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  /Subject (Econ 2 Macro Cheat Sheet)
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    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{Econ 2 Macro Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{Cat\_Wx} via \textcolor{DarkBackground}{\uline{cheatography.com/191326/cs/39760/}}}
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  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Not Yet Published.\\
   Updated 4th August, 2023.\\
   Page {\thepage} of \pageref{LastPage}.
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\begin{tabularx}{17.67cm}{x{8.635 cm} x{8.635 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{17.67cm}}{\bf\textcolor{white}{Key Equations}}  \tn
% Row 0
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 & "\_ \_" denotes subscript (eg. {\emph{P\_t+1\_/P\_t\_}}) \tn 
% Row Count 3 (+ 3)
% Row 1
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\mymulticolumn{2}{x{17.67cm}}{\{\{bb=2\}\}\{\{nobreak\}\} {\bf{Production and Prices}}} \tn 
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% Row 2
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\{\{nobreak\}\}  Production Function & \{\{nobreak\}\} production depends on the inputs of capital, labour and technology factor \{\{nl\}\}\{\{nl\}\}{\emph{Y = F (K, E N)}} \{\{nl\}\}\{\{nl\}\} {\bf{Y}} = production \{\{nl\}\} {\bf{K}} = capital \{\{nl\}\} {\bf{N}} = labour \{\{nl\}\} {\bf{E}} = technology factor \tn 
% Row Count 16 (+ 12)
% Row 3
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Cobb-Douglas Production Function & {\emph{Y = K\textasciicircum{}α\textasciicircum{} (E N)\textasciicircum{}1-α\textasciicircum{}}} \tn 
% Row Count 18 (+ 2)
% Row 4
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Marginal Product of Labour & take derivatice of {\emph{Y = K\textasciicircum{}α\textasciicircum{} (E N)\textasciicircum{}1-α\textasciicircum{}}} with respect to {\emph{N}} \{\{nl\}\}\{\{nl\}\} {\emph{MPL = (1 - α) E\textasciicircum{}1-α\textasciicircum{} (K/N)\textasciicircum{}α\textasciicircum{}}} \tn 
% Row Count 24 (+ 6)
% Row 5
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Monopoloistc Competition Price & {\emph{P = (1+ μ ) MC}} \{\{nl\}\}\{\{nl\}\} {\bf{μ}} = mark-up \tn 
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Marginal Cost & {\emph{MC = W/MPL}} \tn 
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Marginal Cost in term of Cobb-Douglas & {\emph{MPL = K\textasciicircum{}α\textasciicircum{} (1 - α) E\textasciicircum{}1-α\textasciicircum{} N\textasciicircum{}-α\textasciicircum{} = (1 - α) Y/N}} \{\{nl\}\}\{\{nl\}\} and thus \{\{nl\}\}\{\{nl\}\} {\emph{WN/PY = 1-α/1+μ}} \tn 
% Row Count 34 (+ 6)
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\begin{tabularx}{17.67cm}{x{8.635 cm} x{8.635 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{17.67cm}}{\bf\textcolor{white}{Key Equations (cont)}}  \tn
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\mymulticolumn{2}{x{17.67cm}}{\{\{nobreak\}\}} \tn 
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\mymulticolumn{2}{x{17.67cm}}{\{\{bb=2\}\}{\bf{Real Interest Rate, Investment, and Consumption}}} \tn 
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% Row 10
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Inflation & rate of growth of price level \{\{nl\}\}\{\{nl\}\} {\emph{π\_t\_ =  ∆P\_t\_/P\_t-1\_}} \{\{nl\}\}\{\{nl\}\} One plus real interest rate is the price of goods today divided by the discounted price of goods next year \{\{nl\}\}\{\{nl\}\} {\emph{1 + r\_t+1\_ = \seqsplit{P-t/(P\_t+1\_/(1+i\_t\_))} = \seqsplit{1+i\_t\_/(P\_t+1\_/P\_t\_)} = 1+i\_t\_/1+π\_t+1\_}} \{\{nl\}\}or\{\{nl\}\} {\emph{r\_t+1\_ ≈ i\_t\_ - π\_t+1\_}} \tn 
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% Row 11
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Firm Investment & to increase capital stock and replace depreciated capital \{\{nl\}\}\{\{nl\}\} {\emph{I\_t\_ = K\textasciicircum{}d\textasciicircum{}\_t+1\_ - K\_t\_ + δK\_t\_}}\{\{nl\}\}\{\{nl\}\}  {\bf{K\textasciicircum{}d\textasciicircum{}\_t+1\_}} = desired capital stock next year \{\{nl\}\} {\bf{δ}} = depricitation \tn 
% Row Count 30 (+ 10)
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\begin{tabularx}{17.67cm}{x{8.635 cm} x{8.635 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{17.67cm}}{\bf\textcolor{white}{Key Equations (cont)}}  \tn
