Why does savings equal investment (scenario)?

Question

Scenario 1: There's an economy of two people (Joe and Amanda). Joe buys a $500$ dollar car from Amanda (which she made herself from raw materials in her back yard). Amanda takes the $500$ dollars and hides it under her bed. Savings = $500$ dollars, Investment = $0$ dollars. What am I missing?

Scenario 2: Same Amanda and Joe. Joe gets $500$ dollars from the Federal Reserve (they just gave it to him). He puts it in a bank. The bank decides to only lend out $250$ dollars of it. Amanda invests in inventory. S = $500$, I = $250$. Right?

These are two cases where investments do not seem to equal savings. How can these cases be explained?

Answer 1

To clarify the first scenario: you assume Joe can buy this car. However, Joe has to either earn an income (and therefore, produce something himself) or he has to dissave. In the first case, Joe has produced 500 output and earned an income of 500. He spends his income on a car, but Amanda saves the money. As is clarified in other answers, Joe's output goes to inventories (because not purchased by Amanda), which are counted as (unplanned) investments. S = I = 500, C = 500, Y = S + C = 1000. You mention in a comment that most consumers do not produce something. In fact, they do. At work, when earning their income (with which they buy the car), they created added value (this is the production (500) that goes to the inventory when Amanda does not buy it). Think of the income they earn at work as their part in the created added value, their contribution to real production. Consider the second case when Joe does not work.

In the case Joe dissaves to buy the car instead of working and using his income (he just drives around, without producing), 500 savings have to be deducted from your final result for the first scenario, so that S = I = 0, C = 500, Y = S + C = 500.

In the second scenario, forget about Joe's 500 for a while. Assume Amanda invests 250 (one car) in inventory, which means she has produced 250 (one car) first (and sold nothing), so that I = Y - C = 250, C = 0. Consumption is zero because Amanda sold nothing and Joe bought nothing.

An income can only be earned when value added was produced. Therefore, the 500 Joe has received cannot be seen as an income, and since only income can lead to consumption or saving, Joe had neither consumed nor saved. The 500 Joe received is an expansion of money supply (and has no real interpretation) and will increase prices proportionally (assume V and Y to be constant in the fisher equation (MV=PY)). The 250 that Amanda produced has now increased in value, but in real terms her investment in inventory will still refer to the 250 (one car).

This actually illustrates the importance of distinguishing nominal and real variables in the economy. The macro-economic identity you refer to is only about real variables.

Answer 2

In the basic, closed economy model, you are right that Savings=Investment. The reason for this is because, in this model, growing capital stock is not the only item taken into account in Investment. The other item is inventory accumulation. It's a bit difficult to apply it to your scenarios, but here's a rough attempt:

Scenario 1: In this scenario, Joe buys a car for 500 dollars from Amanda, and Amanda stuffs it into her mattress. Now suppose Joe produces something as well. When Amanda turns around and stuffs the money under her mattress instead of buying Joe's goods, Joe has an accumulation of inventory worth 500 dollars. This increases investment by 500 dollars.

Scenario 2: In this scenario, Joe receives 500 dollars from the Fed, and he puts it into a bank, and the bank turns around and loans 250 dollars of it to Amanda who invests in inventory. Again, in this situation, when Joe does not use the other 250 dollars to purchase Amanda's goods, she has an accumulation of inventory worth 250 dollars, which increases investment by an extra 250 dollars.

Like I said, it's a little difficult to apply to a two person economy. When applied to larger economies with many producers, it makes a little more sense.

Answer 3

In macroeconomics, investment is the amount of goods(consumer goods or capital goods) produced or purchased per unit time which are not consumed at the present time. In other words, "investment" is the amount of goods saved for future use which is by definition "Savings". (Saving does not necessarily need to be in the form of cash. It can also be in the form of unused goods)

Therefore, economist has basically termed saving as "investment" and later found out that Saving = Investment. This may confuse people into thinking that savings and investments are separate concepts. However, both are same concept expressed in different vocabulary.

Now, if the word "Investment" means amount of capital goods produced or purchased per unit time which are not consumed at the present time and the word "Saving" means amount of consumer goods produced or purchased per unit time which are not consumed at the present time, "Saving" is not necessarily equal to "Investment". Then, the Y = C + I should be converted to Y = C + S + I to depict more accurate definition and relation between Saving and Investment.

In the scenario 1, Amanda produced 500 dollar car (Y = 500 dollars). Joe buys the car. Depending on the use of the car, Joe may be either consuming or investing(which means consuming at a future date) the car. 500 dollars cash "saved" by Amanda is not a saving in an economical sense. 500 dollars cash is only a medium of exchange held by Amanda. It does not represent real consumer goods or capital goods saved for future use. Therefore in a bigger picture, Y = C + S + I where Y= 500 dollars, C + I = 500 dollars, S = 0 dollar.

Answer 4

Okay, sorry that my previous answer might involve too much extraneous materials.

Anyway, one perspective you might want in thinking about the classical model is think of it as real things get produced rather than in monetary terms.

In a closed economy in the long run, we assumed real output is fixed. Think of it as actual goods piling up. Now, consumption is how much people consume out of this pile, goods and services included. Government purchases is the amount of goods get and use from the pile. Now we are left with investment. Investment is simply the amount of the goods left in the pile. And since we have subtracted all the consummable goods from the pile, what must left must be investment such as machines, warehouses.

Now, consider saving. One way to avoid your confusion is think of saving not in monetary terms (I understand saying saving makes you think of the money not spent, but please reframe from doing so.) Because people's totoal real income equal total actual goods and products produced that year, since people and the government only consume the Consumption and Government Purchases, the rest, the investment, is therefore defined as saving.

I hope this can help a bit.