Economics is a fundamental topic related to finance when funds are considered. However, Economics also deals with the broader issues of employment, production, delivery and consumption. A common issue in finance and micro-economics is the consideration of fixed and variable interest rates as these chart how to finance a business or personal debt and wealth. Distinct issues for macro-economics are the Gross Domestic Product (GDP) and the unemployment rate.

A set of introductory ‘homework’ topics form the basis to learn more complex economic mechanisms. The common theme is to define quantities and formulas to model an activity and perform sample calculations. In the real situations, the known numbers, such as interest rate, might not be firm and have some variability or ‘volatility’ over time. But often decisions have to be made at one point in time and then we live with the decision over time and either benefit or not. Therefore, the uncertainty in the ‘known’ or ‘given’ numbers has an effect on the projection, such as the variable interest rate affecting the overall debt in a mortgage. However, ‘rogue events’ are unanticipated large changes that escape the usual statistical interpretations of mean rate and volatility. Theories that either supplement or replace statistics are needed to handle rogue events. A rogue event could be the accumulation of uncertainty that, hidden in today’s numerical arithmetic, is quickly realized or there is a breaking point when the uncertainty becomes intolerable to a ‘stable’ system.

The micro-economics homework examples deal with interest rate, either fixed or variable, and this could be applied to savings or bonds or to debt. There are three basic features , namely the rate, starting principle and time. For the variable rate, there is the additional feature of possible up and down annual changes and if there are caps on these annual changes or brackets for the overall rate. Then homework is structured as questions such as how quickly a loan is retired, what is the total interest payment over the life of a loan, how much would I borrow if I had a target periodic payment, etc.

These questions are answered by a central model that is a set of formula combining principle, instantaneous rate, time, compounding and summations of interest and principle payments over time. The simplest form is that an interest payment is the principle multiplied by the rate and then multiplied by the time over which the rate is constant. In this format, one approach to calculate a variable rate loan is to cast rate change as uncertainty in a fixed rate. This way the duals arithmetic is used directly and the uncertainty accrues. The alternative is to treat every given number, including the variable rate information, as having its own uncertainty. In this way, the uncertainty calculation assesses the quality of the given information.

The macro-economics homework examples deal with issues from US Government Agencies, namely calculating the Gross Domestic Product (GDP, Commerce) and the National Unemployment Rate (Labor). The data published by these agencies is available online and typically, after a bit of searching, information useful for uncertainty calculations can be found. An additional effect is the scale of numbers, such as dollars or numbers of people. These are large and often numbers are reported as numbers of thousands or with limited precision. Overall, these calculations use a few components, such as the expenditure-based GDP being a combination of consumption spending, investment spending, government spending and net exports. There is at least one formula to combine these into the GDP. Then the implementation of duals arithmetic is to convert all numbers to duals by representing uncertainty in an error vector and convert all calculation steps to duals arithmetic. The end result is the direct calculation of GDP with uncertainty. This provides a statement about the quality of the reported GDP.

A similar process is applied to the calculation of the National Unemployment Rate. The rate is the number unemployed divided by the number in the labor force. Both numbers are reported by the Labor Department and if uncertainty is not reported, the ‘sample counting’ can be considered to establish uncertainty levels for all counts. Afterward, this is easily implemented in duals arithmetic. Now the unemployment rate can be debated (media and politicians) in the context of its information quality indicated by the uncertainty. In duals arithmetic, the error budget is inferred from the error vector components. Therefore we can identify if there is a dominant contribution to the uncertainty and this could be used to show where improvements in accounting will have the greatest impact.