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Profit Maximising Investment Level & the real marginal revenue product minus depreciation is equal to the real interest rate \{\{nl\}\}\{\{nl\}\} {\emph{MPK/I+μ - δ = r}} \tn 
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% Row 13
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Investment Function & investment depends on real interest rate, expected future income and the existing capital stock at the beginning of the  period \{\{nl\}\}\{\{nl\}\} {\emph{I = I (r, Y\textasciicircum{}e\textasciicircum{}, K)}} \{\{nl\}\}\{\{nl\}\} {\bf{r}} = real interest rate \{\{nl\}\} {\bf{Y\textasciicircum{}e\textasciicircum{}}} = expected future income \{\{nl\}\} {\bf{K}} = existing capital stock at beginning of period \tn 
% Row Count 22 (+ 16)
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Utility-maximising Consumption/Savings Decision & ratio of marginal utility of consuming today divided by discounted marginal utility next year is equal to one plus the real interest rate \{\{nl\}\}\{\{nl\}\} {\emph{u'(C\_t\_)/u'(C\_t+1\_)/(1+ρ) = 1 + r\_t+1\_}} \{\{nl\}\}\{\{nl\}\} {\bf{ρ}} = subjective discount rate \tn 
% Row Count 34 (+ 12)
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\begin{tabularx}{17.67cm}{x{8.635 cm} x{8.635 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{17.67cm}}{\bf\textcolor{white}{Key Equations (cont)}}  \tn
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Real Disposable Income & production minus tax payments plus the real interest rate on net claims on government and foreign households and firms \{\{nl\}\}\{\{nl\}\} {\emph{Y\textasciicircum{}d\textasciicircum{} = Y - T +r(D + F)}} \tn 
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Consumption Function & consumption depends on income today, future expected income, the real interest rate and level of assests \{\{nl\}\}\{\{nl\}\} {\emph{C = C(Y\textasciicircum{}d\textasciicircum{}, Y\textasciicircum{}e\textasciicircum{} - T\textasciicircum{}e\textasciicircum{}, r, A)}} \tn 
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\mymulticolumn{2}{x{17.67cm}}{\{\{nobreak\}\}} \tn 
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\mymulticolumn{2}{x{17.67cm}}{\{\{bb=2\}\} {\bf{Long-run Growth}}} \tn 
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Constant returns to scale & production per effective worker depends on the capital stock per effective worker \{\{nl\}\}\{\{nl\}\} {\emph{Y/EN = F (K/EN', 1) = f(k)}} \{\{nl\}\} where {\emph{k = K/EN'}} \tn 
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Steady State Growth Path & capital stock per effective worker is determined by \{\{nl\}\}\{\{nl\}\} {\emph{f'(k*)/1+μ - δ =  r ̅}} \tn 
% Row Count 31 (+ 5)
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\begin{tabularx}{17.67cm}{x{8.635 cm} x{8.635 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{17.67cm}}{\bf\textcolor{white}{Key Equations (cont)}}  \tn
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Constant Capital per Effective Worker on Steady State Growth Path & capital stock and production grow at same rate as the effective number of workers \{\{nl\}\}\{\{nl\}\} {\emph{K = k*EN}},  {\emph{Y = f(k*)EN}} \{\{nl\}\} {\emph{ ∆K/K =  ∆Y/Y = g+n}} \tn 
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Long Run Level of Real Interest Rate (closed econ) & is equal to the subjective discount rate plus the technological growth rate \{\{nl\}\}\{\{nl\}\} {\emph{ r ̅ ≈ ρ + g}} \tn 
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\mymulticolumn{2}{x{17.67cm}}{\{\{nobreak\}\}} \tn 
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\mymulticolumn{2}{x{17.67cm}}{\{\{bb=2\}\} {\bf{The Labour Market and Phillips Curve}}} \tn 
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Unemployment Rate & fraction of labour force not employed \{\{nl\}\}\{\{nl\}\} {\emph{u = U/L = L-N/L}} \tn 
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% Row 26
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Wage-setting Equation & if unemployment is above natural level, firms want to raise wages less than the average wage increase, and conversely \{\{nl\}\}\{\{nl\}\} {\emph{ ∆W\textasciicircum{}d\textasciicircum{}\_t\_/W\_t-1\_ =  ∆W\_t\_/W\_t-1\_ - b(u\_t\_ - u\textasciicircum{}n\textasciicircum{}\_t)}} \tn 
% Row Count 30 (+ 10)
