To derive the PS approximation, data on GDP, Consumption, and Government expenditures was obtained from the website as detailed in the homework. Then using excel I was able to recreate the formula given with the actual data to get the approximation numbers. B. The true measure of PS was obtained much the same way as the approximation, only this time I used data for Private Sector Savings and Private Disposable Income pulled from the database instead of Y, C, and G. C. Attached.
Overall it’s not a terrible approximation. There appears to be a rough five billion dollar inflation in the approximation from the true value, but over the course of time the trends remain similar.
Every now and then you will see a significant dip in the approximation at the same time the true value significantly spikes, but aside from that they behave much the same, with a seemingly uniform $5 bil over-approximation across the years. E. For these two measures to be the same, there can be no government, and no international trading.
The reason for no government is that taxes must be zero to allow for Y to stand alone in both denominators; also there must be no government deficit so as to allow for no interest payments. With no taxes and no deficit, it follows that there can be no government spending whatsoever (this takes care of removing transfer and interest payments from the first equation as well). As for having a closed economy with no imports/exports, this is because the Net Factor Payments have to equal zero to allow for these equations to equal each other.