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Purchasing Power Parity

Forward exchange rates are exactly determined by interest rates through an arbitrage condition. But there is a deeper question here: why is the interest rate in euros higher than the interest rate in U.S. dollars?
Economists are not sure, and here is why. The most important question is whether purchasing  power parity (PPP) holds. The PPP theory of exchange rates posits that prices of identical goods should be the same in all countries, differing only in the costs of transport and duties. But does PPP hold? Do $108.86 dollars buy the same amount of goods—say apples—that €100 buy? If an apple costs $1.0886 in the United States, and €1.00 in Europe, then PPP holds. What if it does not hold? What if, for example, an apple costs $1.00 in the United States and €1.00 in Europe? Then we should export cheaper U.S. apples to Europe, sell them for €1, and earn a profit of $0.08/apple. Transport costs and import/export barriers (such as tariffs) are probably too high to permit an apple arbitrage, but there are other, more easily transportable commodities, ranging from diamonds, to gold, to gasoline. As economists, we expect prices for easily exportable and tradeable commodities to obey PPP. But other goods need not obey PPP: Land in France is not the same as land in Manhattan and it cannot be exported. Concrete is too costly to transport, because shipping costs are too high. Raspberries spoil too easily to transport long distances. Maple syrup has little demand in Europe, and is not easy to resell. A work hour by a Czech hair stylist is not same as a work hour by an American hair stylist. And so on. Indeed, PPP does not even hold inside one country: apartments and plumbers cost more in Manhattan than in New Jersey. Gas costs more in San Francisco (CA) than in San Antonio (TX). The reasons why PPP does not hold inside a country are the same as why PPP does not hold across countries. But, if after taking transport costs into account, gas is too expensive in San Francisco relative to San Antonio, someone will start shipping it from San Antonio to San Francisco sooner rather than later.
Still, let us assume for a moment that PPP does hold—that is, that goods in Europe and goods in the United States are worth the same—and that PPP will also hold in the future. This will allow us to determine relative inflation rates. For example, an apple that costs $1.0886 in the United States today costs €1 in Europe today. If the U.S. dollar inflation rate is 2%, then the apple will cost $1.0886 · 1.02 = $1.1104 next year. We can lock in a future exchange rate of 1.0783 $/€, which means that next year’s U.S. apple will be worth $1.1104/1.0783 = €1.0297. In sum, a Euro-apple, costing €1 today will cost €1.0297 next year, which means that the euro inflation rate is 2.97%.
Another way to state this is that purchasing power parity implies that real interest rates must be equal. After all, a real interest rate is just an inflation-adjusted nominal interest rate. (You can think of money here as a good like apples, but one which increases not only through inflation, but also through interest earnings.)

Other Taxes

In addition to federal income taxes, there are a plethora of other taxes. Most states impose  their own income tax. This typically adds another tax rate of between 0% and 10%, depending on state and income. Worse, each state has its own idea not only of what its tax rate and tax brackets should be, but even how taxable income should be computed. Thus, you need to learn not only the federal tax code, but also your state’s tax code. For example, California has the highest marginal state income tax bracket that is not federal deductible: 9.3%. Montana has the highest marginal state income tax bracket that is tax deductible on your federal income tax: 11%. Alaska, Florida, Nevada, South Dakota, Texas, Washington, and Wyoming levy no state income tax, and New Hampshire and Tennessee tax only interest and dividend income.
Many counties pay for school education with property tax rates. In the richer counties of southwest Connecticut, the tax is about 1% of the value of the house, but it can reach about 4% in the poorer urban counties. In Maine (the second-highest property tax collector in the nation), residents pay 5.5% of their income in property tax. Many states also levy a sales tax. Tennessee and Louisiana have a sales tax of 8.35%; Alaska, Delaware, Montana, New Hampshire, and Oregon levy no sales tax. (A nice summary can be found at www.retirementliving.com/RLtaxes.html. It also includes a ranking of the tax burdens by state—Alaska [with 6% of total income], New Hampshire, Delaware, and Tennessee have the lowest; New York [with 12.9% of total income], Maine, Ohio, and Hawaii have the highest.)
If you have to file in multiple states or even in multiple countries—although there are rules that Complex Complexity. try to avoid double taxation—the details can be hair-raisingly complex. If you find yourself in such a situation, may the force be with you!
Finally, there are social security and medicare contributions. Although these are supposedly insurance premia, any money taken in today is immediately spent by the government on the elderly today. Thus, anyone young today is unlikely to receive much in return from the government in 20 to 30 years—when there will be fewer young people around to pay their retirement benefits. Thus, many financial economists consider social taxes to be as much a form of income tax as the statutory income tax.
This blog also ignores many other non-income taxes. For some taxes, such as the sales tax, it is not clear how to use expertise in finance to lower them. For other taxes, such as the estate tax, you need extremely specialized financial vehicles to avoid or reduce them.