Consider the following simplified national-income model, Y= C + G + 10 (1) C = a + b(Y – 7) (a>0,0<ß< 1) (2) G= 8+ OY (8>0,0< < 1) (3) T= d + tY (d>0,0<<< 1) (4) where Y, C, G and T represent the endogenous variables of national income, private consumption expenditure, government consumption expenditure, and income tax, lo stands for the exogenous variable of investment expenditure, a, b, 8, 0, and d are independent structural parameters, and t is the (private) income tax rate which is considered as a policy or control parameter, respectively

Consider the following simplified national-income model, Y= C + G + 10 (1) C = a + b(Y – 7) (a>0,0<ß< 1) (2) G= 8+ OY (8>0,0< < 1) (3) T= d + tY (d>0,0<<< 1) (4) where Y, C, G and T represent the endogenous variables of national income, private consumption expenditure, government consumption expenditure, and income tax, lo stands for the exogenous variable of investment expenditure, a, b, 8, 0, and d are independent structural parameters, and t is the (private) income tax rate which is considered as a policy or control parameter, respectively. It is also understood that B and 0, standing for private and government consumption rates, respectively, satisfy the reasonable conditions of a - Bd > 0 and B+ 0<1. Denote x = ??? and write equations (1)-(4) in matrix format as: x= Ax + b (5) Question 3 (40 marks) (i) Solve for Y, C, G and T from equations (1)-(4) [or from equation (5)] in terms of the exogenous variable (10) and parameters (a, b, d, 0, d and t), formally called their equilibrium values which are denoted as Yº, C, Gº and Tº, respectively. Indicate the conditions or restrictions (if any) needed in order to find the equilibrium values. (20 marks) (ii) Discuss how the above-solved equilibrium levels Y, C, G and Twill change (i.e., increase or decrease) if the income tax rate (t) is going to be increased. (20 marks)