Assume a two-sector income determination model where consumption depends on inco
ID: 1118445 • Letter: A
Question
Assume a two-sector income determination model where consumption depends on income and investment is autonomous, so that: and equilibrium occurs where Y-C+I (a) Solve for the equilibrium level of income Y' explicitly (b) Use comparative statistic to estimate the effect on Y of a change in autonomous investment I (c)Find the implicit function for the equilibrium condition and then find the same comparative statistic derivative (in b) from the implicit function (d)From (a), evaluate the effect on y'of a change in the marginal propensity to consume b explicitly (e) From (c), evaluate the effect on of a change in the marginal propensity to consume b implicitlyExplanation / Answer
a. Given C = bY and I = I0 ; 0<b<1
And equilibrium occurs at Y = C + I
Substituting the values in equilibrium condition,
Y = bY + I0
(1-b)Y = I0
Y* = I0 / (1-b)
b.Using comparative static to find the effect of a change in autonomous investment on Y*,
d Y*/d I0 = 1 / (1-b) >0
Therefore, any change in autonomous investment is directly proportional to change in Y*. An increase in I0 is associated with an increase in Y* and vice-versa.
c. An implicit function of the equilibrium condition is given as,
Y – C – I =0
Substituting the values,
Y – bY - I0 = 0
Y* = I0 / (1-b)
Using comparative static of the implicit function to the effect of a change in autonomous investment on Y*,
dY / d I0 - bdY/ d I0 - d I0 / d I0 =0
(1-b) dY/ d I0 -1 = 0
d Y*/d I0 = 1 / (1-b) >0
d. To evaluate effect of a change in marginal propensity to consume, b, explicitly,
d Y*/db = - I0/(1-b)2
Therefore, any change in marginal propensity to consume is inversely proportional to change in Y*. An increase in b is associated with a decrease in Y* and vice-versa.
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