{ + Consider the following market model for a single commodity: Demand: Q=d1-a2P+aUo + a_Y Supply: Q = -b + b2P with 21, 22, 23, 24, 61, b>0, where P denotes the endogenous price, Q the endogenous quantity, U, the exogenous utility that consumers have over this commodity (i.e., how much the consumers like this commodity) and Y the exogenous income that consumers earn. According to the above system of equations, one can solve for the equilibrium as such - stbitelty Abbey Use partial differentiation to investigate how the equilibrium (P", Q") reacts to changes in Y and Up PROBLEM 5 Using the market model in Problem 4 answer the following questions, (1) Write the equilibrium condition in a single equation in terms of the equilibrium price P and define the corresponding implicit function, denoted F(P", U.,Y). (2) Do we have continuous partial derivatives and ? (3) Is the partial derivative bore equal to zero at the equilibrium? (4) Suppose that the implicit-function theorem is applicable. Solve for and in terms of relevant partial derivatives and explain the meaning of the results. Are the results the same as the corresponding ones you got from Problem 4? (5) Using the supply function to express the equilibrium quantity as such Q* = -b + by P", find and 88 and explain the meaning of the results. Are the results the same as the corresponding ones you got from Problem 4? (6) The same model can also be analyzed using a system of implicit functions. Let's now define the following system: f (p",Q", Yo,Uo) = Q* - 4; + expo - ago - 21% = 0 {"p",Q",Y, Uo) Q* +b - b, p = 0 Suppose that the implicit-function theorem is applicable. Solve for $6 and as well as SC and 8. using relevatit partial derivatives. Are the results the same as the corresponding ones you got from Problem 4? { + Consider the following market model for a single commodity: Demand: Q=d1-a2P+aUo + a_Y Supply: Q = -b + b2P with 21, 22, 23, 24, 61, b>0, where P denotes the endogenous price, Q the endogenous quantity, U, the exogenous utility that consumers have over this commodity (i.e., how much the consumers like this commodity) and Y the exogenous income that consumers earn. According to the above system of equations, one can solve for the equilibrium as such - stbitelty Abbey Use partial differentiation to investigate how the equilibrium (P", Q") reacts to changes in Y and Up PROBLEM 5 Using the market model in Problem 4 answer the following questions, (1) Write the equilibrium condition in a single equation in terms of the equilibrium price P and define the corresponding implicit function, denoted F(P", U.,Y). (2) Do we have continuous partial derivatives and ? (3) Is the partial derivative bore equal to zero at the equilibrium? (4) Suppose that the implicit-function theorem is applicable. Solve for and in terms of relevant partial derivatives and explain the meaning of the results. Are the results the same as the corresponding ones you got from Problem 4? (5) Using the supply function to express the equilibrium quantity as such Q* = -b + by P", find and 88 and explain the meaning of the results. Are the results the same as the corresponding ones you got from Problem 4? (6) The same model can also be analyzed using a system of implicit functions. Let's now define the following system: f (p",Q", Yo,Uo) = Q* - 4; + expo - ago - 21% = 0 {"p",Q",Y, Uo) Q* +b - b, p = 0 Suppose that the implicit-function theorem is applicable. Solve for $6 and as well as SC and 8. using relevatit partial derivatives. Are the results the same as the corresponding ones you got from Problem 4