Question

GIVEN: Ca = 5,000       

mps = 0.1          

I = 6,000            

G = 4,000

          Ta = 1,000   

mpt = 0.2  

   TR = 1,500

 

REQUIRED: Answer the following questions. Show the solutions.

1.   Formulate the consumption function.

2.   Formulate the savings function.

3.   Derive the equilibrium income for an economy consisting of HHs only and prove that Y = C  &  S = 0 using any approach of your choice.

4.   Derive the equilibrium income for an economy consisting of HHs & BFs and prove that Y = C + I and S = I using any approach of your choice.

5.   Derive the equilibrium income for an economy consisting of HH, BF & G does not impose taxes and prove that Y = C + I + G & S = I + G using any approach of your choice.

6.   Derive the equilibrium income for an economy consisting of HH, BF & G imposes fixed taxes and prove that Y = C + I + G & S + T = I + G using any approach of your choice.

7.   Derive the equilibrium income for an economy consisting of HH, BF & G imposes fixed & behavioral taxes and prove that Y = C + I + G & S + T = I + G using any approach of your choice.

8. Derive the equilibrium income for an economy consisting of HH, BF & G imposes fixed & behavioral taxes but grants transfer payments and prove that Y = C + I + G & S + T = I + G + TR using any approach of your choice. 

Answer 1

$$solution$$

$Y=income\\ MPs=0.1\\ MPc=1-0.1=0.9\\ consumption\ function\ :\\ C=Ca+MPC\times Y\\ C=5000+0.9Y$

$Y= Income\\ Saving \ function:\\ S=-Ca+MPs\times Y\\ S=-5000+0.1Y\\$

$we \ know\ that\ Y=C+S\\ where\ Y=income\\ C=consumption\\ S=saving\\ if \ we \ want \ S=0, then \ Y \ has \ to\ be \ equal\ to\ C\\ let \ us\ replace\ Y with \ C\ in \ the\ consumption\ function \ devised\ in\ part \\ one\ above.\\ we\ found\ that:C=5000+0.9Y\\ we\ can\ replace\ Y\ with\ C\ , and\ the\ equation\ will\ be:\\ C=5000+0.9C\\ 0.1C=5000\\ C=\frac{5000}{0.1}\\ C=50,000\\ Since\ Y\ was\ to\ be\ equal\ to\ C\ ,we\ can\ say\ that\\ Y=I=50,000\\$

$We\ are\ given:I=6000\\ and \ Y=C+S\\ or \ at\ the\ equilibrium\ level\ S=I,we\ can\ also\ write\ it\ as:\\ Y=C+I\\ lets\ substitute \ them\ by\ entering \ in \ the\ values\ of\ I\ and\ the \ whole\ C\ \\ function\ in\ place\ of\ C\ above\\ we\ get :\\ Y=5000+0.9Y+6000\\ Y-0.9Y=5000+6000\\ O.1Y=\frac{11,000}{0.1}=110,000\\ Y=equilibrium\ income=110,000$

$We \ are\ given\ G=4000\\ and : Y=C+I+G\\ or\ at\ equilibrium \ level\\ S=I+G\\ Y=5000+0.9Y+6000+4000\\ Y=15000+0.9Y\\ Y-0.9Y=15000\\ 0.1Y=15000\\ Y=\frac{15000}{0.1}=150,000.\\$