Consider a single neighbourhood in which the housing units might be desirable to two types of individuals called Blues (B) and Greens (G). Suppose that Pg shows the price that Greens would be willing to pay for a house in the neighbourhood. The equation for Pg is given below as a fraction of Greens (x) in this neighbourhood: Blues constitute the relatively richer part of the society. Pb shows the price that Blues are willing to pay for a house in this neighbourhood. The equation for Pb is given below also as a function of Greens (x) in this neighbourhood: Pg and Pb also reflect the preferences of Greens and Blues as Greens and Blues are willing to pay prices based on the "preferable" fraction of Greens. The fraction of Greens in the "next period" is given as x'below as a function of x to take account of the fact that in any period some of the Greens may sell to a Blue while some of the blues may sell to a Green a and 3 are constant positive coefficients. a) What is the fraction of Greens (x) that Greens living in this neighbourhood would prefer to see the most in this neighbourhood? What is the fraction of Greens (x) that Blues living in this neighbourhood would prefer to see the most in this neighbourhood? b) By determining the sign of dAx/dx, indicate all equilibrium(s) of the resulting housing market and indicate which equilibrium(s) are stable in the replicator dynamic in the text. c) Is it possible to have stable equilibria, where the neighbourhood is formed by either all Greens and/or all Blues? d) Now assume that the neighbourhood is at an equilibrium where both Blues and Greens live together. However, the neighbourhood becomes trendy, and the equation for Po changes as below, since the richer group- Blues are willing to pay greater prices for the houses in this neighbourhood. The price equation for Greens does not change, as the Greens cannot change their preferences due to lack of funds. Discuss the impact of Blues' changing preferences on the fraction of Greens living in this neighbourhood (x). Consider a single neighbourhood in which the housing units might be desirable to two types of individuals called Blues (B) and Greens (G). Suppose that Pg shows the price that Greens would be willing to pay for a house in the neighbourhood. The equation for Pg is given below as a fraction of Greens (x) in this neighbourhood: Blues constitute the relatively richer part of the society. Pb shows the price that Blues are willing to pay for a house in this neighbourhood. The equation for Pb is given below also as a function of Greens (x) in this neighbourhood: Pg and Pb also reflect the preferences of Greens and Blues as Greens and Blues are willing to pay prices based on the "preferable" fraction of Greens. The fraction of Greens in the "next period" is given as x'below as a function of x to take account of the fact that in any period some of the Greens may sell to a Blue while some of the blues may sell to a Green a and 3 are constant positive coefficients. a) What is the fraction of Greens (x) that Greens living in this neighbourhood would prefer to see the most in this neighbourhood? What is the fraction of Greens (x) that Blues living in this neighbourhood would prefer to see the most in this neighbourhood? b) By determining the sign of dAx/dx, indicate all equilibrium(s) of the resulting housing market and indicate which equilibrium(s) are stable in the replicator dynamic in the text. c) Is it possible to have stable equilibria, where the neighbourhood is formed by either all Greens and/or all Blues? d) Now assume that the neighbourhood is at an equilibrium where both Blues and Greens live together. However, the neighbourhood becomes trendy, and the equation for Po changes as below, since the richer group- Blues are willing to pay greater prices for the houses in this neighbourhood. The price equation for Greens does not change, as the Greens cannot change their preferences due to lack of funds. Discuss the impact of Blues' changing preferences on the fraction of Greens living in this neighbourhood (x). Consider a single neighbourhood in which the housing units might be desirable to two types of individuals called Blues (B) and Greens (G). Suppose that Pg shows the price that Greens would be willing to pay for a house in the neighbourhood. The equation for Pg is given below as a fraction of Greens (x) in this neighbourhood: Blues constitute the relatively richer part of the society. Pb shows the price that Blues are willing to pay for a house in this neighbourhood. The equation for Pb is given below also as a function of Greens (x) in this neighbourhood: Pg and Pb also reflect the preferences of Greens and Blues as Greens and Blues are willing to pay prices based on the "preferable" fraction of Greens. The fraction of Greens in the "next period" is given as x'below as a function of x to take account of the fact that in any period some of the Greens may sell to a Blue while some of the blues may sell to a Green a and 3 are constant positive coefficients. a) What is the fraction of Greens (x) that Greens living in this neighbourhood would prefer to see the most in this neighbourhood? What is the fraction of Greens (x) that Blues living in this neighbourhood would prefer to see the most in this neighbourhood? b) By determining the sign of dAx/dx, indicate all equilibrium(s) of the resulting housing market and indicate which equilibrium(s) are stable in the replicator dynamic in the text. c) Is it possible to have stable equilibria, where the neighbourhood is formed by either all Greens and/or all Blues? d) Now assume that the neighbourhood is at an equilibrium where both Blues and Greens live together. However, the neighbourhood becomes trendy, and the equation for Po changes as below, since the richer group- Blues are willing to pay greater prices for the houses in this neighbourhood. The price equation for Greens does not change, as the Greens cannot change their preferences due to lack of funds. Discuss the impact of Blues' changing preferences on the fraction of Greens living in this neighbourhood (x).