Question
In: Economics
Amy has utility function u (x1, x2) = min { 2*(x1)^2*x2, x1*(x2)^2 }. Derive Amy's demand...
Amy has utility function u (x1, x2) = min { 2*(x1)^2*x2, x1*(x2)^2 }. Derive Amy's demand function for x1 and x2. For what values (if any) of m, p1, and p2 are the goods gross complements or gross substitutes of each other?
Solutions
Rahul Sunny answered 1 year agoRelated Solutions
1. Amy's utility function is U(x1 , x2) = x1x2, where x1 and x2 are Amy's...
1. Amy's utility function is U(x1 , x2) =
x1x2, where x1 and x2
are Amy's consumption of banana and apple, respectively. The price
of apples is $1, the price of bananas is $2, and his income is
$40.
(a) Find out the Amy's optimal consumption bundle. (Note that Amy's
utility function is Cobb-Douglas.)
(b) If the price of apples now increases to $6 and the price of
bananas stays constant, what would Amy's income have to be in order...
Amy's utility function is U(x1 , x2) = x1x2, where x1 and x2 are Amy's consumption...
Amy's utility function is U(x1 , x2) =
x1x2, where x1 and x2
are Amy's consumption of banana and apple, respectively. The price
of apples is $1, the price of bananas is $2, and his income is
$40.
(a) Find out the Amy's optimal consumption bundle. (Note that Amy's
utility function is Cobb-Douglas.)
(b) If the price of apples now increases to $6 and the price of
bananas stays constant, what would Amy's income have to be in order
to...
Nigella has the following utility function over two goods (x1, x2): U(x1, x2) = min {0.5x1,...
Nigella has the following utility function over two goods (x1,
x2):
U(x1, x2) = min {0.5x1, 3x2}
a.What is the Nigella’s utility level if x1= 20 andx2= 3?
b.Suppose P1= 1 andP2= 3(where P1is the price x1andP2is theprice
of x2) and Nigella has an income of 18. What is Nigella’s budget
constraint? Illustrate it in a graph
c.Solve for the Nigella’s utility maximizing bundle of
x1andx2.
Lauren’s utility function is uL(x1,x2) = min{x1, x2} and Humphrey’s utility function is uH (x1, x2)...
Lauren’s utility function is uL(x1,x2) = min{x1, x2} and
Humphrey’s utility function is uH (x1, x2) = ?(x1) + ?(x2). Their
endowments are eL = (4,8) and eH = (2,0).
a) Suppose Humphrey and Lauren are to simply just consume their
given endowments. State the definition of Pareto efficiency. Is
this a Pareto efficient allocation? As part of answering this
question, can you find an alternative allocation of the goods that
Pareto dominates the allocation where Humphrey and Lauren consume...
Burt’s utility function is U(x1, x2)= min{x1,x2}. Suppose the price of good 1 is p1, the...
Burt’s utility function is U(x1, x2)=
min{x1,x2}. Suppose the price of good 1 is p1, the price
of good p2, the income is y.
a. Derive ordinary demand functions.
b. Draw indifference curves and budget line for
the case when the price of good 1 is 10, the price of good 2 is 20,
the income is 1200.
c. Find the optimal consumption bundle.
Sara’s utility function is u(x1, x2) = (x1 + 2)(x2 + 1). a. Write an equation...
Sara’s utility function is u(x1, x2) = (x1 + 2)(x2 + 1).
a. Write an equation for Sara’s indifference curve that goes
through the point (2,8).
b. Suppose that the price of each good is 1 and that Clara has
an income of 11. Draw her budget line. Can Sara achieve a utility
of 36 with this budget? Why or why not?
c. Evaluate the marginal rate of substitution MRS at (x1, x2) =
(1, 5). Provide an economic interpretation...
5) Derive the demand function for x1 and x2 for each of the following utility functions....
5) Derive the demand function for x1 and
x2 for each of the following utility functions.
a. U(x1,x2) =
5x1x2
b. U(x1,x2) = x1/31
x2/32
c. U(x1,x2) = x1 +
3x2
d. U(x1,x2) =
{x12x2}
Assume a consumer has the utility function U (x1 , x2 ) = ln x1 +...
Assume a consumer has the utility function U (x1 , x2 ) = ln x1
+ ln x2 and faces prices p1 = 1 and p2 = 3 . [He,She] has income m
= 200 and [his,her] spending on the two goods cannot exceed her
income.
Write down the non-linear programming problem. Use the Lagrange
method to solve for the utility maximizing choices of x1 , x2 , and
the marginal utility of income λ at the optimum.
(a) Calculate the marginal utility of x1 and x2 for the following utility function u (x1;...
(a) Calculate the marginal utility of x1 and x2 for the
following utility function u (x1; x2) = x 1 x 2
(b) What must be true of and for the consumer to have a positive
marginal utility for each good?
(c) Does the utility function above exhibit a diminishing
marginal rate of substitution? Assume that and satisfy the
conditions from Part b. (Hint: A utility function exhibits a
diminishing marginal rate of substitution if the derivative of the
marginal...
Bridgit’s utility function is U(x1, x2)= x1 + ln x2 x1 - stamps x2 - beer...
Bridgit’s utility function is U(x1, x2)= x1 + ln x2 x1 -
stamps
x2 - beer
Bridgit’s budget p1 x1 + p2 x2 = m
p1 – price of stamps
p2 – price of beer
m – Bridgit’s budget
a) What is Bridgit’s demand for beer and stamps?
b) Is it true that Bridgit would spend every dollar in
additional income on stamps?
c) What happens to demand when Bridgit’s income changes (i.e.
find the income elasticity)?
d) What happens...
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