Question 1: There are two agents (A and B) in the economy. They demand for two goods:
1 and 2. Agent A's utility is UA (x₁, x₂) = ln x₁ + 2ln x2; agent B's utility is UB (x1, x₂) =
2 lnx₁ + Inx2. We also know agent A's endowment is (1,2), which means that she has
one unit of good 1 and two units of good 2. In addition, agent B's endowment is (2,1).
Suppose the prices for goods 1 and 2 are p₁ and p2, respectively.
1. Derive agent A's demands for goods 1 and 2: x4 and x.
2. Derive agent B's demands for goods 1 and 2: x and x2.
3. Derive agent A's excess demands for goods 1 and 2: z and z.
4. Derive agent B's excess demands for goods 1 and 2: z
and 22.
5. Derive aggregate excess demands for goods 1 and 2: Z₁ and Z₂.
6. Obtain the Walrasian equilibrium prices for goods 1 and 2: p₁ and p2.
7. Comment on your findings.
Answers
For points A and B in the economy:
x₁ = 2p₂/p₁ and x₂ = p₂/p₁.
x₁ = 2p₁ / p₂ and x₂ = p₁ / p₂.
2 - p₂ / p₁
1 - p₁ / p₂
2 - p₂ / p₁ + 1 - p₁ / p₂
The market clears for both items at the Walrasian equilibrium, and the aggregate excess demands are zero.
How to determine demand of goods?1. To derive agent A's demands for goods 1 and 2, maximize her utility subject to her budget constraint:
max ln x₁ + 2ln x₂
s.t. p₁x₁ + p₂x₂ ≤ p₁(1) + p₂(2)
Using Lagrange multiplier method:
1/x₁ = p₁/(2p₂)
1/x₂ = p₁/p₂
Solving for x₁ and x₂:
x₁ = 2p₂/p₁
x₂ = p₂/p₁
So, agent A's demands for goods 1 and 2 are x₁ = 2p₂/p₁ and x₂ = p₂/p₁.
2. To derive agent B's demands for goods 1 and 2, maximize her utility subject to her budget constraint:
max 2ln x₁ + ln x₂
s.t. p₁x₁ + p₂x₂ ≤ p₁(2) + p₂(1)
Using Lagrange multiplier method:
2/x₁ = p₁/p₂
1/x₂ = p₂/p₁
Solving for x₁ and x₂:
x₁ = 2p₁/p₂
x₂ = p₁/p₂
So, agent B's demands for goods 1 and 2 are x₁ = 2p₁ / p₂ and x₂ = p₁ / p₂.
3. Agent A's excess demands for goods 1 and 2 are:
z₁ = 1 - x₁ = 1 - 2p₂ / p₁
z₂ = 2 - x₂ = 2 - p₂ / p₁
4. Agent B's excess demands for goods 1 and 2 are:
z₁ = 2 - x₁ = 2 - 2p₁ / p₂
z₂ = 1 - x₂ = 1 - p₁ / p₂
5. The aggregate excess demands for goods 1 and 2 are:
Z₁ = z₁ᵃ + z₁ᵇ = 1 - 2p₂ / p₁ + 2 - 2p₁ / p₂
Z₂ = z₂ᵃ + z₂ᵇ = 2 - p₂ / p₁ + 1 - p₁ / p₂
6. At Walrasian equilibrium, Z₁ and Z₂ are both equal to zero. So, solve the system of equations:
1 - 2p₂ / p₁ + 2 - 2p₁ / p₂ = 0
2 - p₂ / p₁ + 1 - p₁ / p₂ = 0
Solving for p₁ and p₂:
p₁ = 2
p₂ = 1
So, the Walrasian equilibrium prices for goods 1 and 2 are p₁ = 2 and p₂ = 1.
7. At the Walrasian equilibrium, the market clears for both goods and the aggregate excess demands are zero. This means that the prices are set such that both agents are willing to buy exactly what is being sold in the market.
