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2. Consider three interdependent commodities that satisfy 2P +4PR 77 2R +P +33 -48 a) b)...
Question v) to question viii) Thank you An economy has three agents, A. B and C,...
Question v) to question viii)
Thank you
An economy has three agents, A. B and C, and three goods 1, 2 and 3. The endowments of the three consumers are as follows e (3,0,0); e (i) Write down the total endowment vector of the economy. (0,5,0); (1,1,1) Given a price vector p (p,P2 Pa), the demand functions of the three agents for cach of the three goods are as follows (I am giving these to you rather than ask you...
2. Consider the following model of Supply and Demand. where P is the price of the...
2. Consider the following model of Supply and Demand. where P is the price of the good, Qd is quantity demanded and Q5 is quantity supplied. (i) What condition should b satisfy in order for the first equation to be a reasonable demand function? (ii) What condition should b and d satisfy in order for this system to have a unique equilibrium? (ii) Assuming a unique equilibrium exists express the system in matrix form and use matrix algebra to find...
Q3. Consider the vector space P, consisting of all polynomials of degree at most two together...
Q3. Consider the vector space P, consisting of all polynomials of degree at most two together with the zero polynomial. Let S = {p.(t), p2(t)} be a set of polynomials in P, where: pi(t) = -4 +5, po(t) = -3° - 34+5 (a) Determine whether the set S = {P1(t).pz(t)} is linearly independent in Py? Provide a clear justification for your solution. (8 pts) (b) Determine whether the set S = {p(t),p2(t)} spans the vector space P ? Provide a...
Question 4.1 (9 marks): Consider a basis B = {pl,p2.p3} of polynomials in P, , where...
Question 4.1 (9 marks): Consider a basis B = {pl,p2.p3} of polynomials in P, , where pl :=1-x: p2 := x-x: p3 := 1+x: a Use the definition of coordinate vector to find the polynomial p4 in P, the vector of coordinates of which in the basis B is c4=(2,2,-2). b. Find the transition matrix StoB from the standard basis in P, to the basis B. What are the coordinates of the three standard coordinate vectors of the basis Sin...
Pcoer IS approximately ES0 2. Consider the following model of Supply and Demand. where P is...
Pcoer IS approximately ES0 2. Consider the following model of Supply and Demand. where P is the price of the good, Q is quantity demanded and QS is quantity supplied. (i) what condition should δ satisfy in order for the second equation to be a reasonable supply function. (ii) What condition should B and 6 satisfy in order for this system to have a unique equilibrium. Ģi Assuming a unique equilibrium exists express the system in matrix form and use...
Consider the following closed economy: There are three sectors: S, S2, S3. Sector one consumes 90...
Consider the following closed economy: There are three sectors: S, S2, S3. Sector one consumes 90 percent of it's own product, sells 10 percent to sector two and nothing to sector three. Sector two consumes 40 percent of it's own product, sells 40 percent to sector one and 2 percent to sector three. Sector three consumes 20 percent of it's own product, sells 40 percent to sector 1 and 40 percent to sector 2. 1. Write a se t of...
Please show work Answer shown below Problem 2: Consider the three-spring structure given below. It is...
Please show work
Answer shown below
Problem 2: Consider the three-spring structure given below. It is fixed at the far right end (node 4) and is subject to nodal forces as given below. из 144 lu 142 Pi Kj Ki P2 The element (spring) stiffnesses are: Ki- K2- 200 k/in and Ks-250 k/in The forces applied at the nodes are: P 150 k, P--50 k, Ps 150 k E.g. the stiffness a) Write the stiffness equilibrium equations for nodes 1,...
Consider a three-level system where the Hamiltonian and observable A are given by the matrix Aˆ...
Consider a three-level system where the Hamiltonian and
observable A are given by the matrix Aˆ = µ 0 1 0 1 0 1 0 1 0
Hˆ = ¯hω 1 0 0 0 1 0 0 0 1 (a) What are the possible
values obtained in a measurement of A (b) Does a state exist in
which both the results of a measurement of energy E and observable
A can be...
(2) Consider the following game: P U M D LR 3,1 0,2 1,2 1,1 0,4 3,1...
(2) Consider the following game: P U M D LR 3,1 0,2 1,2 1,1 0,4 3,1 (a) Show that M is a dominated strategy when mixed strategies are used. (b) Using the observation in part (a) above, find the mixed strategy NE for this game. (3) (Bertrand Model with sequential move) Consider a Bertrand duopoly model with two firms, F and F2 selling two varieties of a product. The demand curve for Fi's product 91 (P1.p2) = 10 - P1...
