# Math is very simple, unless you depend on the peasants who pay your way.

Saturday quiz – January 21, 2011 – answers and discussion Posted on Sunday, January 22, 2012 by bill

Here are the answers with discussion for yesterday’s quiz. The information provided should help you understand the reasoning behind the answers. If you haven’t already done the Quiz from yesterday then have a go at it before you read the answers. I hope this helps you develop an understanding of Modern Monetary Theory (MMT) and its application to macroeconomic thinking. Comments as usual welcome, especially if I have made an error.

**Question 1:**

*A program of fiscal austerity will always undermine attempts by the private domestic sector to reduce its indebtedness when the nation exports less than they import (including net income flows).*

The answer is **True**.

Fact – when a nation exports less than they import (including net income flows) we say they have an external deficit (current account deficit).

This is a question about the sectoral balances – the government budget balance, the external balance and the private domestic balance – that have to always add to zero because they are derived as an accounting identity from the national accounts. The balances reflect the underlying economic behaviour in each sector which is interdependent – given this is a macroeconomic system we are considering.

To refresh your memory the balances are derived as follows. The basic income-expenditure model in macroeconomics can be viewed in (at least) two ways: (a) from the perspective of the **sources** of spending; and (b) from the perspective of the **uses** of the income produced. Bringing these two perspectives (of the same thing) together generates the sectoral balances.

From the **sources** perspective we write:

GDP = C + I + G + (X – M)

which says that total national income (GDP) is the sum of total final consumption spending (C), total private investment (I), total government spending (G) and net exports (X – M).

From the **uses** perspective, national income (GDP) can be used for:

GDP = C + S + T

which says that GDP (income) ultimately comes back to households who consume (C), save (S) or pay taxes (T) with it once all the distributions are made.

Equating these two perspectives we get:

C + S + T = GDP = C + I + G + (X – M)

So after simplification (but obeying the equation) we get the sectoral balances view of the national accounts.

(I – S) + (G – T) + (X – M) = 0

That is the three balances have to sum to zero. The sectoral balances derived are:

- The private domestic balance (I – S) – positive if in deficit, negative if in surplus.
- The Budget Deficit (G – T) – negative if in surplus, positive if in deficit.
- The Current Account balance (X – M) – positive if in surplus, negative if in deficit.

These balances are usually expressed as a per cent of GDP but that doesn’t alter the accounting rules that they sum to zero, it just means the balance to GDP ratios sum to zero.

A simplification is to add (I – S) + (X – M) and call it the non-government sector. Then you get the basic result that the government balance equals exactly $-for-$ (absolutely or as a per cent of GDP) the non-government balance (the sum of the private domestic and external balances).

This is also a basic rule derived from the national accounts and has to apply at all times.

The following graph with accompanying data table lets you see the evolution of the balances expressed in terms of percent of GDP. I have held the external deficit constant at 2 per cent of GDP (which is artificial because as economic activity changes imports also rise and fall).

To aid interpretation remember that (I-S) > 0 means that the private domestic sector is spending more than they are earning; that (G-T) < 0 means that the government is running a surplus because T > G; and (X-M) < 0 means the external position is in deficit because imports are greater than exports.

http://bilbo.economicoutlook.net/blog/?p=17850

*Never let the idiots on TV try to convince you how math really works*

– Atomizer