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Related Questions
Let Q be an orthogonal matrix with an eigenvalue λ1=1. Let x be an eighenvector beloinging to λ1. Show that x is also an eigenvector of QT
Answers
If Q is an orthogonal matrix with an eigenvalue λ1 = 1, then x, the eigenvector corresponding to λ1, is also an eigenvector of QT with an eigenvalue λ2 = λ1 * (QT * x).
To show that x is also an eigenvector of QT, we need to demonstrate that QT * x is a scalar multiple of x.
Given that Q is an orthogonal matrix, we know that QT * Q = I, where I is the identity matrix. This implies that Q * QT = I as well.
Let's denote x as the eigenvector corresponding to the eigenvalue λ1 This means that Q * x = λ1 * x.
Now, let's consider QT * x. We can multiply both sides of the equation Q * x = λ1 * x by QT:
QT * (Q * x) = QT * (λ1 * x)
Applying the associative property of matrix multiplication, we have:
(QT * Q) * x = λ1 * (QT * x)
Using the fact that Q * QT = I, we can simplify further:
I * x = λ1 * (QT * x)
Since I * x equals x, we have:
x = λ1 * (QT * x)
Now, notice that λ1 * (QT * x) is a scalar multiple of x, where the scalar is λ1. Therefore, we can rewrite the equation as:
x = λ2 * x
where λ2 = λ1 * (QT * x).
This shows that x is indeed an eigenvector of QT, with the eigenvalue λ2 = λ1 * (QT * x).
In conclusion, if Q is an orthogonal matrix with an eigenvalue λ1 = 1, then x, the eigenvector corresponding to λ1, is also an eigenvector of QT with an eigenvalue λ2 = λ1 * (QT * x).
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The park and school are 3 centimeters apart on the map and 15 meters apart in real life. What is the scale factor on the map?
Answers
Answer:
The scale factor of the map is 1: 500
Step-by-step explanation:
The scale factor of a map can be found out by dividing a particular distance given on the map by that given in real life, provided their units of measurement are the same.
The distance of the park from the school is 3cms on the map and 15 meters in real life.
Converting 15 meters to a common unit of centimetres:
1 meter = 100 cms
15 meters = 1500 cms
=> Scale factor = distance on map/ distance in real life
= 3/ 1500
= 1/ 500
Representing in the form of ratio:
Scale factor =1: 500
The chart shows the number of rabbits a farmer observed on his farm over a period of nine weeks.
Find the third quartile of the data set.
Answers
The third quartile of the data set is 20, and option C is correct.
What are datasets?A data set is a structured group of data. As we are all aware, data is a grouping of information that has been gathered by observations, measurements, research, or analysis. Facts, figures, names, and even simple descriptions of objects could be included in it. Data can be arranged for our study in the form of graphs, charts, or tables.
Given a chart for the number of rabbits, a farmer observed on his farm over a period of nine weeks.
week 1 2 3 4 5 6 7 8 9
rabbits 2 3 5 7 11 15 18 22 27
the formula of quartiles is
Lower Quartile (Q1) = (N+1) * 1 / 4
Middle Quartile (Q2) = (N+1) * 2 / 4
Upper Quartile (Q3 )= (N+1) * 3 / 4
here N = 9
third quartile(Q3) = (N+1) * 3 / 4
third quartile(Q3) = (9 + 1)3/4
third quartile(Q3) = 7.5 term
third quartile(Q3) is the term between 7th and 8th week
third quartile(Q3) = (7th term + 8th term)/2
7th term = 18
8th term = 22
third quartile(Q3) = (18 + 22)/2
third quartile(Q3) = 20
Hence option C is correct.
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Which of the following has four, eight and one nine??
A.88889
B.4819
C.888819
D.489
Answers
Answer:
D. 489
Step-by-step explanation:
489 has the number,
four - 4
eight - 8
and ONE nine - 9
Hope this helps :)
What is the value of the expression?
3 • [(30 - 8) ÷ 2 + 2]
Answers
Answer: 39
Step-by-step explanation:
30-8=22
22/2=11
11+2=13
13 times 3 =39
nichole bought a gift for her friend. she placed the gift in a box with a length of 10 inches, width of 5 inches, and height of 2 inches. what is the surface area of the box?
