John Edward, a resident of Chelmsford who earned his master’s degree at UMass Lowell and who teaches economics at Bentley University and UMass Lowell, contributed the following column.

Some simple math can help illustrate policy issues that divide our world.

Ratios are a handy device to explore relationships. If you want to compare two data points A and B, use the ratio, or fraction, A/B (A over B). If you perform the division you can report the result as a decimal or percentage. Exploring how changing A or changing B can alter the result can show you how to change the world.

A = National Debt; B = Gross Domestic Product

This ratio compares how much the federal government owes and the size of the economy. The national debt is currently $16.7 trillion. In 2012, Gross Domestic Product (GDP) was $16.2 trillion. Debt is 103 percent of GDP.

There has been a lot of debate over this ratio. One school of thought says when it gets over 90 percent the economy is heading for trouble. Others say there is no cause for immediate concern. Both sides agree that in the long run the ratio should come down.

Exploring the math, there are three ways to make a ratio smaller:

1. reduce A,
2. increase B, or
3. increase B faster (or decrease B slower) than A relative to the current ratio.

Option 3 gets a little complicated so let’s focus on options 1 and 2. We can either reduce the debt (A) or grow the economy (B). Either way, the ratio decreases.

The problem with reducing A when the economy is not doing well is that it pretty much guarantees B will decrease. Sequestration is slowing down the U.S. economy right now. Austerity (i.e., less government spending and more taxes) in Europe helped drive the continent back into recession. Enforced austerity is keeping some countries in Europe in a severe and prolonged recession.

The time to reduce the debt was when the economy was doing well. Right now the path to recovery is to focus on growing the economy. The time for deficit reduction will come again if we do it right.

One final note: the federal government owns much of the national debt. If A were defined as the “debt owned by the public” the percentage is only 74 percent.

A = The Unemployed; B = The Labor Force

In this example, A over B is how we calculate the official unemployment rate. The unemployment rate for July was 7.4 percent. We want the ratio to go down. However, why it goes down is important. We want the unemployment rate to decrease because people are getting jobs. That means A goes down and B stays the same, or goes up.

What we do not want to see is the rate go down because unemployed people are giving up and dropping out of the labor force. The Bureau of Labor Statistics (BLS) calls these people “marginally attached.” In July, the number of marginally attached was 250,000 more than in May.

We need to create jobs, not have people lose hope and lose job skills. We can see the negative impact of too much focus on government deficits. In the last 5 years, 680,000 government jobs have been lost. Whenever people lose their job it has a negative multiplier effect and slows down the economy.

One final note: there is another ratio used to measure unemployment. It includes the marginally attached and people who have part-time jobs only because they cannot find full-time work. The BLS calls this ratio “u6.” A more descriptive name is the “underemployment rate.” In July, u6 was 14 percent.

A = Taxes Paid; B = Gross Income

This ratio is the effective tax rate. This is the bottom line. You made a certain amount of money last year, how much of it did you have to pay to the government.

Massachusetts taxes income at 5.25 percent. The effective income tax rate is lower due to credits, deductions, and exemptions. However we also pay sales, excise, and property taxes.

The average effective tax rate in Massachusetts is over 9 percent. A lot of people ask why the ratio has to be that high. That is the wrong question.

The important question is why the ratio varies so much. The average tax rate is very deceptive. In the Commonwealth of Massachusetts taxes vary greatly depending on level of income.

The Institute on Taxation and Economic Policy conducted a study on effective tax rates. For the top 1 percent of income earners the effective tax rate was only 4.9 percent. For the bottom 20 percent of income earners A over B was 10 percent! The state with a reputation for liberalism has a very regressive tax structure.

One final note: we do not live in taxachusetts. In 2012, twenty-four states collected more tax revenue as a percentage of income. The Tax Foundation ranking of states by business tax climate has twenty-eight states rated lower than Massachusetts.

A = Housing Expenses; B = Gross Income

This ratio is an important budgeting tool. The generally accepted guideline is that households should spend no more than 30 percent of their pre-tax (gross) income on housing expenses. Housing expenses include a mortgage or rent, plus insurance, utilities, and maintenance.

As you would expect, the ratio varies considerably from household to household. As you would expect, high-income earners tend to have lower ratios. When low-income households spend more than 30 percent of their income on housing it puts them in the position of making difficult choices. Do they:

a) pay their utility bills this month,
b) fill their medical prescriptions,
c) make sure their children have a nutritionally adequate diet,
d) take educational courses to help them raise their income.

All of the above is often not a choice.

In both Lowell and Chelmsford, almost half of households that rent have a ratio greater than 30 percent. In Chelmsford, over 400 households pay rent and other housing expenditures that add up to over 50 percent of their income!

To fix the problem of unaffordable housing we need to lower the ratio for low-income households. That means either lower A or raise B. In this case, all of the above is the best choice. We need to increase the supply of affordable housing, and increase incomes.

Increasing the minimum wage would help. More government spending on education, even if it increases the debt temporarily, would help. More government spending on infrastructure, even if it increases the debt temporarily, would create well-paying jobs. If Massachusetts did not have a very regressive tax structure it would help.

One final note: Massachusetts paid out more in tax credits last year for one Hollywood Movie (RIPD) then it did for all affordable housing projects. However, the key to producing more affordable housing is not more government intervention, it is less government intervention. More on that in an upcoming column.