Answer:
Explanation:
a) To determine the endogenous variables, we need to identify the variables that are determined within the model equation. In the given model, the endogenous variable is Y (output or national income).
b) Let's find Y, C, and T step-by-step:
Start with the equation Y = C + I0 + g0.
Substitute C from the equation C = a + b(y - T).
Y = (a + b(y - T)) + I0 + g0.
Substitute T from the equation T = d + tY.
Y = (a + b(y - (d + tY))) + I0 + g0.
Expand the equation:
Y = a + by - bd - btY + I0 + g0.
Rearrange the equation to isolate Y:
Y + btY = a + by - bd + I0 + g0.
Y(1 + bt) = a + by - bd + I0 + g0.
Y = (a + by - bd + I0 + g0) / (1 + bt).
Now, Y is expressed in terms of the exogenous variables a, b, d, I0, g0, and the endogenous variable Y itself, along with the parameter t.
To find C and T, we can substitute the obtained Y value back into the respective equations:
Substitute Y into the equation C = a + b(y - T):
C = a + b(y - T) = a + b(y - (d + tY)) = a + by - bd - btY.
C = a + by - bd - bt[(a + by - bd + I0 + g0) / (1 + bt)].
Now, C is expressed in terms of the exogenous variables a, b, d, I0, g0, and the endogenous variable Y, along with the parameter t.
Substitute Y into the equation T = d + tY:
T = d + tY = d + t[(a + by - bd + I0 + g0) / (1 + bt)].
Now, T is expressed in terms of the exogenous variables d, t, and the endogenous variable Y, along with the parameters a, b, I0, and g0.
It's important to note that in the given model, there is only one endogenous variable, Y (national income/output). C and T are determined based on the values of Y and the exogenous variables.