Question
In: Economics
Suppose an individual’s utility function is u = x11/2x21/2. Let p1=4, p2=5, and income equal $200....
Suppose an individual’s utility function is u = x11/2x21/2. Let p1=4, p2=5, and income equal $200.
a. With a general equation and general prices, derive the equal marginal principle. Graphically illustrate equilibrium and disequilibrium conditions and how consumers can reallocate their consumption to maximize utility.
b. What is the optimal amount of x1 consumed?
c. What is the optimal amount of x2 consumed?
d. What is the marginal rate of substitution at the optimal amounts of x1 and x2?
e. As functions of p1, p2, and m, derive x1’s demand curve?
f. As functions of p1, p2, and m, derive x2’s demand curve?
Solutions
Rahul Sunny answered 2 years agoRelated Solutions
Suppose that the utility function is equal to U(XY)= 2YX2 . What is the slope of...
Suppose that the utility function is equal to U(XY)=
2YX2 . What is the slope of the
indifference curve when Y = 5 and X = 2? Assume
that good X is on the horizontal axis and good Y
is on the vertical axis.
Suppose that the utility function is equal to U(XY)= 2YX2 . What is the slope of...
Suppose that the utility function is equal to U(XY)=
2YX2 . What is the slope of the
indifference curve when Y = 2 and X = 7? Assume
that good X is on the horizontal axis and good Y
is on the vertical axis.
1.4/7
2.7
3.3
4.1
Suppose that the utility function is equal to U(XY)= 3YX2 . What is the slope of...
Suppose that the utility function is equal to U(XY)= 3YX2 . What
is the slope of the indifference curve when Y = 3 and X = 3? Assume
that good X is on the horizontal axis and good Y is on the vertical
axis.
1. Suppose that the utility function is equal to U(XY)= 2YX2 . What is the slope...
1. Suppose that the utility function is equal to U(XY)=
2YX2 . What is the slope of the
indifference curve when Y = 2 and X = 7? Assume
that good X is on the horizontal axis and good Y
is on the vertical axis.
A. 7
B.3
C. 1
D. 4/7
2.Kyle's utility function is U = 2X +
3Y, where X is units of good X, and
Y is units of good Y. What is the marginal
utility...
maximise utility u=q1q2 when p1=1 p2=4 and ones budget = 120 estimate effect of an -1...
maximise utility u=q1q2 when p1=1 p2=4 and ones budget = 120
estimate effect of an -1 increase unit increase in the budget
A individual has a utility function u(c) = √ c, where c is the individual’s consumption....
A individual has a utility function u(c) = √ c, where c is the
individual’s consumption. (The individual consumes his entire
wealth.) The individual’s wealth is $40,000 per year. However,
there is a 2% chance that he will be involved in a catastrophic
accident that will cost him $30,000.
PLEASE SHOW WORK
a. What is the individual’s utility from consumption if there is
no accident? What is his utility if there is an accident? What is
his expected utility?
b....
Suppose an individual has the following utility function: U(x, y) = −4(x − 5.5)^2 − 2(y...
Suppose an individual has the following utility function: U(x,
y) = −4(x − 5.5)^2 − 2(y − 3.5)^2 Further assume that the price of
good x, px = $6, the price of good y, py = $8, and the individual
has an income m = $65
a) Draw an indifference curve (one IC is enough) that represents
this person’s preferences. Please label the graph properly
including values for x and y.
b) Intuitively, and without formally solving, can you guess...
Suppose an individual has the following utility function: U(x, y) = −4(x − 5.5)^2 − 2(y...
Suppose an individual has the following utility function: U(x,
y) = −4(x − 5.5)^2 − 2(y − 3.5)^2
Further assume that the price of good x, px = $6, the price of
good y, py = $8, and the individual has an income m = $65
a) Draw an indifference curve (one IC is enough) that represents
this person’s preferences. Please label the graph properly
including values for x and y.
b) Intuitively, and without formally solving, can you guess...
Suppose an individual has the following utility function: U(x, y) = −4(x − 5.5)^2 − 2(y...
Suppose an individual has the following utility function: U(x,
y) = −4(x − 5.5)^2 − 2(y − 3.5)^2
Further assume that the price of good x, px = $6, the price of
good y, py = $8, and the individual has an income m = $65
a) Draw an indifference curve (one IC is enough) that represents
this person’s preferences. Please label the graph properly
including values for x and y.
b) Intuitively, and without formally solving, can you guess...
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.
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