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\begin{tabularx}{17.67cm}{x{8.635 cm} x{8.635 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{17.67cm}}{\bf\textcolor{white}{Key Equations (cont)}}  \tn
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Unemployment on Natural Level & in the long run desired wages must be equal to actual wage increases, so unemployment must be on a natural level \{\{nl\}\}\{\{nl\}\} {\emph{N\textasciicircum{}n\textasciicircum{} = (1 - u\textasciicircum{}n\textasciicircum{})L}} \tn 
% Row Count 8 (+ 8)
% Row 28
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Phillips Curve & assuming that a share 1- λ of wages is set in advance \{\{nl\}\}\{\{nl\}\} {\emph{∆W/W = ∆W\textasciicircum{}e\textasciicircum{}/W - b ̂ (u - u\textasciicircum{}n\textasciicircum{})}} \{\{nl\}\} ; {\emph{b ̂ = λb/1-λ}} \tn 
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% Row 29
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Rate of Wage Increase (short run) & depends on the expected wage increase and unemployment \{\{nl\}\} short-run analysis disregard capital, so inflation is the rate of wage increase minus productivity growth \{\{nl\}\}\{\{nl\}\} {\emph{π = ∆W/W - ∆E/E}} \tn 
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Phillips Curve (inflaation) & relates inflation to expected inflation, the output gap and a cost-push shock \{\{nl\}\}\{\{nl\} {\emph{π = π\textasciicircum{}e\textasciicircum{} + βY ̂+ z}} \{\{nl\}\}\{\{nl\}\} {\bf{{\emph{π\textasciicircum{}e\textasciicircum{}}}}} = expected inflation \{\{nl\}\} {\bf{{\emph{Y ̂}}}} = output gap - has a circumflex  \{\{nl\}\} {\bf{{\emph{z}}}} = cost-push shock \tn 
% Row Count 39 (+ 13)
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\begin{tabularx}{17.67cm}{x{8.635 cm} x{8.635 cm} }
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\mymulticolumn{2}{x{17.67cm}}{\bf\textcolor{white}{Key Equations (cont)}}  \tn
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\mymulticolumn{2}{x{17.67cm}}{\{\{nobreak\}\}} \tn 
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\mymulticolumn{2}{x{17.67cm}}{\{\{bb=2\}\} {\bf{Government Debt}}} \tn 
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Change in Real Government Debt & equal to the primary deficit plus the real interest rate \tn 
% Row Count 5 (+ 3)
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\begin{tabularx}{17.67cm}{x{8.635 cm} x{8.635 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{17.67cm}}{\bf\textcolor{white}{General (intro)}}  \tn
% Row 0
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Macroeconomics & - production \{\{nl\}\} - employment \{\{nl\}\} - price increase \{\{nl\}\} - interest rates \{\{nl\}\} Macroeconomic models \tn 
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% Row 1
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Three Markets & - labour \{\{nl\}\} - goods - credit (money) \tn 
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Three Decision-makers & - typical firm \{\{nl\}\} - typical household \{\{nl\}\} - policymakers \tn 
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Monetary Policy & {\bf{central banks}} \{\{nl\}\} - set the interest rate \tn 
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Fiscal Policy & {\bf{government}} \{\{nl\}\} - decides taxes and government expenditure \tn 
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Basic Model Factors & {\bf{typical firm}}\{\{nl\}\}- price-setting \{\{nl\}\} - wage-setting \{\{nl\}\} - investment \{\{nl\}\} {\bf{typical consumer}} \{\{nl\}\} - consumption \tn 
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Open Economy & trades with the rest of the world \tn 
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Keynes Theory & nominal wages are 'rigid'/'sticky' \tn 
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\begin{tabularx}{17.67cm}{x{8.635 cm} x{8.635 cm} }
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\mymulticolumn{2}{x{17.67cm}}{\bf\textcolor{white}{General (intro) (cont)}}  \tn
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Classical Theory (real business cycle theory) & wages and prices are adjustable to equate supply and demand marets \tn 
% Row Count 4 (+ 4)
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Neoclassical Synthesis & even if wages and prices are sticky in the short run,\{\{nl\}\} we expect them to respond to changes in economic conditions over the long run \tn 
