Economics Missive #1

Economic Missive of the Week

PI = PS + CS + GS,

PI = Private Investment
PS = Private Savings
CS = Corporate Savings
GS = Government Savings, i.e. surplus

Written in terms of output (we assume that people either consume or save all their personal income), we have:

PI = αpYp + αcYc + GS

Where αp and αc are the marginal propensities to save for the private and corporate sectors, respectively. We also know that people save after-tax dollars, and so we introduce taxation into the equation. Because government has some residual costs of upkeep, we postulate that it is always greater than zero, i.e. government entropy.

PI = αp[(1 - τp)Yp] + αc[(1 - τc )Yc] + [Τ – GC], Σ[Yxτx] = Τ and GC > 0

Where τp and τc are the private and corporate aggregate tax rates, which represent the fraction of the private sector’s output that are remitted to government and is equal to the government’s total tax revenue of Τ.

So what can we infer from this identity now that we have broken it down into its various components? We see that the marginal propensity to save has a huge effect in on private investment. This is quite obvious – if a firm or individual wants to consume, it will save just that much less. What is not quite as obvious is the relationship between personal and corporate savings. Economic intuition would dictate that when individuals consume goods and services, the providing firms would see an increase in income. Firms will then invest a proportion of those savings to enhance their operations, some of which will feed back to individuals via increased or new wages.

This savings-consumption cycle can flow the opposite way. In this case, we have individuals who have saved previous income investing it in firm equity. This provides the capital firms need to produce goods and services that are sold to other consumers – the future earnings that end up back with the investor via dividends and coupon payments. The question is not so much about which way the cycle flows, but which agent, the firm or the individual, has that initial savings to start it.

Another interesting discussion is the affect taxation has on private investment. First, taxation merely redistributes income from the private and corporate parts of the equation to the government part. Secondly, given government entropy, this re-allocation would result in diminishing private investment by the amount of the costs of maintaining government. So why would the government want to modify the balance of investment when it results in a smaller final amount? This question will be answered in next week’s missive.