The Lump Sum Principle In the 1980s Margaret Thatcher

Question

was the British Prime Minister. She was very popular and e�ective until
she pushed for the idea of a so called lump-sum tax. The lump-sum tax is
one in which every citizen pays a single �xed payment.
Consider the scenario, in which a consumer chooses consumption and
the fraction of the day she works subject to income constraints, given taxes
and prices p;w. Let non-labor income be I and suppose the consumers
preferences are given by:
u(c; l) = c:5(1 􀀀 l):5 (1)
(a.) Set up the maximization problem assuming a proportional tax, T (i.e.

at tax, T constant, : : :, the one we did in class)
b.) Set up the maximization problem assuming a lump-sum tax, S.
c.) Suppose that the government must raise G < I pounds. (That is
wTl = G or S = G) Show that the consumer's utility is higher under
the lump-sum tax regime than it is under the
at tax regime(Plug in
numbers for everything but c and l if you want.

Answer 1

First, I don't understand your utility function; I think the Jiskha site modified or eliminated some "special" characters you may have been using.
Second, I don't see a question.

That said, a proportional income tax should lower the marginal utility from working, while a lump sum tax should have no direct impact on a person's leisure/labor choice.