I've got the following problem in my macroeconomics 2 paper:
Consider the following simple Keynesian diagonal cross model: consumption is given by C = 100 + 0.75(1 - t)Y where t is the constant income tax rate, Y is national income, investment (I) is exogenously equal to 100, and government spending is exogenously given and equal to 200. Calculate the appropriate rate of income tax to balance the budget.
The way I see it, the way to solve this is to go to the balanced budget formula T - G = 0, substitute T with tY since it's an income tax and G with 200 since it's exogenously given, so tY = 200, and t = 200/Y.
Then I go substitute t in the equilibrium output formula Y = C + I + G, hence:
Y = 100 + 0.75(1 - 200/Y)Y + 100 + 200,
and when I solve this I get Y = 1000, and therefore t = 200/1000 = 0.2, 20%
I'd be glad if some macro geek would confirm this is correct. Thanks