Question

1. Emily has preferences for two goods x, y while her marginal rate of substitution (MRS) between x and y is given by 3y/x. Her budget constraint is m ≥ pxx + pyy, where m = income and px, py are prices of x, y respectively. (a) Emily's expenditure on y (i.e., pyy) is 1/3 of her expenditure on x (i.e., pxx). Is this true Are x and y normal goods? (b) Andrew has different preferences: his marginal rate of substitution (MRS) between x and y is equal to 3 for all x, y > 0. His budget constraint is the same as Emily's. What can you say about his demands for x, y?

Answer #1

(a) MRS = 3y / x

At optimality MRS = Px/Py => 3y / x = Px / Py

=> 3Y * Py = XPx

=> YpY = XPx / 3 ....... (1)

Budget constraint: XPx + YPy = M

From eq (1)

YPy = 1/3 * (XPx)

where YPy is expenditure on Y and XPx is the expenditure on X.

So it is True.

(b) MRS = 3

Budget constraint: XPx + YPy =M

MRS = MUx / MUy = 3 => MUx = 3MUy

If Px> 3Py then X= 0 and Y = M/Py

If Px < 3Py then X= M/Px and Y=0

If Px=3Py then XPx + YPy = M

Additional:

3Py X + YPy = M

3X + Y =M/Py

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pyy,
where m is income
and px, py
are the prices
of x, y respectively.
(a) Someone says that Jasina’s expenditure on
y (i.e., pyy) is
always one third of her expenditure
on x (i.e.,
pxx). Is this correct? Are
x and y normal goods?
(b) Jason has different preferences to Jasina: his marginal rate
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Jasina has preferences for two goods x, y and her marginal rate
of substitution (MRS) between x and y is given by 3y/x. Her budget
constraint takes the form m ≥ pxx + pyy, where m is income and px,
py are the prices of x, y respectively. (Word limit per question:
400 words (200 words per part of question).
(a) Someone says that Jasina’s expenditure on y (i.e., pyy) is
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Question 1
Jasina has preferences for two goods x,
y and her marginal rate of substitution (MRS) between
x and y is given
by 3y/x. Her budget constraint takes
the form m ≥ pxx +
pyy,
where m is income
and px, py
are the prices
of x, y respectively.
(a) Someone says that Jasina’s expenditure on
y (i.e., pyy) is
always one third of her expenditure
on x (i.e.,
pxx). Is this correct? Are
x and y normal goods?
(b) Jason has different preferences to Jasina: his marginal rate
of substitution...

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of (x,y) with no space)
Now the price of x increases to $3 while price of y remains the
same Her new optimal consumption bundle is: ____________ (write in
the form of (x,y) with no space)
Her Equivalent Variation is: $ ____________

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y3/4 . Emily faces prices (px,py)
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Her optimal consumption bundle is: _______
(write in the form of (x,y) with no space)
Now the price of x increases to $3 while price of y remains the
same
Her new optimal consumption bundle
is:_______ (write in the form of (x,y) with no
space)
Her Equivalent Variation is:
$__________

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Now the price of x increases to $3 while price of y remains the
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b) Her new optimal consumption bundle
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Her new optimal consumption bundle is:
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