Sept '09 Q20 - value of income, Y

An open economy has the following characteristics:

Consumption expenditure = 0.6Y
Investment expenditure = £200 million
Government expenditure = £500 million
Exports = £300 million
Imports = 0.3Y
The rate of taxation is 50% of all income, where Y is national income.

Determine the value of Y.

A £500 million
B £700 million
C £1,000 million
D £1,300 million




I have Y to be £1,428. Reasoning:

If Consumption expenditure is 0.6Y, import expenditure is 0.3Y ==> Cd = 0.3Y.

Y = C + I + G + X - M
Y = 0.6Y + 200 + 500 + 300 - 0.3Y
Y = 1,428.57

OR

Y = Cd + I + G + X
Y = 0.3Y + 200 + 500 + 300
Y =1,428.57

Alternatively, since tax rate is 0.5Y, Cd is 0.3Y and Cimport is 0.3Y, then net savings must be -0.1Y. Then, using J = W (assuming market is in equilibrium, which I think is a reasonable assumption):

200 + 500 + 300 = -0.1Y + 0.5Y + 0.3Y
1000 = 0.7Y
Y = 1,428.57

Thanks

 

Again, there's a question of the same sort later in the paper that doesn't make sense to me.

The following information is given on Country A:

Autonomous consumption expenditure £8 billion
Investment expenditure £5 billion
Government expenditure £6 billion
Export expenditure £3 billion
The income tax rate is 25 per cent of all income, the marginal propensity to consume is 0.8 and the marginal propensity to import is 0.15.

(i) Calculate the equilibrium level of national income.


The answer:


C = 8 + 0.8 (1 - 0.25)Y
I = 5
G = 6
X = 3
M = 0.15Y

Y = 8 + 0.8 (1 - 0.25) Y + 5 + 6 + 3 - 0.15Y

0.55Y = 22

Y = £40 billion

It appears that the marginal propensity to consume is a factor of the income left after tax (i.e. 0.8 of 0.75Y), while the marginal propensity to import ignores tax, which seems inconsistent.

 

50% of consumption is taxed.

Y = 0.5*Cd + I + G + X
Y = 0.5*0.6Y + 200 + 500 + 300 - 0.3Y
Y = 0.3Y + 1000 - 0.3Y
Y = 1000

so C 1000, is correct


It's a similar situation in the other question, you have 0.8Y consumption of which 25% is taxed thus leaving you with 0.8Y(1-0.25). Just try and think that the tax rate is applied to the amount that is consumed rather than as a proportion of Y.

 

Thanks for the reply.

I'm not sure about your notation. If you assume Consumption Expenditure (=0.6Y) relates only to domestic goods - which it appears you do as you've labelled it Cd - then we shouldn't need to net off imports (0.3Y).

If there's a mixup in your notation, and you're referring to total consumption (i.e. domestic and imports) in the first term, then I understand now why we take total consumption to be 0.5*0.6Y, but shouldn't we also do the same to imports? I.e. imports = 0.5*0.3Y.

Which gives us:

Y = 0.5*0.6Y + 200 + 500 + 300 - 0.5*0.3Y
Y = 1000 + 0.15Y
Y = 1,176.47 ................different to the answer I first calculated, but still not what the answer says it should be.

The logic seems to be (from both questions) that the Consumption Expenditure factor relates to disposable income, while the Import Expenditure factor relates to total income. I find that hard to agree with, but that's how it seems.

 

Apologies, I meant Y = C + I + G + X - M

You make a valid point re the imports being taxed, I'd guess imports are being treated as outgoings rather than income and are therefore free from this tax.

Looking at the ASET for inspiration, these questions have been amended, with the tax parts removed. So either these questions contain an error, or we no longer have to worry about these style questions!

 

Ooh, that's good to know. Thanks for the quick replies - much needed at this late stage!

 

I'm afraid this part of the syllabus changed in April 2010, so using the old questions from the profession's website could cause some confusion (and obviously has!).

Under the old syllabus, consumption and savings were given out of disposable income (ie income after tax) but imports and taxation were given out of national income. Under the new syllabus, consumption, savings, imports and taxation are all given out of national income.

Lots of items have changed since 2010, so you might find this problem in other topics too. Past questions used in ActEd's materials (such as ASET or the revision booklets) have all been amended to be consistent with the new syllabus.