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Consider an IS – LM model with the following elements:
s = s ( y − t.θ . y ),
0 < s ′(.) < 1
(1)
i = i (r ), i ′(.) < 0 (2)
l = l ( y, r ), (3)
l1 (.) > 0, l 2 (.) < 0
where s is the desired private saving, y is the real GNP, θ is the
(exogenously given) labour’s share in GNP, t is the proportionate tax rate
on labour earnings, i is the desired real physical investment, r is the
interest rate and l is the desired real money holdings. The real money
balance
M
, together with the real government spending g and the tax –
P
rate t, are exogenous.
(i)
The Laffer curve plots equilibrium tax collections on the
vertical axis against t on the horizontal axis. Laffer’s
famous formula was that the curve slopes downwards.
Show analytically whether or not that can happen here.
(ii)
Suppose t is imposed on all factor payments, that is, on
GNP. Reformulate equation (1) for this case. Does your
answer to part (i) change?
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