Question

In: Economics

3.3. Assume S = –N$200m + 0.08Yd; M= 0.1Y; I = N$300m; G = N$150m; X...

3.3. Assume S = –N$200m + 0.08Yd; M= 0.1Y; I = N$300m; G = N$150m; X = N$140m and t = 0.21Y.
(a) Calculate the total-spending function and equilibrium income. Illustrate this on a graph. [5 marks]
(b) Indicate on the graph the effect of an N$100 million increase in investment spending and comment on the magnitude of change in the equilibrium income relative to the change in investment spending. Calculate the new equilibrium income. [5 marks]
(c) Assume the marginal tax changes to 0.25Y. How will this change influence the total spending curve? Illustrate this on your graph. [5 marks

Solutions

Expert Solution

(a) We know the national income identity is:

Y=C+I+G+X-M (Eqn 1)

S=Y-C   (Eqn 2)

Therefore, from the first two equations: S=I+G+X-M

Putting the values,

-200+0.08Yd=300+150+140-0.1Y (Eqn 3)

Now Yd= Y-taxes=Y-0.21Y=0.79Y (Eqn 4)

Now substituting Eqn 4 in Eqn 3, we get,

-200+0.08*0.79Y=300+150+140-0.1Y

Solving, Y = 4840.7 ($, mln)

See Graph 1

(b) Now I increases by 100. So the aggregate demand curve will shift up by 100 (See Graph 2). Y will also increase by 100. New Y=4840.7

(c) Tax changed to 0.25Y. This will increase the slope of consumption curve and aggregate demand curve. See Graph 3.

New Y = C+I+G+X-M

C=Y-S

=Y+200-0.08(Y-0.25Y)=0.94Y

therefore, new Y= 0.94Y+400+150+140-0.1Y

Y=4312.5


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