Problem Set 1 Due Date: Wednesday, January 25,2017 1. Consider the following demand function of an...
Problem Set 1 Due Date: Wednesday, January 25,2017 1. Consider the following demand function of an individual for good 1: where p" p2, ps are the prices of good 12, and 3, respectively, and Y represents the income the individual. Suppose good 1 and 2 are substitutes while good 1 and 3 are complements. (a) Describe in words what B,,B,, B, and B, measure. (b) Can you say anything about the expected signs of p.B.B, and B, in the demand...
Question v) to question viii)
Thank you
An economy has three agents, A. B and C, and three goods 1, 2 and 3. The endowments of the three consumers are as follows e (3,0,0); e (i) Write down the total endowment vector of the economy. (0,5,0); (1,1,1) Given a price vector p (p,P2 Pa), the demand functions of the three agents for cach of the three goods are as follows (I am giving these to you rather than ask you...
2. Consider the following model of Supply and Demand. where P is the price of the good, Qd is quantity demanded and Q5 is quantity supplied. (i) What condition should b satisfy in order for the first equation to be a reasonable demand function? (ii) What condition should b and d satisfy in order for this system to have a unique equilibrium? (ii) Assuming a unique equilibrium exists express the system in matrix form and use matrix algebra to find...
Q3. Consider the vector space P, consisting of all polynomials of degree at most two together with the zero polynomial. Let S = {p.(t), p2(t)} be a set of polynomials in P, where: pi(t) = -4 +5, po(t) = -3° - 34+5 (a) Determine whether the set S = {P1(t).pz(t)} is linearly independent in Py? Provide a clear justification for your solution. (8 pts) (b) Determine whether the set S = {p(t),p2(t)} spans the vector space P ? Provide a...
Question 4.1 (9 marks): Consider a basis B = {pl,p2.p3} of polynomials in P, , where pl :=1-x: p2 := x-x: p3 := 1+x: a Use the definition of coordinate vector to find the polynomial p4 in P, the vector of coordinates of which in the basis B is c4=(2,2,-2). b. Find the transition matrix StoB from the standard basis in P, to the basis B. What are the coordinates of the three standard coordinate vectors of the basis Sin...
Pcoer IS approximately ES0 2. Consider the following model of Supply and Demand. where P is the price of the good, Q is quantity demanded and QS is quantity supplied. (i) what condition should δ satisfy in order for the second equation to be a reasonable supply function. (ii) What condition should B and 6 satisfy in order for this system to have a unique equilibrium. Ģi Assuming a unique equilibrium exists express the system in matrix form and use...
Consider the following closed economy: There are three sectors: S, S2, S3. Sector one consumes 90 percent of it's own product, sells 10 percent to sector two and nothing to sector three. Sector two consumes 40 percent of it's own product, sells 40 percent to sector one and 2 percent to sector three. Sector three consumes 20 percent of it's own product, sells 40 percent to sector 1 and 40 percent to sector 2. 1. Write a se t of...
Please show work
Answer shown below
Problem 2: Consider the three-spring structure given below. It is fixed at the far right end (node 4) and is subject to nodal forces as given below. из 144 lu 142 Pi Kj Ki P2 The element (spring) stiffnesses are: Ki- K2- 200 k/in and Ks-250 k/in The forces applied at the nodes are: P 150 k, P--50 k, Ps 150 k E.g. the stiffness a) Write the stiffness equilibrium equations for nodes 1,...
Consider a three-level system where the Hamiltonian and
observable A are given by the matrix Aˆ = µ 0 1 0 1 0 1 0 1 0
Hˆ = ¯hω 1 0 0 0 1 0 0 0 1 (a) What are the possible
values obtained in a measurement of A (b) Does a state exist in
which both the results of a measurement of energy E and observable
A can be...
(2) Consider the following game: P U M D LR 3,1 0,2 1,2 1,1 0,4 3,1 (a) Show that M is a dominated strategy when mixed strategies are used. (b) Using the observation in part (a) above, find the mixed strategy NE for this game. (3) (Bertrand Model with sequential move) Consider a Bertrand duopoly model with two firms, F and F2 selling two varieties of a product. The demand curve for Fi's product 91 (P1.p2) = 10 - P1...
Problem Set 1 Due Date: Wednesday, January 25,2017 1. Consider the following demand function of an individual for good 1: where p" p2, ps are the prices of good 12, and 3, respectively, and Y represents the income the individual. Suppose good 1 and 2 are substitutes while good 1 and 3 are complements. (a) Describe in words what B,,B,, B, and B, measure. (b) Can you say anything about the expected signs of p.B.B, and B, in the demand...
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