Consider the problem of utility over territory. Let’s start simply
with a one-dimensional representation. Consider two actors, 1
and 2, with utility functions defined over a single-dimensional
issue space X = [0, 1], but where the actors can own sections or
“provinces” of the interval. The boundaries between sections are
defined by a vector B = (b1, b2, b3, . . . , bn, 1).
Thus, there are n+ 1 provinces. Define a “size” vector containing the lengths of
each province, S = (b1, b2 − b1, b3 − b2, . . . , 1 − bn). Define for
each actor an “ownership” vector Oi with 1s in the place of the
provinces that it owns and 0s elsewhere.
1. Assume that each actor’s utility function is a simple sum of
how much of the space they own so ui=∑n+1,j=1, oj,sj
(a) Can the players both be made better off by exchanging
existing provinces?
(b) Can the players both be made better off by altering the
boundaries of the existing provinces while preserving the
ownership structure?
(c) Can the players both be made better off by reducing the
number of provinces – for instance, by consolidating
contiguous provinces that are owned by the same actor?
2. Now assume that the utility function is a function of the sum
of the squares of the provinces owned, indicating that there are
increasing returns to the size of a province ui=∑n+1,j=1, (oj,sj)^2
(a) Can the players both be made better off by exchanging
existing provinces (without doing anything else)?
(b) Can the players both be made better off by reducing the
number of provinces – for instance, by consolidating
contiguous provinces that are owned by the same actor?
(c) If the actors are free to adjust both the number of
provinces and the ownership structure, what set of
boundaries is Pareto optimal with this utility function?
2.2 (see formula in the attachments) Consider two states, state 1 and state 2, which can unilaterally
set their tariff rates on imported goods, ti ≥ 0. Each state has an
ideal level for its own tariff, and prefers that the other
side’s tariff be 0, Assume that each side’s utility declines
with the distance between the tariff levels and their ideal point,
as follows
1. Draw the t1, t2 quadrant and draw in the ideal points for each
player.
2. Draw in sample indifference curves for the two states around
their ideal points. What shape are they?
3. Draw in the contract curve between the two ideal points. What
shape is it and why? What equation describes it?
4. The contract curve divides the t1, t2 quadrant into two regions.
How do they differ in terms of how the players could realize
joint gains in each region?
2.3 Consider the utility function u(x) = xρ, where ρ > 0 and x ∈ [0,
1]. Under what conditions would a player with such preferences
be risk acceptant, risk neutral, and risk averse?
A figure lies entirely in Quadrant I. The figure is reflected in the x-axis. In which quadrant is the image?
Answer: quadrant 4 i think...
Step-by-step explanation:
Answer:
Quadrant IV (4).
Step-by-step explanation:
It will be in the quadrant below which is Quadrant IV.
The distance between Mars and Venus is 3.7 X 10^14 miles. A rocket ship only has enough fuel to travel half that distance. How far can the rocket ship travel?
PLEASE HELP ME
FIRST TO ANSWER WILL GET BRAINLIEST
Answer:
1.85 X 10^14
Step-by-step explanation:
(x2 +2xy +y2)+(x2- 2xy + y2)=
Answer:
2x^2 + 2y^2
Step-by-step explanation:
Combine like terms.
(x^2 + 2xy + y^2) + (x^2 - 2xy + y^2) =
= x^2 + 2xy + y^2 + x^2 - 2xy + y^2
= x^2 + x^2 + 2xy - 2xy + y^2 + y^2
= 2x^2 + 2y^2
Answer:
2x^2 + 2y^2
Step-by-step explanation:
Given a triangle JLM with vertices J(-4,3), L(-2,7), and M(2,7). What would the coordinates be if it was reflected across the line y=1?
Answer: M'(2, - 5), L'(-2, -5), j'(-4, - 1)
Step-by-step explanation:
When we do a reflection over a given line, the distance between all the points (measured perpendicularly to the line) does not change.
The line is y = 1.
Notice that a reflection over a line y = a (for any real value a) only changes the value of the variable y.
