vertical axis scaled to fit the deficit and surplus range
        \draw[->] (0, -45) -- (0, 40) node[above] {Budget Balance ($BB$)};
    
        % The Budget Balance Line: BB = 0.1Y - 30
        % Coordinates: (0, -30) and (500, 20)
        \draw[thick, color=blue] (0, -30) -- (500, 20) node[above right] {$BB = 0.1Y - 30$};
    
        % Y-intercept label
        \filldraw[black] (0, -30) circle (1.5pt) node[left] {$-30$};
    
        % Deficit marker at Y = 100
        \draw[dashed, color=gray] (100, 0) -- (100, -20) -- (0, -20);
        \filldraw[color=red] (100, -20) circle (2pt);
        \node[below] at (100, 0) {100};
        \node[left] at (0, -20) {$-20$};
        \node[below right, color=red] at (100, -20) {Deficit};
    
        % Break-even point at Y = 300
        \filldraw[black] (300, 0) circle (1.5pt) node[above left] {300};
    
        % Surplus marker at Y = 400
        \draw[dashed, color=gray] (400, 0) -- (400, 10) -- (0, 10);
        \filldraw[color=green!60!black] (400, 10) circle (2pt);
        \node[below] at (400, 0) {400};
        \node[left] at (0, 10) {$10$};
        \node[above left, color=green!60!black] at (400, 10) {Surplus};
    
        % Shading labels - positioned relative to the new scale
        \node[anchor=north west, font=\small] at (20, -35) {Fixed Tax ($T=10$)};
        \node[anchor=north west, font=\small] at (20, -40) {Spending ($G=40$)};
      \end{tikzpicture}
    \end{document}
    

• 18
  • Federal Govt Debt is 1 trilly
    • Per capita debt is around $25k$
    • The debt to gdp ratio is around $40\mathrm{\%}$
      • $\frac{1}{2.5}=0.4$
      • $\frac{\text{Debt}}{\text{GDP}}$
      • Is a $40\mathrm{\%}$ debt to income ratio good?
        • Not really much when you account mortgages on homes.
    • Debt interest payments represent around $7\mathrm{\%}$ of government spending
      • That's a lot, if interest rates go up, they might spend a lot of their total govt budget as just interest payments.
      • Spending needs to go down and taxes need to go up. In the future it's gonna flip eventually.
    • Debt is an intergenerational Transfer
• 19
  • Real GDP
  • Chaining
    • New Product Bias
    • $2015$ GDP on $2014$ Prices
    • Base year can be fixed for a certain period
    • Estimates suffer because of New Product Bias
    • Chaining uses a base year of last year.
• 20
  • (ECO102 - Week 2, p.6)
  • The Consumer Price Index (Applying Concepts 4-2) a. Why inflation matters b. Statistics Canada https://www150.statcan.gc.ca/t1/tbl1/en/tv.action?pid=1810000401 c. Laspeyres Chained CPI (Use table from previous question) d. Compute Inflation Rates
  • To make a price index, use quantity as weights.
  • $$\begin{array}{cccccccc}& 2013& & 2014& & 2015& & 2016\\ & \text{Vol}& \text{Price}& \text{Vol}& \text{Price}& \text{Vol}& \text{Price}& \text{Vol}& \text{Price}\\ \text{Good X}& 10& 2& 10& 2& 15& 4& 20& 5\\ \text{Service Y}& 5& 1& 10& 2& 10& 2& 20& 5\\ \text{GDP}& 25& & 40& & 80& & 200\\ \text{\%}\mathrm{\Delta }\\ \text{Price Index}& & & 30& & 60& & 125\\ \mathrm{\%}\mathrm{\Delta }P& & 20\mathrm{\%}& & 50\mathrm{\%}& & 56.25\mathrm{\%}\end{array}$$
  • Price index of 2014 is volume of 2013 times prices of 2014
  • $\mathrm{\%}\mathrm{\Delta }P$ is $\frac{30}{25}$
  • CPI
  • Base year, then CPI is 100. Unlike real gdp which is just nominal.
  • Increase it by the $\mathrm{\%}\mathrm{\Delta }P$.
  • Why does inflation matter?
    • Inflation erodes purchasing power because $100$ buys you $50\cdot 2$ loaves of bread.
    • Now loaves of bread goes to $2.5$
    • So we have $100$ buys you $40\cdot 2.5$
    • Hurts savers, benefits borrowers.