Question

Exercise 4.1 Rewrite the market model (3.12) in the format of 4.1
2. with the variables arranged in the following order: Q_d1, Q_s1, Q_d2, Q_s2, P_1, P_2. write out the coefficient matrix, the variable vector, and the constant vector.
4. Rewrite the national-income model (3.23) in the format of (4.1), with U asbtye first variable. Write out the coefficient matrix and the constant vector.

3.12 model

If a solution exists, there will be a set of prices /" and corresponding quantities : s that all the n equations in the equ ch ilibrium condition will be simultaneously satisfied. Two-Commodity Market Model To illustrate the problem, let us discuss a simple model in which only two commodities are related to each other. For simplicity, the demand and supply functions of both commodities are assumed to be linear. In parametric terms, such a model can be written as (3.12) where the a and b coefficients pertain to the demand and supply functions of the first com modity and the and & coefficients are assigned to those of the second. We have not both

3.23 model

4.1 matrices and vectors

The pictures are only a samplebso you could solved the problems.

Answer 1

Q_d1 - Q_s1 = 0 Q_d1 = a_0 + a_1 P_1 + a_2 P_2 Q_s1 = b_0 + b_1 P_1 + b_2 P_2 (a_0 + a_1 P_1 + a_2 P_2) - (b_0 + b_1 P_1 + b_2 P_2) = 0 implies (a_0 - b_0) + (a_1 - b_1)P_1 + (a_2 - b_2)P_2 = 0 (1) Q_d2 - Q_s2 = 0 Q_d2 = alpha_0 + alpha_1 P_1 + alpha_2 P_2 Q_s2 = beta_0 + beta_1 P_1 + beta_2 P_2 (alpha_0 + alpha_1 P_1 + alpha_2 P_2) - (beta_0 + beta_1 P_1 + beta_2 P_2) = 0 implies (alpha_0 - beta_0) + (alpha_1 - beta_1)P_1 + (alpha_2 - beta_2)P_2 = 0 (ii) Consider equation (i) and (ii) (i) rightarrow (a_1 - b_1)P_1 + (a_2 - b_2)P_2 = -(a_0 - b_0) (ii) rightarrow (alpha_1 beta_1)P_1 + (alpha_2 - beta_2)P_2 = -(alpha_0 - beta_0) It can be written as [(a_1 - b_1) (alpha_1 - beta_1) (a_2 - b_2) (alpha_2 - beta_2)] [P_1 P_2] = [- (a_0 - b_0) - (alpha_0 - beta_0)] \r\n Y = C + I_0 + G_0 (*) C = a + by (**)