Question

. A consumer faces the following
utility function: U=xM, with M representing dollars spent on all
goods other than good x (therefore P_{M} º 1).
Assume that P_{x} =$1 and I = $100.

a. Find the optimal consumption bundle and the level of utility at that bundle. Show the result from this part on a graph. Place x on the horizontal axis and M on the vertical axis.

b. Suppose the government
provides the consumer with $20 worth of X-stamps. Find the new
optimal consumption bundle. HINT: To find the solution you should
assume that the consumer received a gift of $20 *cash*.
(QUESTIONS TO PONDER: Why can make we make this assumption—after
all, the consumer received food stamps not cash? Can we always make
this assumption?). Show this result on the same graph as used in
part (a).

c. Suppose the government replaces its food stamp program with a per-unit subsidy program. The per-unit subsidy is selected so as to allow the consumer to achieve the same level of utility as under the food stamp program. Using the indirect utility function, find the per-unit subsidy that would be required to achieve this result. (NOTE: The per-unit subsidy equals $1 minus price of X under the per-unit subsidy. Notice that we are implicitly assuming that the supply of X is perfectly elastic and therefore the entire subsidy is passed on to consumers).

Find x, M, and the cost to the government of providing this subsidy. Show this outcome on the same graph as used in parts (a) and (b). On your graph, indicate the cost to the government of each program.

Answer #1

10. A consumer faces the following utility function: U=xM, with
M representing dollars spent on all goods other than good x
(therefore PM ? 1). Assume that Px =$1 and I = $100.
a. Find the optimal consumption bundle and the level of utility
at that bundle. Show the result from this part on a graph. Place x
on the horizontal axis and M on the vertical axis.
b. Suppose the government provides the consumer with $20 worth
of X-stamps....

Consider a consumer with a utility function U =
x2/3y1/3, where x and y are the quantities of
each of the two goods consumed. A consumer faces prices for x of $2
and y of $1, and is currently consuming 10 units of good X and 30
units of good Y with all available income. What can we say about
this consumption bundle?
Group of answer choices
a.The consumption bundle is not optimal; the consumer could
increase their utility by...

1. A consumer has the utility function U = min(2X, 5Y ). The
budget constraint isPXX+PYY =I.
(a) Given the consumer’s utility function, how does the consumer
view these two goods? In other words, are they perfect substitutes,
perfect complements, or are somewhat substitutable? (2 points)
(b) Solve for the consumer’s demand functions, X∗ and Y ∗. (5
points)
(c) Assume PX = 3, PY = 2, and I = 200. What is the consumer’s
optimal bundle?
(2 points)
2....

Let U (F, C) = F C represent the consumer's utility function,
where F represents food and C represents clothing. Suppose the
consumer has income (M) of $1,200 , the price of food (PF) is $10
per unit, and the price of clothing (PC) is $20 per unit. Based on
this information, her optimal (or utility maximizing) consumption
bundle is:

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

Julie has preferences for food, f, and clothing, c, described by
a Cobb-Douglas utility function u(f, c) = f · c. Her marginal
utilities are MUf = c and MUc = f. Suppose that food costs $1 a
unit and that clothing costs $2 a unit. Julie has $12 to spend on
food and clothing.
a. Sketch Julie’s indifference curves corresponding to utility
levels U¯ = 12, U¯ = 18, and U¯ = 24. Using the graph (no algebra
yet!),...

In a research paper an economist assumes that the typical
consumer has a utility U(X, Y) = X^0.25Y^0.75 and a budget of
$1,000.
a) Consider the utility function. What is the consumer’s
attitude towards mixing X and Y? What is the shape of the
consumer’s indifference curves? Do you expect this consumer to
choose a bundle in the interior of the budget line or a bundle at
one of the corners? Discuss.
b) Now, turn your attention to the budget...

3. Nora enjoys fish (F) and chips(C). Her utility function is
U(C, F) = 2CF. Her income is B per month. The price of fish is
PF and the price of chips is PC. Place fish
on the horizontal axis and chips on the vertical axis in the
diagrams involving indifference curves and budget lines.
(a) What is the equation for Nora’s budget line?
(b) The marginal utility of fish is MUF = 2C and the
Marginal utility of chips...

7. ????????? ?? ????h????
Samantha purchases housing (h) and other goods (?) with the utility
function ? = h?. Her income is 120. Housing is measured in units of
square feet. The price of a housing is 2 (per square foot) and the
price of other goods 1.
a. How much housing does she consume when she maximizes
utility?
b. The government has recently completed a study suggesting that
everyone should have at least 80 square feet of housing (i.e.,...

1. Suppose utility for a consumer over food(x) and clothing(y)
is represented by u(x,y) = 915xy. Find the optimal values of x and
y as a function of the prices px and py with an income level m. px
and py are the prices of good x and y respectively.
2. Consider a utility function that represents preferences:
u(x,y) = min{80x,40y} Find the optimal values of x and y as a
function of the prices px and py with an...

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