 ## Simple Mathematical Economics You can refer to Page 60 to see how the folowing marginal concepts are used in analysis.

Economists often use mathematics to clarify the analysis of the circular flow of income model.

Income is passed on in the circular flow of income through consumer spending or leaked out though savings, taxation or spending on imports.

The proportion of national income (Y) spent on consumption (C) is called the average propensity to consume (APC). It is the amount used for consumption out of each unit of income (1 Real, GBP or \$US for example) The proportion of national income saved is called the average propensity to save (APS) (NB APC + APS = 1) in words: all income is either spent or saved (where saved means not spent)

Economists are most concerned with what happens at the margin, or when variables change in an incremental way (each additional unit of a given variable).

Anytime there is an incremental change in national income, consumption, savings, taxation and imports will also change by a certain proportion. Whereas average propensity is concerned with the proportion of total national income that is passed on or leaked from the circular flow of income, marginal propensity is used to describe the proportion of an incremental (additional or extra) change in income that is either spent or leaked from the circular flow of income, .

We can, therefore, identify the marginal propensity to consume as the proportion of a change in national income that is spent on consumption Similarly, the proportion of a change in national income that is saved, is called the marginal propensity to save (MPS) The proportion of a change in national income that is paid to the government in tax, is called the marginal rate of taxation (MRT) The proportion of a change in national income that is spent on imported goods, is called the marginal propensity to import (MPM)  Now have a go at the following questions:

1. Assuming a two sector closed economy and that the APC = 0.6 and national income is \$1000, calculate the:
1. level of consumer spending
2. level of savings in the economy.
2. Assuming a three sector open economy and that the MPS and MRT and MPM are all 0.2, and national income changes by £2000, calculate the change in the level of:
1. consumer spending
2. tax revenue
3. import spending
3. Assuming a three sector open economy (however would also be the case for a two sector closed and open economy) the MPC is 0.5, and national income falls by £1500, calculate:
1. the change in the amount of money that leaks out of the circular flow of income
2. the change in the amount of consumer spending.

These concepts will be revisited later in later section when we look at what causes national income to change.