Let's reflect the points:
J(-4, 3)
The distance between 3 and 1 is:
D = 3 - 1 = 2.
Then the new value of y must also be at a distance 2 of the line y = 1
1 - 2 = 1
The new point is:
j'(-4, - 1)
L(-2, 7)
The distance between 7 and 1 is:
7 - 1 = 6.
The new value of y will be:
1 - 6 = -5
The new point is:
L'(-2, -5)
M(2,7)
Same as above, the new point will be:
M'(2, - 5)
An ice cream shop is testing some new flavors of ice cream they invent 25 new flavors for customers to try and throw out the 13 least popular flavors the shop makes 80 cartons of each of the remaining flavor it takes two cartons to get on liter of ice cream. How much total ice cream is in the cartons
Answer:
480
Step-by-step explanation:
25-13=12
12 x 80=960
960 divided by 2=480
NO ONE IS HELPING ME PLEASE IM FINNA CRY
The first term in an arithmetic sequence is 5. The third term in the sequence is -1. The tenth term in the sequence is -22.
Which of the following functions can be used to find the nth term of the arithmetic sequence?
A.
f(n) = -n
B.
f(n) = n + 4
C.
f(n) = -3n + 8
D.
f(n) = 0.5(n+5) + 2
MATH HELP ME ASAP PLEASE
Answer:
53lbs.
Step-by-step explanation:
If Kevin bought 3 20lbs. Bags of gravel he would have 60 lbs. of gravel. In the end he has 7 lbs. of gravel left he used 53 pounds.
Equations:
7+x=60 or 60-7=53 lbs.
Answer:
3 pounds of gravel
Step-by-step explanation:
If you look at the chart, each bag of gravel is 20 lbs. If he bought 4 then that is 20 x 4. That equals 80. If he only used 77 pounds of it, then you get 80-77. That equals 3
BRAINLIST!!!!! Do you know the sample response?!
Answer:
The graph and equation both match and are a function. there is one specific output fro each input
Step-by-step explanation:
Use the graph shown to complete the following sentence.
when x = 1, then y = ___
Answer:
-2
Step-by-step explanation:
On the graph when the X value is equal to 1, the Y value is equal to -2.
-3,-8,-13,-18 write an equation for the nth term then solve
Answer:
nth term = -3-5(n-1)
Step-by-step explanation:
Which graph represents the function f(x) = –|x + 3|?
Answer:
Step-by-step explanation:
f(x) = –|x + 3| is a case of the absolute value function
f(x) = -|x - {a}| + c, where (a, c) is the vertex. Comparing them, we see that
the value of a must be -3 and that of c must be 0.
Thus, the vertex of the graph is at (-3, 0), and the graph opens up; it looks like a "v" shape.
Next time, kindly share the given graphs.
Answer:
third graph
Step-by-step explanation:
Mike, Larry, and Daryl are brothers that own a shoe store. For every pair of shoes sold, they earn $18.00 in profits. At the end of the day, they split the profits equally among them. Which of the following equations can be used to find P, the profit each brother earns if n pairs of shoes are sold in one day?
Answer:
The answer is $18n/3= p
What is −3/8÷7 1/2? −3 2/7 −1 4/9 −9 1/4 −7 3/2
Answer:
-7097/315
Step-by-step explanation:
Answer:
7097/315
Step-by-step explanation:
i just need the points
What does this mean?
Answer:
Its the symbol "pi" which is 3.14
Answer:
it means pi.
Step-by-step explanation:
pi = 3.14..........
pi goes on forever, it never ends.
what is Evaluate 4/5-3/7
Answer:
[tex] \frac{13}{35} [/tex]
Step-by-step explanation:
To add or subtract two or more fractions from each other, the denominators have to be the same. To make the denominators the same, we should find the least common multiple of 5 and 7. The least common multiple of 5 and 7 is 35. 5 should be multiplied with 7 to get 35 and 7 should be multiplied with 5 to get 35 (with both numerators).
