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?

What is the midpoint between n(- 4, 4) and (- 2, 2)

1. (02.01 MC) Celine has a bottle that contains 20% milk and the rest water. The bottle has 1 liter of water. Part A: Write an equation using one variable that can be used to find the total number of liters of milk and water in the bottle. Define the variable used in the equation. (5 points) Part B: How many liters of milk are present in the bottle? Show your work. (5 points) (10 points)

What is the value of f-1(4)

Click to review the online content. Then answer the question(s) below, using complete sentences. Scroll down to view additional questions.
Online Content: Site 1

In a scatterplot what does the term outlier mean?

PLEASE HELP f(x)= x-2. Find the inverse of f(x)

8 out of every 20 spectators were girls. There were a total of 1560 spectators at the game. How many of the spectators were girls

Write −0.48 as a fraction in simplest form.

−0.48=
I would also like an explanation too please! please answer ASAP

Question 4
2 pts
If a = -3, b = 2 and c = -4 find the value of the expression.
a2 +b²

For the pair of points, find the slope of the line that passes through both points.
(1,1) and (7,5)

How are the key features of a linear function identified and interpreted from a description?
Help I’m dying with math lol

Question 2
Identity the numbers that make the statement below tree
58=-= a postave number
A
B
6.3
c
500
D
5.9
E
-7.3
F
8.2
PLEASE HELP TIMED TEST!!!!!

D=(x2+x1)+(y2-y1) this is the formula I need number 19 Please will mark brainliest and 50 points

Find f'(a)/ f(x)=[tex]\sqrt{2-2x}[/tex]

Which equation can be used to find T the number of tickets each class needs to sell so that the total amount raised is the same for both classes

Olivia is a stockbroker. She earns 4% commission when she sells stocks. Last week, she earned 7200 in commission. a. What was the total amount of her sales?

“without using technology describe the end behavior of f(x) equals negative 3X to the 4th+ 7X squared -12 X +13” PLEASE HELP!!!!

Please help if possible thank you♥️

HELO ASAP CONVERT ALL OF THE FOLLOWING TO STANDARD NOTATIONS

In City A, the temperature rises 7 degrees F from 8AM to 9AM. Then the temperature drops 6 degrees F from 9AM to 10AM. In City B, the temperature drops 2 degrees F from 8AM to 9AM. Then the temperature drop 4 degrees F from 9AM to 10AM. Write an expression that represents the change in temperature from 8AM to 10AM for each city. Simplify and interpret each sum.

7 -14m = 2m - 5 multi step variables on both sides

Determine whether AB and MN are parallel, perpendicular, or neither.
Graph each line to verify your answer: A(-1,4), B(2.-5), M(-3,2). N(3, 0)

If f(x) = 3x + 2, what is f(5)?​

Which of the following situations can be modeled by the expression -8 + 35?

While Shawn was sleeping, the temperature decreased by 8°F. If the temperature was 35°F when Shawn went to bed, what was the temperature when Shawn woke up?

When Shawn woke up, the temperature was -8°F. By noon, the temperature had increased by 35°F. What was the temperature at noon?

None of the above.

When Shawn woke up, the temperature was -8°F. By noon, the temperature had increased to 35°F. By how much did the temperature change?

What is the result of solving this equation for x?

y−b=m(x−a)

Find the sum of 3-7i and 8+4i
A. 22-8i
B. 11+3i
C. -22+8i
D. 11-3i

Which equation does not represent a function? Why? A) y = x2; There are two outputs for each input. B) y2 = 4x; There are two outputs for each input. C) y = x; The output value is the same as the input value. D) y = −x; The output value is the opposite of the input value.

Number 10 will be marked brainliest

which line has a constant of proportionality between y and x of 5

Last year, 140 people in a community had cell phones. This year, the number
of people in the community with cell phones has increased by 65%.
A. Wat is the percent of increase?
65%
B. What is the change in the number of people with cell phones?
C. How many people in the community have cell phones this year?

Taxi A charges $3.00 plus $0.30 for every
mile.
Taxi B charges $3.25 plus $0.20 for every mile.
How much money, in dollars, does Kelly save by using Taxi B instead of Taxi A?