Hence, Marshallian demand function for good q and good 2 respectively are
X1 = 0.4*m/P1
X2 = 0.6*m/P2
Transcribed Image Text:8.
In a 2-good model, where the goods are denoted x, and x2, the consumer's utility
1 1
function is as follows: U =
Money income available is denoted m. All of this income is spent on the two goods.
The prices of the two goods are P1 and p2 respectively.
(a)
By minimising expenditure, subject to the utility function, find the compensated
(Hicksian) demand functions; that is, demand for each good expressed in terms of U,
P1 and P2. Do not check the second order conditions.
(b)
Substitute these conditional demand functions back into the objective function to find
the expenditure function; that is, m in terms of U, P, and p2.
(c)
Show that the derivative of the expenditure function with respect to P1 is the
conditional demand function for x1-
(d)
Now maximise utility subject to the budget constraint and thus find the ordinary
(Marshallian) demand functions; that is, demand for each good expressed in terms of
m, Pi and P2. Do not check the second order conditions.
(e)
Substitute the demand functions in (d) into the utility function and re-arrange the term
so that the dependant variable is m.
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