Pat’s preference is given by u(x1, x2) = min {x1, x2}.
Currently, prices are p =...
Pat’s preference is given by u(x1, x2) = min {x1, x2}.
Currently, prices are p = (p1, p2) and Pat’s income is I. Is he
better off if the price of good one is halved so that p = (p1/2
,p2), or if his income is doubled to 2I?
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?
u(x1, x2) = min {x1/2, x2/3}
if the price of good 1 is $7/unit, the price of good 2 is
$4/unit and income is 114..
What is this person's optimal consumption level for good 2?
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.
1. Assume a consumer has as preference relation represented by
u(x1; x2) = x1a +
x2 for a E (0,1); with x E C =
R2+: Answer the following:
a. Show the preference relation this consumer is convex and
strictly monotonic.
b. Compute the MRS between good 1 and good 2, and explain why it
coincides with the slope of an indifference curve.
c. Write down the consumer optimization problem, and construct
the first order conditions for this problem.
d....
Your preference is represented by the utility function:
u(x1, x2) =
x10.5x20.5
where x1 is potato chips (in bags) and
x2 is chocolate bars.
The price of a bag of potato chips is $5 and the price of a
chocolate bar is $10.
(a)You have no income, but you received a gift from your uncle.
The gift is 9 bags of potato chips and 1 chocolate bar. What is
your utility from consuming the gift? Assume that you cannot
exchange...
Let the utility function be given by
u(x1, x2) = √x1 + x2.
Let m be the income of the consumer, P1 and P2 the prices of good 1
and good 2, respectively.
To simplify, normalize the price of good 1, that is P1 = £1.
(a) Write down the budget constraint and illustrate the set of
feasible bundles using a figure.
(b) Suppose that m = £100 and that P2 = £10. Find the optimal
bundle for the consumer....
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.
If the consumer preference on (x1, x2) can be represented as the
following utility function: U = 0,75 log ?1 + 0,25 log ?1 s.t. ?1?1
+ ?2?2 = ?
a. Find the walrasian/marashallian demand function for both
goods
b. Find the Indirect Utility Function
c. Show using example that the indirect utility function is
homogenous of degree zero in p and I
Suppose that a consumer has a utility function U(x1,x2) = x1
^0.5 x2^0.5 . Initial prices are p1 =1and p2 =1,andincomeism=100.
Now, the price of good1 increases to 2. (a) On the graph, please
show initial choice (in black), new choice (in blue), compensating
variation (in green) and equivalent variation (in red). (b) What is
amount of the compensating variation? How to interpret it? (c) What
is amount of the equivalent variation? How to interpret it?