Consider the following simplified national-income model, Y=C+G+ Io C = a + B(Y-T) G = 8...
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Consider the following simplified national-income model, Y=C+G+ Io C = a + B(Y-T) G = 8 + ØY T= d+tY where Y, C, G and T represent the endogenous variables of national income, private consumption expenditure, government consumption expenditure, and income tax, Io stands for the exogenous variable of investment expenditure, a, ß, 6, 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 and 0, standing for private and government consumption rates, respectively, satisfy the reasonable conditions of a-ßd>0 and ß+ 0 < 1. Denote x = (a>0,0<B<1) (8>0,00<1) (d>0,0<t<1) and write equations (1)-(4) in matrix format as: x = Ax + b (3) (4) (5) (i) (ii) Solve for Y, C, G and T from equations (1)-(4) [or from equation (5)] in terms of the exogenous variable (Io) and parameters (a, B, 8, 0, d and t), formally called their equilibrium values which are denoted as Y, C, G and T, respectively. Indicate the conditions or restrictions (if any) needed in order to find the equilibrium values. (20 marks) Discuss how the above-solved equilibrium levels Y, C, Ge and Te will change (i.e., increase or decrease) if the income tax rate (t) is going to be increased. (20 marks) Consider the following simplified national-income model, Y=C+G+ Io C = a + B(Y-T) G = 8 + ØY T= d+tY where Y, C, G and T represent the endogenous variables of national income, private consumption expenditure, government consumption expenditure, and income tax, Io stands for the exogenous variable of investment expenditure, a, ß, 6, 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 and 0, standing for private and government consumption rates, respectively, satisfy the reasonable conditions of a-ßd>0 and ß+ 0 < 1. Denote x = (a>0,0<B<1) (8>0,00<1) (d>0,0<t<1) and write equations (1)-(4) in matrix format as: x = Ax + b (3) (4) (5) (i) (ii) Solve for Y, C, G and T from equations (1)-(4) [or from equation (5)] in terms of the exogenous variable (Io) and parameters (a, B, 8, 0, d and t), formally called their equilibrium values which are denoted as Y, C, G and T, respectively. Indicate the conditions or restrictions (if any) needed in order to find the equilibrium values. (20 marks) Discuss how the above-solved equilibrium levels Y, C, Ge and Te will change (i.e., increase or decrease) if the income tax rate (t) is going to be increased. (20 marks)
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i Solve for Y C G and T from equations 14 or from equation 5 in terms of the exogenous variable lo and parameters a B 8 0 d and t formally called their equilibrium values which are denoted as Ye C G a... View the full answer
Related Book For
Essentials of Statistics for the Behavioral Sciences
ISBN: 978-1285056340
8th Edition
Authors: Frederick J Gravetter, Larry B. Wallnau
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