Need help with a solution

Flamed Diving

Just recently been doing some revision of the early chapters of my economics textbooks and I cam across a problem that I couldn't find the correct solution for. I must be missing a trick somewhere cause the question looks easy enough and its just simple algebra, so if someone could shed light on this, I'd appreciate it.

Question:

In the following macroeconomic model, the unknowns are Y (national income), C (consumption) and T (tax collection):

Y = C + I + G

C = 2 + 0.8(Y-T)

T = 1 + 0.2Y

I (investment) and G (gov exp) are assumed to be known. Find Y, C and T in terms of I and G.

Seems easy enough, but I can't arrive at the numbers for in the solution provided below:

Substitute the expression for T into that for C and the resulting expression for C into that for Y . Solving the resulting equation for Y gives:

Y = 3.33 + 2.78(I + G), C = 3.33 + 1.78(I + G), T = 1.67 + 0.56(I + G)

.

I know its gonna be something stupid I'm forgetting. Put me out of my misery.

Time Magazine

Pfft, noob :pac:

[latex]C = 2 + 0.8(Y-T)[/latex]
[latex]T = 1 + 0.2Y \\[/latex]
[latex]\Rightarrow C = 2 + 0.8[Y - (1 + 0.2Y)] \\[/latex]
[latex]C = 2 + 0.64Y - 0.8\\[/latex]
[latex]C = 1.2 + 0.64Y \\[/latex]

[latex]Y = C + I + G \\[/latex]
[latex]Y = 1.2 + 0.64Y + I + G \\[/latex]
[latex](1-0.64)Y = 1.2 + I + G\\ [/latex]
[latex]Y = 3.3 + 2.78(I + G)[/latex]

Don't bother your arse revising if it's for a masters, enjoy your time off.

Flamed Diving

Oh FFS...

I forgot about the Y on the left (on the second line of the second section there)... d'oh!

Yeah, I was thinking the same but I clearly need to get my mind into maths mode again, I have gotten rusty!

Économiste Monétaire

Time off? Someone needs to up their nerd game . If you have the Simon-Blume book, that would be good to look over, again.

Flamed Diving

The book I am working through is Mathematics For Economists by Pemberton & Rau. Although no book teaches you how not to be sloppy and complacent.

http://www.amazon.com/Mathematics-Economists-Malcolm-Pemberton/dp/0719033411

Time Magazine

Économiste Monétaire wrote: »

Simon-Blume

Nyom. I bought that copy a year ago and it came to €16. A lot better value than the typical €43 price you'll usually find.

I'm very much of the opinion that summertime is for reading those books you've wanted to get around to. Don't bother yer hole studying imho. Go read some Kant or something. Or Antoin Murphy's new book, if you haven't already.

But if you do want to study, go over simple calculus. You don't want to be stuck trying to remember what the first derivative of a log is.

Flamed Diving

The Economist wrote: »

Nyom. I bought that copy a year ago and it came to €16. A lot better value than the typical €43 price you'll usually find.

I'm very much of the opinion that summertime is for reading those books you've wanted to get around to. Don't bother yer hole studying imho. Go read some Kant or something. Or Antoin Murphy's new book, if you haven't already.

But if you do want to study, go over simple calculus. You don't want to be stuck trying to remember what the first derivative of a log is.

Ah, I read my pleasure books too. The way I see it, I am doing cognitive keepy-uppy's. Although I'm spilling the ball quite a bit, atm.

Time Magazine

Flamed Diving wrote: »

Ah, I read my pleasure books too. The way I see it, I am doing cognitive keepy-uppy's. Although I'm spilling the ball quite a bit, atm.

While we're on the topic, if you have a few quid to spare I think you'd do well to snap up the previous edition of Verbeek for €10.

Old edition, but the matrix derivation of OLS and tests for heteroskedasticity haven't changed all that much over the past three years or so.