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National Accounts & - flows of production, incomes, savings and investments in a period of time (year/quater) \tn 
% Row Count 16 (+ 5)
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Balance of Payements Statistics & - flow of payments connected to exports, imports, international transfers, capital flows \tn 
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% Row 12
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Value of Production (output) & sales of all firms and value of production in public sector added \{\{nl\}\} \{\{nl\}\} {\bf{output not a good measure as large share of output is used as input in other firms}} \tn 
% Row Count 30 (+ 9)
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\begin{tabularx}{17.67cm}{x{8.635 cm} x{8.635 cm} }
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\mymulticolumn{2}{x{17.67cm}}{\bf\textcolor{white}{General (intro) (cont)}}  \tn
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Intermediate Goods & goods that are used as inputs in other firms \tn 
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Value Added & subtract value of intermediate inputs from value of output \tn 
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\begin{tabularx}{17.67cm}{x{8.635 cm} x{8.635 cm} }
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\mymulticolumn{2}{x{17.67cm}}{\bf\textcolor{white}{The Open Economy Long Run (Ch13)}}  \tn
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Real Exchange Rate & price level in an open economy relative to the price level abroad, where price levels are converted to the same currency \{\{nl\}\}\{\{nl\}\} determinant of aggregate demand in the open country \tn 
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% Row 1
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Real Exchange Rate & price level of domestic goods relative to foreign goods \{\{nl\}\}\{\{nl\}\}{\emph{ε}}={\emph{eP}}/{\emph{P*}} \{\{nl\}\} {\bf{P}} = price of good production at home in domestic currency \{\{nl\}\} {\bf{P*}}= price of good produced abroad in foreign currency \{\{nl\}\} {\bf{{\emph{e}}}} = nominal exchange rate - price of domestic currency in  terms of foreign currency \{\{nl\}\} {\bf{{\emph{ε}}}} = real exchange rate - price of domestically produced goods in terms of goods produced abroad \tn 
% Row Count 32 (+ 22)
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\begin{tabularx}{17.67cm}{x{8.635 cm} x{8.635 cm} }
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\mymulticolumn{2}{x{17.67cm}}{\bf\textcolor{white}{The Open Economy Long Run (Ch13) (cont)}}  \tn
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Current Account & difference between savings and real investments in the country \{\{nl\}\}\{\{nl\}\}  deficit = borrowing from abroad \{\{nl\}\}government/private sector/both borrowing to finance consumption and real investments in excess of income \tn 
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(open) Interest Parity Condition & links interest rate differentials between countries to expected changes in exchange rate \tn 
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Interest Parity Condition & for foreign lenders, the expected returns on loans in the currency of the small open economy must be the same as the expected return or loans in the foreign currency \{\{nl\}\}\{\{nl\}\} {\emph{i + ∆}}e\textasciicircum{}e\textasciicircum{}/e = {\emph{i*}} \{\{nl\}\} {\bf{left}}= interest rate in small open economy plus expected appreciation of currency \{\{nl\}\} {\bf{right}} = return on loans in foreign currency \tn 
% Row Count 34 (+ 18)
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\begin{tabularx}{17.67cm}{x{8.635 cm} x{8.635 cm} }
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\mymulticolumn{2}{x{17.67cm}}{\bf\textcolor{white}{The Open Economy Long Run (Ch13) (cont)}}  \tn
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Long-run Analysis & - analyse the effects of changes in exogenous variables \{\{nl\}\} - assume that prices and wages have time to adjust, employment and production at natural levels \{\{nl\}\} - assume international financial markets are completely integrated, free flow of financial capital and interest parity condition holds \tn 