Answers
Answer:
\(10 \ \text{by} \ 5 = 50\)
\(10 \ \text{by} \ 5 = 50\)
\(10 \ \text{by} \ 2 = 20\)
\(10 \ \text{by} \ 2 = 20\)
\(2 \ \text{by} \ 5 = 10\)
\(2 \ \text{by} \ 5 = 10\)
\(\bold{100+40+20=160}\)
someone plzz help me plzzzzzzz
Answers
Answer:
5
Step-by-step explanation:
|-2 + 5 | - |3 - 12| - 13=
Answers
Answer:
-19
3 - 9 - 13 = -19
Step-by-step explanation:
32a + 28 = factor completely
Answers
Answer:
Step-by-step explanation:
common factor is 4
4(8a+7)
One-fourth of the students in a twelve-student roster are completing outside for recess. How many students are inside for recess?
Answers
9 stduents
1/4 of 12 is 3
12-3=9
given the following venn diagram, where a and b are each represented by an oval: exam image which regions make up ( aexam imagebc )c?
Answers
The correct answer is U - II = I + III + IV.
In order to solve problems based on these sets, we can use a Venn diagram to depict the logical relationship between sets and their components. Although other closed figures like squares may be used, a Venn diagram commonly uses intersecting and non-intersecting circles to indicate the relationship between sets.
c represent the compliment of the particular state.
U is the union set
∩ represent intersection between the neighbouring sets
Therefore,
Bc = U - B = I + II
Bc∩A = Area common in Bc and A = II
(Bc∩A)c = Area in U but not in (Bc∩A) = U - II = I + III + IV
So, answer is d.
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what are the first 3 composite numbers that are multiples of 4 and greater than 10.¯\_(•_•)_/¯
Answers
Answer:
12,16,20
Step-by-step explanation:
First list the multiples of 4
4,8,12,16,20,24,28
We want the ones that are greater than 10
12,16,20
X- y = -7 slope intercept form
Answers
Answer:
\(y=x+7\)
Step-by-step explanation:
Let's simply rearrange bringing y to the RHS, -7 to the LHS and reading right to left:
\(x+7=y \rightarrow y=x+7\)
Consider the following quadratic function. Y=x^2-2x+3Graph this quadratic function by identifying two points on the parabola, other than the vertex and zeros.Your answer must be between -10 and 10.
Answers
We can find two points different than the vertex and zero by giving some values to the variable x. For instance, if we choose the value x=1, we have
\(y=1^2-2(1)+3\)which gives
\(\begin{gathered} y=1-2+3 \\ y=2 \end{gathered}\)so we have obtained the point
\(A=(1,2)\)Similarly, we can substitute the value x=2 and get
\(\begin{gathered} y=2^2-2(2)+3 \\ \text{then} \\ y=4-4+3 \\ y=3 \end{gathered}\)then, we have obtained the point
\(B=(2,3)\)Then, the graph is
A dairy farmer wants to mix 35% protein supplement in a standard 10% protein ration to make 1300 pounds of high grades 25% protein ration how many pounds of each should he use
Answers
Answer:
Therefore, you need 2600 pounds of 35% supplement and 1300 - 2600 = -1300 pounds of 10% ration.
Step-by-step explanation:
The unknown variable is x, which is the amount of 35% supplement needed. The other expressions are derived from the given information and the fact that the total amount of solution is 1300 pounds.
The equation from the fourth column is:
0.35x + 0.10(1300 - x) = 0.25(1300)
Solving for x, we get:
x = (0.25(1300) - 0.10(1300)) / (0.35 - 0.10) x = 650 / 0.25 x = 2600
HELPPP!!!
Solve the equation
6(2y−1)−2(2y)=6
y=?
