{"id":1435,"date":"2021-11-24T16:13:15","date_gmt":"2021-11-24T08:13:15","guid":{"rendered":"https:\/\/fanyuzhao.com\/?p=1435"},"modified":"2022-03-02T16:52:15","modified_gmt":"2022-03-02T08:52:15","slug":"the-fiscal-policy-of-price-level","status":"publish","type":"post","link":"https:\/\/fanyuzhao.com\/?p=1435","title":{"rendered":"Government Deficits Cause Inflation"},"content":{"rendered":"\n<p>Recall <a href=\"https:\/\/fanyuzhao.com\/?p=75\"><em>A Cash-in-Advance Model<\/em><\/a>, the government deficits cause inflation.<\/p>\n\n\n\n<p>Here, I would apply the equation of exchange and government budget constraint to explain how inflation is generated by government deficits. Recalling the government budget constraint,<\/p>\n\n\n\n<p class=\"has-small-font-size\">  <span class=\"katex math multi-line\">\\overbrace{p_t g_t}^{Gov Spending} + \\overbrace{i_t d_t}^{Interest Payment} = \n\\underbrace{(d_{t+1}-d_t)}_{Increase in Debt Position}+\\underbrace{T_t}_{Tax Revenue}+\\underbrace{m_t-m_{t-1}}_{Print Money}<\/span><\/p>\n\n\n\n<p>devide by \\( p_t\\) to get the equation in the real term,<\/p>\n\n\n\n<p>$$ g_t+i_t \\frac{d_t}{p_t}=\\frac{d_{t+1}-d_t}{p_t}+\\tau_t+\\frac{m_t-m_{t-1}}{p_t} $$<\/p>\n\n\n\n<p>, where \\( \\tau_t=\\frac{T_t}{p_t}\\).<\/p>\n\n\n\n<p>By denoting real government debt as \\( \\hat{d}_t=\\frac{d_t}{p_{t-1}}\\), and replace \\( (1+r_t)=(1+i_t)\\frac{P_{t-1}}{P_t}=\\frac{1+i_t}{1+\\pi_t} \\) and \\( m_t = p_t y_t \\), then we get all variables are in real terms,<\/p>\n\n\n\n<p>$$ g_t &#8211; \\tau_t +(1+r_t)\\hat{d}_t =\\hat{d}_{t+1}+\\frac{p_t y_t-p_{t-1}y_{t-1}}{p_t}$$<\/p>\n\n\n\n<p>At the steady state \\( g_t=g_{t+1}=g, \\tau_t=\\tau_{t+1}=\\tau \\) and so on, and thus,<\/p>\n\n\n\n<p>$$ \\underbrace{g+r\\hat{d}-\\tau }_{Growth\\ of \\ interest\\ deficits}= \\underbrace{\\frac{p_t-p_{t-1}}{p_t}}_{Seignorage} \\times y$$<\/p>\n\n\n\n<p>From the above equation, we can find that if inflation increases then it means the RHS increases. The LHS consists of two parts. Government Spendings \\( g + r\\hat{d}\\) and government revenues \\( \\tau \\). That means the government is getting deficits if the LHS rises. Meanwhile, the RHS increases and so inflation grows. <\/p>\n\n\n\n<p>In sum, we find that government deficits, in the long run, would induce inflation. The zero-inflation condition is to make the LHS of the equation equal to zero (government spendings offset government revenue).<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Recall A Cash-in-Advance Model, the government deficits cause inflation. Here, I would apply the equation of exchange and government budget constraint to explain how inflation is generated by government deficits. Recalling the government budget constraint, \\overbrace{p_t g_t}^{Gov Spending} + \\overbrace{i_t d_t}^{Interest Payment} = \\underbrace{(d_{t+1}-d_t)}_{Increase in Debt Position}+\\underbrace{T_t}_{Tax Revenue}+\\underbrace{m_t-m_{t-1}}_{Print Money} devide by \\( p_t\\) to get &hellip; <a href=\"https:\/\/fanyuzhao.com\/?p=1435\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">Government Deficits Cause Inflation<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[9,6,13],"tags":[],"_links":{"self":[{"href":"https:\/\/fanyuzhao.com\/index.php?rest_route=\/wp\/v2\/posts\/1435"}],"collection":[{"href":"https:\/\/fanyuzhao.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/fanyuzhao.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/fanyuzhao.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/fanyuzhao.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1435"}],"version-history":[{"count":5,"href":"https:\/\/fanyuzhao.com\/index.php?rest_route=\/wp\/v2\/posts\/1435\/revisions"}],"predecessor-version":[{"id":1440,"href":"https:\/\/fanyuzhao.com\/index.php?rest_route=\/wp\/v2\/posts\/1435\/revisions\/1440"}],"wp:attachment":[{"href":"https:\/\/fanyuzhao.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1435"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/fanyuzhao.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1435"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/fanyuzhao.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1435"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}