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Real Interest Rate & determines real cost of borrowing and required return on investment \{\{nl\}\} - open economy it is tied to real in the world financial market\{\{nl\}\} - independent of savings and investment in the small open economy\{\{nl\}\} - adjusts in long run to bring equality between aggregate demand and natural level of production \tn 
% Row Count 32 (+ 16)
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\begin{tabularx}{17.67cm}{x{8.635 cm} x{8.635 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{17.67cm}}{\bf\textcolor{white}{The Open Economy Long Run (Ch13) (cont)}}  \tn
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Nominal Exchange Rate & {\emph{e=ε   P*/P}} \tn 
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Constant Real Exchange Rate & relative change in the nominal exchange rate is equal to foreign inflation minus domestic inflation \{\{nl\}\}\{\{nl\}\} {\emph{∆e/e = π*-π}} \{\{nl\}\}\{\{nl\}\} {\emph{r=r*}} \tn 
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% Row 9
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Long Run Trends in Nominal Exchange rates & shown by {\emph{∆e/e = π*-π}} \{\{nl\}\} - inflation differentials between countries \{\{nl\}\} high inflation = depreciating nominal exchange rate \{\{nl\}\} high inflation for number of years = constant nominal exchange rate \{\{nl\}\} - exporters will find hard so must depreciate at some point \tn 
% Row Count 24 (+ 14)
% Row 10
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Long Run Equilibrium & expected change in exchange rate is equal to the actual change \{\{nl\}\}\{\{nl\}\} {\emph{i-π = i* -π*}} \{\{nl\}\}  {\bf{ left}}= real interest rate in the small open economy \{\{nl\}\} {\bf{right}} = world real interest rate \{\{nl\}\} \{\{nl\}\}can also be written\{\{nl\}\}\{\{nl\}\} {\emph{i-i*= π-π*}} \tn 
% Row Count 38 (+ 14)
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\begin{tabularx}{17.67cm}{x{8.635 cm} x{8.635 cm} }
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\mymulticolumn{2}{x{17.67cm}}{\bf\textcolor{white}{The Open Economy Long Run (Ch13) (cont)}}  \tn
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Nominal Interest Rate & a country with high inflation and depreciating currency must have a higher nominal interest rate to compensate international investors so that the real return is the same on loans in different currencies \tn 
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% Row 12
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Natural Level of Production & Y\textasciicircum{}{\emph{n}}\textasciicircum{} = F ( K, E ( 1 - u\textasciicircum{}{\emph{n}}\textasciicircum{} ) L ) \tn 
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IS Equation & determines aggregate demand and production in the small open economy \{\{nl\}\}\{\{nl\}\}\{\{nobreak\}\} {\emph{Y=C ( Y\textasciicircum{}d\textasciicircum{}, Y\textasciicircum{}e\textasciicircum{} - T\textasciicircum{}e\textasciicircum{}, r*, A ) + I ( r*, Y\textasciicircum{}e\textasciicircum{}, K) + G + NX ( ε, Y*, Y )}} \{\{nl\}\} \{\{nl\}\} {\bf{C}}= private consumption (units of domestic goods) \{\{nl\}\} {\bf{NX}} = net exports ( units of domestic goods) \{\{nl\}\} {\bf{Y\textasciicircum{}d\textasciicircum{}}} = disposable income \{\{nl\}\} {\bf{Y\textasciicircum{}e\textasciicircum{}}} = expected future income \{\{nl\}\} {\bf{r*}} = real interest rate \{\{nl\}\} {\bf{A}} = assests \{\{nl\}\} {\bf{G}} = government spending \{\{nl\}\} {\bf{K}} = capital \{\{nl\}\} {\bf{I}} = investment \{\{nl\}\} {\bf{ε}} = real exchange rate \{\{nl\}\}  {\bf{Y*}} = \{\{nl\}\} {\bf{T\textasciicircum{}e\textasciicircum{}}} = \{\{nl\}\}\{\{nl\}\} where \{\{nl\}\} {\emph{Y\textasciicircum{}d\textasciicircum{} = Y\textasciicircum{}n\textasciicircum{} - T +r* ( D + F )}} \tn 
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\begin{tabularx}{17.67cm}{x{8.635 cm} x{8.635 cm} }
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\mymulticolumn{2}{x{17.67cm}}{\bf\textcolor{white}{The Open Economy Long Run (Ch13) (cont)}}  \tn
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Natural Real Exchange Rate (open) & real exchange rate that is consistent with production at natural level \{\{nl\}\}\{\{nl\}\} {\emph{ε\textasciicircum{}n\textasciicircum{}}} \tn 
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