Answers
Answer:
The answer is 4y
Step-by-step explanation:
6×2y-6×1-2×2y=6y
Can we say there is a 95% probability that the interval [50.53,55.53][50.53,55.53] contains the true percentage of the population that votes for Imm Thai as the best Berkeley Thai restaurant
Answers
Answer:
The answer is"statement is true".
Step-by-step explanation:
Yeah, they may claim that it is possible, that 95% of the population would vote for Imm Thai as the best Barkeley Thai restaurant as well as the probability that such an interval will include the proportion of the trust interval of Imm Thai outside is 5% which would be \alpha 5%
Find the probability that a randomly selected point within the square falls in the red shaded square
Answers
The probability that a randomly selected point within the square falls in the red shaded square is 1/16
What is probability?A probability is a number that reflects the chance or likelihood that a particular event will occur. The certainty of an event to occur is 1 and it is 100% in percentage.
Probability = sample space /total outcome
sample space is the area of the red shaded square and the total outcome is the big square.
Area of red shaded square = 1 × 1 = 1unit²
area of the big square = 4 × 4 = 16 units²
Therefore the probability that a point selected falls on the red shaded square
= 1/16
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What is the shape of the cross section of the figure that is perpendicular to the triangular bases and passes through a
vertex of the triangular bases?
A
a parallelogram that is not a rectangle
O a rectangle
O a triangle that must have the same dimensions as the bases
O a triangle that may not have the same dimensions as the bases
Answers
Answer:
a triangle that may not have the same dimensions as the bases
Step-by-step explanation:
The cross section of the figure that is perpendicular to the triangular bases and passes through a vertex of the triangular bases would be a triangle that may not have the same dimensions as the bases.
Find the perimeter of this shape
Answers
The perimeter of the given shape as represented in the task content is; 29 cm.
What is the perimeter of the given shape?It follows from the task content that the perimeter of the given shape on the centimeter grid as required is to be determined.
Since each grid line has 1cm as it's length;
The perimeter of the shape is the sum of all side lengths of the shape;
Perimeter, P = 6+2+3+2+2+1+3+2+2+2+2+1
P = 29 cm
Hence, the perimeter of the shape is; 29 cm.
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In the equation, what is the value of s?
3(s + 1) - 8 = 6s(2 - 4)
A) -3
B) - 1/3
C) 3
D) 1/3
Answers
Answer:
B
Step-by-step explanation:
Help plsssjsnsnsnsnndndndndnfnfnfnnffnnccnncncncnfnf
Answers
9514 1404 393
Answer:
A) 3x +10y = 36
Step-by-step explanation:
The graph tells us the x-intercept is 12. The x-intercept is the value of x when y = 0. For some equation coefficients ax+by=36, the x-intercept is ...
x-intercept = 36/a
Then the coefficient 'a' is ...
a = 36/(x-intercept) = 36/12 = 3
Only one answer choice has an x-coefficient of 3 -- the correct one.
3x +10y = 36
the expression negative five eighths times k minus 8 plus the expression 2 plus one third times k
7 over 24 times k plus negative 6
negative 4 over 11 times k plus negative 10
negative 7 over 24 times k plus negative 6
negative 23 over 24 times k plus negative 10
Answers
After solving the expression, the value is negative 7 over 24 times k plus negative 6. Therefore, option C is correct.
What is an expression?Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both. Adding, subtraction, multiplying, and division are all reflection coefficient operations.
A mathematical operation such as reduction, addition, multiplication, or division is used to integrate terms into an expression.
As per the given statement for the expression,
-(5/8)k - 8 + 2 + (1/3)k
Take LCM as 24 and solve the equation,
(-7k - 144) / 24
= (-7/24)k - 6
Therefore, this concludes that option C is correct.
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The hole for a support needs to be6 feet deep. It is currently 2 feet 9 inches deep. How much deeper must the hole be. Use the conversion factor 12 inches/ 1 foot
Answers
The hοle needs tο be 39 inches deeper.
