Destinas sat 2: Polley dilemma: interest rate, exchange rate and ?????????
Suppose the economy's IS and PB curves can be summarized in the following
structural equations:
$S_t = I_t$
$S = S_p + S_g$
$S_p = s_p + s_pY$
$I_t = I_o + I_1Y - I_2r$
$T = t_o + t_1Y$
$G = G_o$
$I = I_o + I_1Y - I_2r$
$BP = CA + KA = 0$
$CA = X - M$
$X = X_o + X_1Y^f + X_2R$
$M = M_o + M_1Y - M_2R$
$K = K_o + K_1r - K_2r^f$
As the equations show, national saving (S) is composed of private saving (5p) and
public saving (5G). The economy's output (GDP) is depicted as Y. Government
revenue is realized from tax (T) which is a sum of indirect tax (to) and direct tax
(11). Further, government spending is purely exogenous and represented by Go.
Planned investment is in three part: the startup investment (Io), part of investment
that depends on income (11) and part that depends on interest rate (r). Equilibrium
in the real (goods) market requires that planned investment (I) is equal to national
saving (S) (equation 1). The balance of payments (BP) will be at equilibrium when
current accountt (CA) just equal to capital/financial account (KA) (equation 8).
Current account is net export (X-M). Export is determined by foreign income (YF)
and exchange rate (R) defined as the quantity of foreign currency per unit of
domestic currency. Import is determined by domestic income and exchange rate.
Capital/financial account is determined by domestic interest rate and foreign
interest rate (r^f)
(i) Starting from the initial position, establish the IS and BP relation [hint:
express IS in terms of Y and BP in terms of r].
(ii) Show that increase in income will lead to increase in interest rate [hint
use the BP relation you have derived]
