File:Asinobstfeldrogoff.png

Summary[edit]

The curve is as in Maurice Obstfeld, Kenneth S. Rogoff, Foundations of International Macroeconomics, Massachusetts Institute of Technology, 1996, ISBN 0262150476 (chapter 8, Money and Exchange Rates under Flexible Prices, section 2, The Cagan Model of Money and Prices, paragraph 6, Seigniorage, pp. 523-525). The matlab code to generate the image is as follows (although I made some minor manual adjustments):

gm = [0:0.001:8];
eta = 1;
S = gm .* ((1 + gm) .^ (-eta - 1));

gm_star = 1 / eta;
S_star = gm_star * ((1 + gm_star) ^ (-eta - 1));
G = 0.2;
syms x real;
gm_G = eval(solve(x * ((1 + x) ^ (-eta - 1)) - G, 'x'));

figure1 = figure('Position', [393 18 782 686], 'PaperPosition',[0.1322 5.764 20.67 18.14], 'PaperSize',[20.98 29.68], 'PaperType','a4letter');
set(gcf, 'Color', 'none');
plot([-2, 8], [S_star, S_star], '--', 'Color', [0, 200, 50] / 255, 'LineWidth', 2)
hold on
plot([gm_star, gm_star], [0, S_star], '--', 'Color', [0, 200, 50] / 255, 'LineWidth', 2)
plot([gm_G(1), gm_G(1)], [0, G], '--r', 'LineWidth', 2)
plot([gm_G(2), gm_G(2)], [0, G], '--r', 'LineWidth', 2)
plot([-2, 10], [G, G], '--r', 'LineWidth', 2)

plot([-2, 8], [0, 0], '-k', 'LineWidth', 5)
plot([0, 0], [-0.1, 0.4], '-k', 'LineWidth', 5)
plot(gm, S, '-', 'LineWidth', 5)

plot(gm_G(1), G, '.r', 'MarkerSize', 40)
plot(gm_G(2), G, '.r', 'MarkerSize', 40)
plot(gm_star, S_star, '.', 'Color', [0, 200, 50] / 255, 'MarkerSize', 40)


set(gca, 'XLim', [-1, 8]);
set(gca, 'YLim', [-.05, .35]);

set(gca, 'Color', 'none', 'LineWidth', 2, 'FontSize', 16, 'FontWeight', 'bold', 'Box', 'off', 'Position', [0.0179028 0.0335277 0.971867 0.950437], ...

'OuterPosition', [-0.14512 -0.0947522 1.25402 1.16618])

set(gca, 'Visible', 'off')

annotation1 = annotation(...

figure1, 'textbox', ...

'BackgroundColor', 'none', ...

'FitHeightToText', 'off', ...

'FontSize', 24, ...

'FontWeight', 'bold', ...

'HorizontalAlignment', 'center', ...

'LineStyle', 'none', ...

'Position', [0.8963 0.0609 0.0875 0.1143],...

'String',{'\mu'});

annotation2 = annotation(...

figure1, 'textbox', ...

'BackgroundColor', 'none', ...

'FitHeightToText', 'off', ...

'Color', 'r', ...

'FontSize', 24, ...

'FontWeight', 'bold', ...

'HorizontalAlignment', 'center', ...

'LineStyle', 'none', ...

'Position', [0.2480 0.0624 0.0875 0.1143],...

'String',{'\mu_1'});

annotation3 = annotation(...

figure1, 'textbox', ...

'BackgroundColor', 'none', ...

'FitHeightToText', 'off', ...

'Color', 'r', ...

'FontSize', 24, ...

'FontWeight', 'bold', ...

'HorizontalAlignment', 'center', ...

'LineStyle', 'none', ...

'Position', [0.5805 0.0609 0.0875 0.1143],...

'String',{'\mu_2'});

annotation4 = annotation(...

figure1, 'textbox', ...

'BackgroundColor', 'none', ...

'FitHeightToText', 'off', ...

'Color', [0, 200, 50] / 255, ...

'FontSize', 24, ...

'FontWeight', 'bold', ...

'HorizontalAlignment', 'center', ...

'LineStyle', 'none', ...

'Position', [0.3656 0.0610 0.0875 0.1143],...

'String',{'\mu*'});

annotation5 = annotation(...

figure1, 'textbox', ...

'BackgroundColor', 'none', ...

'FitHeightToText', 'off', ...

'Color', [0, 200, 50] / 255, ...

'FontSize', 24, ...

'FontWeight', 'bold', ...

'HorizontalAlignment', 'center', ...

'LineStyle', 'none', ...

'Position', [0.1239 0.7184 0.0875 0.1143],...

'String',{'\sigma*'});

annotation6 = annotation(...

figure1, 'textbox', ...

'BackgroundColor', 'none', ...

'FitHeightToText', 'off', ...

'FontSize', 24, ...

'FontWeight', 'bold', ...

'HorizontalAlignment', 'center', ...

'LineStyle', 'none', ...

'Position', [0.1162 0.8641 0.0875 0.1143],...

'String',{'\sigma'});

annotation7 = annotation(...

figure1, 'textbox', ...

'BackgroundColor', 'none', ...

'FitHeightToText', 'off', ...

'Color', 'r', ...

'FontSize', 24, ...

'FontWeight', 'bold', ...

'HorizontalAlignment', 'center', ...

'LineStyle', 'none', ...

'Position', [0.1253 0.5449 0.0875 0.1143],...

'String',{'G'});

annotation6 = annotation(...

figure1, 'textbox', ...

'BackgroundColor', 'none', ...

'FitHeightToText', 'off', ...

'FontSize', 24, ...

'FontWeight', 'bold', ...

'HorizontalAlignment', 'center', ...

'LineStyle', 'none', ...

'Position', [0.1162 0.8641 0.0875 0.1143],...

'String',{['Real Signiorage v Inflation Rate:'; ' a Laffer Curve ']});

Licensing[edit]

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Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue

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