[tex] \frac{4}{5 } - \frac{3}{7} [/tex]
[tex] \frac{4 \times 7}{5 \times 7} - \frac{3 \times 5}{7 \times 5} [/tex]
[tex] \frac{28}{35} - \frac{15}{35} [/tex]
[tex] \frac{13 }{35} [/tex]
When subtracting, only subtract the numerators (the denominators are kept as is).
Answer:
the answer is 13/35
Step-by-step explanation:
Which list shows the absolute values in order form least to greatest?
What is the definition of no solution?
Answer:
No solution would mean that there is no answer to the equation.
Step-by-step explanation:
It is impossible for the equation to be true no matter what value we assign to the variable. Infinite solutions would mean that any value for the variable would make the equation true.
There is no answer to that problem. There is either a critical error in the problem, or it's just impossible to calculate. For example, x/0 is literally nothing. You can't solve it.
What is the length of the third side of the window frame below?
A. 10 inches
B. 12 units
C. 16 units
D. 20 units
Answer:
20 units
Step-by-step explanation:
a^(2)+b^(2)=c^(2)
48^(2)+b^(2)=52^(2)
2304+b^(2)=2704
2304-2304+b^(2)=2704-2304
b^(2)=400
\sqrt(b^(2))=\sqrt(400)
b=20
therefore,20 is the length of the unknown side
-plz mark brainliest-i try hard to help u guys
if you have a question on som else let me know
Question 10 of 10
Solve 3 ax + 4ax = 5ax + 4 for x. Assume at 0.
A. X = 2
a
B. x= 2a
C. x =
За
D. X = 3a
[tex]x = \frac{2}{a} [/tex]
Step-by-step explanation:
3 ax + 4ax = 5ax + 4, combine like terms
7ax = 5ax + 4, minus 5ax from both sides
2ax = 4, divide 2a on both sides
you'll be left with x = 2/a
Question 3
If a = -3, b = 2 and c = -4 find the value of the expression.
6a – 3b + 2c
Answer: -32
Step-by-step explanation:
You just have to plug in where you see the variables
6(-3) - 3(2) + 2(-4)
-18 - 6 - 8
Answer:
-32
Step-by-step explanation:
An employee at an organic food store is assembling gift baskets for a display. Using wicker baskets, the employee assembled 2 small baskets and 4 large baskets, using a total of 60 pieces of fruit. Using wire baskets, the employee assembled 2 small baskets and 10 large baskets, using a total of 132 pieces of fruit. Assuming that each small basket includes the same amount of fruit, as does every large basket, how many pieces are in each?
The small baskets each include______pieces and the large ones each include_____pieces.
Answer:12 and 15
Step-by-step explanation:
(b) What is the slope of y = -2x and what does this mean?
Answer:
The slope is up 2, left 1. The slope is negative, meaning the graphgoes from left to right.
Step-by-step explanation:
In 9 minutes heather can type 54 words what is her rate in words per minute
Answer:
6wpm
Step-by-step explanation:
a correction of "six less than twice the value of x" is
Answer:
2x-6
I don't know what you mean by correction, but that's in expression form.
Answer:
2x-6
Hope this helps!!
Help please this is due at 2:00 :(
Answer: your independent variable will be the group that receives the placebo. the dependent variable would be the group that received serum B, and your experimental group are the agents from both groups. I say that because both groups received the experimental serum, whereas the first group got a placebo. not sure if your teacher only wants one answer for each questions, but this is what I believe to be correct.
Step-by-step explanation:
A line contains the points (-26, -37) and (-32, -61). What is the slope of the line in simplified form? -3 −14 14 3
If Yafet raises $18 and Darnell raises $24, what fraction of Darnell’s goal did Yafet raise?
Answer:
4/3 or 1 1/3
Step-by-step explanation:
a-b-c=9, solve for a
Answer:
d
Step-by-step explanation:
Answer: a = 9 +b + c
Steps: a - b - c = 9
Subtract -b and -c from both sides: a - b - c - (-b -c) = 9 - (-b -c)
Simplify: a = 9 +b + c
Plz mark brainliest:)
Find the value of x using segment addition.