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Donald consumes goods x1 and x2. His utility function is U(x1, x2) = x1(x2)3. He is...

Donald consumes goods x1 and x2. His utility function is U(x1, x2) = x1(x2)3. He is endowed with 43 units of x1 and 7 units of x2. The price of x1 is $1 and the price of x2 is $3. Find his net demand for x1.

a) LaTeX: -27

b) LaTeX: -9

c) LaTeX: 16

d) LaTeX: 27

e) LaTeX: 59

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Answer #1

a) -27

(e1 = 43, e2 = 7
Value of endowment = P1*e1 + P2*e2 = 1*43 + 3*7 = 43 + 21 = 64

We find the gross demand first.
It is determined where MRS = p1/p2

MRS = MU1/MU2 = 器 x23x2 器 3x1r2 = 31

So, MRS = p1/p2 gives,
x2/3x1 = 1/3
So, x2 = 3x1(1/3) = x1

Budget constraint: P1*x1 + P2*x2 = value of endowment
So, x1 + 3*x1 = 64 (as x2 = x1)
So, 4x1 = 64
So, x1 = 64/4
So, x1 = 16

Net demand for x1 = x1 - e1 = 16 - 43 = -27)

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