Question

1. This question asks you to work with a simple short-run macroeconomic model. In this model, there are only two types of decision-makers: firms and households (no government and no international considerations). A description of the behavior of the two groups is that firms choose how much to produce (Y) and how much newly produced capital goods they would like to purchase and households choose how much of their income they would like to spend and how much they would like to save.

(1) Firms produce what they expect to sell.

(2) Firms want to purchase 200 (million $) of newly produced capital goods; i.e., I = 200.

(3) Households spend as follows: if Y (income) is zero they spend 100 (million$) and if income rises by $1 they spend $0.80; i.e., C = 100 +0.8*Y.

1. 1.1) If firms expect to sell 2000 and thus produce 2000, how much will they actually sell?
2. 1.2) Do firms end up with inventories they did not intend to have? If so, how much?
3. 1.3) What is the level of actual investment (as opposed to the desired investment)?
4. 1.4) How much do households save when Y = 2000?
5. 1.5) Find the equilibrium level of GDP (Y).
6. 1.6) Produce a graph with aggregate expenditures on the vertical axis and GDP on the horizontal axis. Identify the unplanned inventories when firms expect to sell 2000 and the equilibrium level of GDP (that is, the equilibrium value for Y).
7. 1.7) How much do households save when the economy is in equilibrium?

Now suppose that households change behaviour: they want to save 100 more (i.e., the savings

function shifts up by 100).

1. 1.8) Find the new equilibrium levels of income (Y) and savings (S).
2. 1.9) If firms did not anticipate the change in behavior they would have produced too much. How much too much? How much would household save? What is the actual level of investment spending?
3. 1.10) In the new equilibrium I = S = 200 which is the same as in the original equilibrium. Why hasn’t S increased?
4. 1.11) The result in Question 3.10 is known as “the paradox of thrift” and it is a classic example of the fallacy of composition. Define the “fallacy of composition” and explain why the paradox of thrift is an illustration of the fallacy of composition.

Answer 1

1.1)Since in an economy without government and foreign trade, whatever is produced is eithjer purchased or added to stocks and additions to stock are counted as part of investment by firms we get the identity that Y=C+I.

So when Y=2000(Output) : C=100+0.8Y or, C=1700.. thus, sell is 1700.

1.2) Yes, firms end up with inventories. In the current period, value of sales= expenditure of the buyers. Here, expenditure is 1700, so unsold goods is worth 300. This 300 are added to inventories or stock.

1.3) The additional stock 300 is conventionally taken as investment expenditure by the firms on their own product. I=200 was their planned investment, but actual investment is 300 here.

1.4) savings = income - consumption

OR, S = Y - C

or, S = Y - (100+0.8Y)

or, S = 0.2Y - 100 ( savings function)

when Y=2000,

S = 0.2(2000)-100

or, S = 300 ( S=I)

1.5) For equilibrium level of GDP, AS=AD,  Since C + S = Y, the national income equilibrium can be written as : Y = C + I

1.6)

1.7) S=I = 300

1.8)Savings function lifts by 100, so now, S=400

S= 0.2Y-100

or, 400 = 0.2Y -100

or, Y=2500

1.9) Firms would produce an extra of (2500-2000=500) . Would have produced extra of 500.

When Y=2500, C=2100

Now, S=Y-C or, S = 2500-2100= 400

1.10)here, S didnt increase( after lift of 100) because before Y=2000, now, Y=2500

1.11) The error of assuming that what is true of a member of a group is true for the group as a whole.

The fallacy of composition arises when one infers that something is true of the whole from the fact that it is true of some part of the whole. A trivial example might be: "This tire is made of rubber, therefore the vehicle of which it is a part is also made of rubber."

Paradox of Saving (also known as paradox of thrift) - This is a classic example of the fallacy of composition. It states that individuals try to save more during an economic recession, which essentially leads to a fall in aggregate demand and hence in economic growth. Such a situation is harmful for everybody as investments give lower returns than normal. It is the belief that if one individual can save more money by spending less, then society or an entire economy can save more money by spending less. However, this simply isn't true.