Answer to Question #271576 in Macroeconomics for Maphula

Question

 A researcher estimated the following regression equation , 

Yt from the use of various amounts , X1 and X2 on a hectare 

basis using time series data from 2001 to 2010.

The operation model is:

Yt = B0 + B1X1 + B2X2 + ei

The estimated regression equation is:

Yt = 31.98 + 0.65X1 + 1.10X2

(0.24) (0.27) (0.25)

Adjusted R2 = 0.989

Figures in parenthesis are standard error of estimates.

i) Estimate the t-values for each of the coefficients

ii) Interpret the results 

Answer 1

Income(Y) = Consumption + Investment  ........................1

Income(Y) = Consumption + Savings  ....................2

From 1 and 2, we get:

Investment = Savings

Step 2

autonomous investment = 2,000 shillings

consumption function , c=800 + 0.25Y

Y = 800 + 0.25Y + 2000

⇒

⇒Y - 0.25Y = 2800

⇒

⇒Y =1

0.75

10.75×

× 2800  (where 1.75 is multiplier and 2800 is autonomous expenditure)

⇒

⇒Y = 3733.33

Income=3733.33shillings

Consumption=800 + 0.25(3733.33) = 1733.33shillings

 

Step 3

When investment increases by 250, national income increases by:

multiplier×

×250=1

0.75

10.75×250

×250 = 333.33shillings

Step 4

When the level of planned investment is to the ceilings and the saving function is S=-800 + 0.25Y, then

Y = Consumption + Savings

⇒

⇒Y = 1733.33 + (-800 + 0.25Y)

⇒

⇒Y - 0.25Y = 933.33

⇒

⇒Y = 1244.44

Income = 1244.44shillings