The Federal Funds Rate, often referred to as the "Fed Prime Rate," is the interest rate at which depository institutions (such as banks and credit unions) lend reserve balances to other depository institutions overnight [1]. In fact, the "Prime Rate" is different from the "Federal Funds Rate," though they are confused frequently by the media [2]. The Federal Funds Rate is established by the Federal Open Market Committee (FOMC), a component of the Federal Reserve System [3]. The prime rate is the rate that banks charge their most creditworthy customers [4]. When the Federal Reserve increases the Federal Funds Rate, it becomes more expensive for banks to borrow money. This increased cost reduces the demand for loans at every level of creditworthiness and decreases the velocity of money in the economy [5]. Higher interest rates can make savings accounts and other fixed-term interest-bearing investments more appealing than riskier investments like stock or loans, potentially drawing money away from these instruments towards bonds and savings accounts [6].

The Fed does not employ a particular formula for rate-setting, but the existing approximations need mathematical scrutiny. The Taylor Rule relates inflation rates to target rates and the real and potential output of an economy [7]. It is a linear function i(r, p, y) = r + p + 0.5 * (dp + dy), where r is the equilibrium fed funds rate, dp is the difference between the observed and desired inflation rate, and dy is the difference of the log real and log potential outputs [7]. The formula assumes that fed policy and tax policy are segregated and that ideal and actual economic output are calculable [7]. One can make statistical approximations for each of the terms, but the errors are potentially egregious. The equal weight of 0.5 given to dp and dy is potentially not mathematically defensible in light of the interplay among interest rates, energy prices, and local tax rates as represented by the Laffer Curve.

Put succinctly, the Laffer Curve is a theoretical representation of the relationship between tax rates and the amount of tax revenue collected by governments [8]. The curve suggests that increasing tax rates beyond a certain point is counter-productive for raising further tax revenue [8]. The Laffer Curve is primarily used to illustrate the concept of taxable income elasticity-i.e., taxable income will change in response to changes in the rate of taxation [9]. If a government decreases tax rates with the goal of stimulating economic activity (a move suggested by Laffer Curve principles for certain situations), this could potentially lead to increased aggregate demand for goods and services, changing the values of dp and dy in the Taylor Rule.

High inflation might make a government consider tax rate adjustments to decrease aggregate demand and consumer price indices, but such decisions would also need to consider the trade-off with tax revenues as suggested by the Laffer Curve [10]. In this situation, the Taylor coefficient of 0.5 would only provide a crude approximation for the weight of dp. One reason for this effect is the fact that government spending rarely decreases with falling tax revenues [11]. From an inflationary perspective, it may be possible to temporarily "tax oneself into prosperity" by avoiding an ascent into inflationary spirals presented by firms' extra expenditures on capital. Because the short horizon holds diminished purchasing power for constant cash reserves, high inflation rates present an immediate opportunity cost to firms that hold cash [12]. The Taylor Formula doesn't account for this nonlinearity.

Another weakness in the Taylor Formula is that changes in the federal funds rate can affect the cost of American imports and exports in nonlinear ways. If the rate increases and strengthens the U.S. dollar, imports become cheaper (since more foreign goods can be bought with a strong dollar), but exports become more expensive for foreign buyers [13]. Conversely, if the rate decreases and weakens the U.S. dollar, imports become more expensive, but exports become cheaper for foreign buyers [13]. The federal funds rate can influence the value of the U.S. dollar against other currencies, which is not accounted for in the dp term of the Taylor Rule. When the Federal Reserve raises the federal funds rate, it can attract foreign investors seeking higher returns, which can increase demand for the U.S. dollar and subsequently strengthen its value more than changes in domestic inflation can dampen it.

Conversely, if the Federal Reserve lowers the federal funds rate, it can reduce foreign investment in the U.S., which can decrease demand for the U.S. dollar and weaken its value more than domestic deflation can increase it. One prominent mechanism by which this process may occur is in the denomination of crude, which heavily influences the production possibility frontier in a manner that is not reflected in the uniform 0.5 coefficient for dp and dy. If the rate increases and the U.S. dollar strengthens, oil - which is typically denominated in U.S. dollars globally - can become more expensive for countries with weaker currencies [14]. This can decrease demand for oil, potentially lowering its price in a non-uniform way across global futures and energy exchanges [15]. If the federal funds rate decreases and the U.S. dollar weakens, oil can become cheaper for countries with stronger currencies, potentially increasing demand and raising its price [14]. Because these countries and their citizens are holders of American sovereign and corporate debt, there is a strong relationship between the interest rates offered on fixed-term debt instruments (set indirectly by FOMC decisions) and the ideal production capacity of the economy [16].

Works Cited.

https://medium.com/@jonathanjkenigson/taylor-rule-and-inflation-sources-ead6c9aa7ab4