What is the cοnversiοn factοr?A cοnversiοn factοr is a number used tο change οne set οf units tο anοther, by multiplying οr dividing. When a cοnversiοn is necessary, the apprοpriate cοnversiοn factοr tο an equal value must be used. Fοr example, tο cοnvert inches tο feet, the apprοpriate cοnversiοn value is 12 inches equals 1 fοοt.
The current depth οf the hοle is 2 feet 9 inches, which is the same as 2 + 9/12 = 2.75 feet (since there are 12 inches in 1 fοοt).
Tο find οut hοw much deeper the hοle needs tο be, we need tο subtract the current depth frοm the required depth:
6 feet - 2.75 feet = 3.25 feet
Hοwever, we are asked tο express the answer in inches, sο we need tο cοnvert the 3.25 feet tο inches using the given cοnversiοn factοr:
3.25 feet x 12 inches/1 fοοt = 39 inches
Therefοre, the hοle needs tο be 39 inches deeper.
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The interior angles formed by the sides of a quadrilateral have measures that sum to 360°.
What is the value of x?
Enter your answer in the box.
x =
Answers
Answer:
The answer is in the images
Step-by-step explanation:
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the null hypothesis for the sign test always states that the mean difference between the matched or paired samples is zero T/F
Answers
True. The null hypothesis for the sign test always states that the mean difference between the matched or paired samples is zero.
Therefore, the null hypothesis always states that the mean difference between the matched or paired samples is zero.Sign Test for Comparing Two Matched SamplesThe sign test is used to compare two related or matched samples to determine if they are significantly different from one another. It is based on the idea that the difference between two related samples should be zero. The null hypothesis of the sign test states that the mean difference between the two matched or paired samples is zero, meaning that there is no difference between the two samples.
The alternative hypothesis is that the mean difference between the two samples is not zero, indicating that there is a significant difference between the two samples. The sign test is used to determine if the two samples are significantly different from one another.
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PLEASE HELP (IMAGE ATTACHED)
The answer I get is -3x^9 +2x^8 -8 over x^4
What does it simplify to? Use positive exponents only
Answers
Answer:
Step-by-step explanation:
To simplify the expression, we need to divide -3x^9 + 2x^8 - 8 by x^4.
The procedure is as follows:
Divide -3x^9 by x^4: -3x^9 / x^4 = -3x^5
Divide 2x^8 by x^4: 2x^8 / x^4 = 2x^4
Divide -8 by x^4: -8 / x^4 = -8x^-4
Combine the results from steps 1-3: -3x^5 + 2x^4 - 8x^-4
Note that the exponent of x in each term is either positive or zero. We can't simplify the expression further since we can't simplify the exponents any more.
2.Simplify the following mathematical expression?
a.555+(22+343-(16÷8+3-15)
Answers
Answer:
\(930\)
Step-by-step explanation:
STEP 1: Remove parentheses.
STEP 2: Simplify each term.
STEP 3: Simplify by adding numbers.
Select all rational numbers
help ASAP please
15 points
Answers
The resulting rational number is √100
Rational numbers:
A rational number is a number that can be represented a/b where a and b are integers and b is not equal to 0.
Given,
Here we have the following list of numbers
√75, -√25, 2√7, √100, √0.36, √0.0144, √3/7 , -√36/49
Now, we need to identify whether these are the rational numbers or not.
AS per the definition of rational number,
When we take the root for the value √75, we get 8.660 that is a non-whole square root, 8.660 is not a rational number.
The value -√25 takes the negative value so it is not a rational number.
The number 2√7, this one also produce on-whole square root, so this one is not a rational number.
The value of √100 is 10, and it is a rational number.
The value of √0.36 is 0.6 which is less than 0, so it is not a rational number.
The value of √0.0144 is 0.012 which is less than 0, so it is not a rational number.
The value of √3/7 this one also produce on-whole square root, so this one is not a rational number.
The value -√36/49 takes the negative value so it is not a rational number.
Therefore, the rational number is √100.
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Find the sum. 1. -7+(-5)
O-12
O-2
0 2
0 12
Answers
Answer:
-12
Step-by-step explanation:
-7+(-5)=
-7-5=
-12