你如何計算通貨膨脹對貨幣價值的影響？
If the US govt prints X amount of money per year is there a way to find out how the value of the dollar will change. Essentially if the value of the dollar is solely a function of how much money is printed, what is the function?
This question really is not about the US (I just used it as an example), but for any currency in general. Assume that inflation is the only variable that affects the value of the currency.
EDIT: The value of the dollar using cpi as the metric. EDIT: The amount of money printed rather than inflation
Value of money is not solely function of money supply (see Mankiws Macroeconomics or Woodford Interest and Prices). Consequently, it is not possible to appropriately calculate value of money (measured by CPI) solely from money supply.
Price level is determined via supply demand interactions on money market equilibrium. Supply and demand on money market equilibrium are in turn determined by wider state of an economy.
Depending how detailed or accurate you want to be there are various different models of money market equilibrium. If you want just something very simplistic for back of the envelope calculation you could use the equation of exchange (see Mankiw Macroeconomics pp 87):
[Math Processing Error]$$ MV=PY \tag{*} $$ where [Math Processing Error] $ M $ is money supply, [Math Processing Error] $ V $ velocity of money, [Math Processing Error] $ P $ price level and [Math Processing Error] $ Y $ real output. You could just solve it for [Math Processing Error] $ P=MV/Y $ , but given the simplicity of the model you should not expect answer to be very precise.
Something still very simple would be taking a bit more complex version of (*):
[Math Processing Error]$$ M/P=L(Y,i) $$ 在哪裡[Math Processing Error] $ L $ 是貨幣需求。你可以單獨估計貨幣需求的參數。貨幣需求應該看起來像 $ L(Y,i) = a_0 + a_1 Y - a_2 i $ . 之後，你可以解決[Math Processing Error] $ P $ . 這將比前面的範例更精確（儘管仍然不夠精確，以防您想要做出一些認真的預測）。
如果您想要一個比玩具模型更嚴肅的東西，那麼您可以估計整個經濟體的動態隨機一般均衡 (DSGE) 模型，您可以根據經濟體的所有其他估計參數確定什麼價格水平。您可以在 Wickens Macroeconomic Theory 中查看此類模型的概述。
There is also a plethora of intermediate models, such as Philips curve estimations, that can deliver solid CPI predictions, but they do not directly utilize money supply, but rather infer how prices change from other variables, such as output or past prices. Hence, I omit them since you wanted a model with a money supply.