Question

Andrew’s utility function is *U*(*x*_{1},
*x*_{2}) = 4*x*^{2}_{1} +
*x*_{2}. Andrew’s income is $32, the price of good 1
is $16 per unit, and the price of good 2 is $1 per unit. What
happens if Andrew’s income increases to $80 and prices do not
change? (Hint: Does he have convex preferences?) *show work***

1. He will consume 48 more units of good 2 and the same number of units of good 1 as before.

2. He will increase his consumption of both goods.

3. He will reduce his consumption of good 2.

4. He will consume the same number of units of good 2 and 3 more units of good 1 as before.

5. None of the above.

Answer #1

Qin has the utility function U(x1, x2) = x1 + x1x2, where x1 is
her consumption of good 1 and x2 is her consumption of good 2. The
price of good 1 is p1, the price of good 2 is p2, and her income is
M.
Setting the marginal rate of substitution equal to the price
ratio yields this equation: p1/p2 = (1+x2)/(A+x1) where A is a
number. What is A?
Suppose p1 = 11, p2 = 3 and M...

Imran consumes two goods, X1 and X2. his
utility function takes the form: u(X1, X2)=
4(X1)^3+3(X2)^5. The price of X1
is Rs. 2 and the price of X2 is Rs. 4. Imran has
allocated Rs. 1000 for the consumption of these two goods.
(a) Fine the optimal bundle of these two goods that Imran would
consume if he wants to maximize his utility. Note: write bundles in
integers instead of decimals.
(b) What is Imran's expenditure on X1? On
X2?...

Consider the following utility function: U(x1,x2)
X11/3 X2
Suppose a consumer with the above utility function faces prices
p1 = 2 and
p2 = 3 and he has an income m = 12. What’s his optimal
bundle to consume?

Consider a consumer who consumes two goods and has utility
function
u(x1,x2)=x2 +√x1.
The price of good 2 is 1, the price of good 1 is p, and income is
m.
(1) Show that a) both goods are normal, b) good 1 is an ordinary
good, c) good 2 is a gross substitute for good 1.

Consider a two good economy. A consumer has a utility function
u(x1, x2) = exp (x1x2). Let p = p1 and x = x1.
(1) Compute the consumer's individual demand function of good 1
d(p).
(2) Compute the price elasticity of d(p).
Compute the income elasticity of d(p).
Is good 1 an inferior good, a normal good or neither?
Explain.
(3) Suppose that we do not know the consumer's utility function
but we know that the income elasticity of his...

1. Al Einstein has a utility function that we can describe by
u(x1, x2) = x21 +
2x1x2 + x22
. Al’s wife, El Einstein, has a utility function v(x1,
x2) = x2 + x1.
(a) Calculate Al’s marginal rate of substitution between
x1 and x2.
(b) What is El’s marginal rate of substitution between
x1 and x2?
(c) Do Al’s and El’s utility functions u(x1,
x2) and v(x1, x2) represent the
same preferences?
(d) Is El’s utility function a...

Determine the optimal quantities of both x1 and
x2 for each utility function. The price of good 1
(p1) is $2. The price of good 2 (p2) is $1.
Income (m) is $10.
a.) U(x1,x2) =
min{2x1, 7x2}
b.) U(x1,x2) =
9x1+4x2
c.) U(x1,x2) =
2x11/2 x21/3
Please show all your work.

A consumer has the Cobb-Douglas utility function
u(x1,x2)=x3.51x42u(x_1, x_2) = x_1^{3.5}x_2^{4}
The price of good 1 is 1.5 and the price of good 2 is 3. The
consumer has an income of 11.
What amount of good 2 will the consumer choose
to consume?

3. Suppose that a consumer has a utility function
u(x1, x2) =
x1 + x2. Initially the
consumer faces prices (1, 2) and has income 10. If the prices
change to (4, 2), calculate the compensating and equivalent
variations. [Hint: find their initial optimal consumption
of the two goods, and then after the price increase. Then show this
graphically.]
please do step by step and show the graph

Alice’s preferences over two goods are described by the utility
function u(x1, x2) = 2x1+ 4x2. Her income is m= 100 and p1= 4, p2=
5. Assume now that the price of good 1 falls to p01= 2.
a) Find the substitution, income, and total effect for good
1.
b) Find the substitution, income, and total effect for good
2.
c) Verify that the Slutsky equation holds for both goods

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