Macro econ

Use the Keynesian model for this problem. Assume the following model of the economy, where c, t, and nx are positive constants:

C= 200 0 + c(Y-T)
T= 400 + tY
Ip = 1500
G = 2000
NX = 1000 - nxY
where c=.75, t=.2, nx = .10

a) What is the magnitude of autonomous spending?
b) spending multiplier?
c) equilibrium output?
d) government budget surplus/deficit?
e) trade surplus/deficit?

I cannot solve this problem b/c I feel there is always too many missing variables in every equation I try to derive. Any help?

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  1. First, solve for Y. Y=C+I+G+NX.
    Substitute for all components. SO,
    Y=2000+.75*(Y-400-.1Y) + 1500 + 2000 + (1000 - .1Y)
    You have one equation and one unknown. Solve for Y.
    Hint: I get Y=12400

    a) Im uncertain on this. I think of autonomous spending as spending unrelated to income. So, I think autonomous spending is C=2000,I=1500,G=2000,X=1000 = 6500. Please check your definition of autonomous spending.
    b) spending multiplier is 1/(1-mpc(1-t) = 1/1-.75*(1-.2) = 1/.4 = 2.5

    c) calculate tax based in Y=12400

    d) calculate NX based on Y=12400

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