Answer to Question #96175 in Economics for Faye Teepsuwan

Question

Consider the macro model (i) Y = C + ¯I + G, (ii) C = b(Y − T) and (iii) T = tY where the parameters b and t lie in the interval (0, 1), Y is the gross domestic product (GDP), C is consumption, ¯I is total investment, and T denotes taxes, and G is government expenditure.
(a) Express Y and C in terms of ¯I, G and the parameters.
(b) What happens to Y and C if t increases?

Answer 1

(a) Y and C in terms of ¯I, G and the parameters are:

Y = b(Y − T) + ¯I + G = bY - btY + ¯I + G,

Y = (¯I + G)/(1 - b + bt),

C = Y - (¯I + G) = (¯I + G)/(1 - b + bt) - (¯I + G) = (¯I + G) ×(1 - 1 + b - bt)/(1 - b + bt) = (¯I + G)×b(1 - t)/(1 - b(1 - t))

(b) Both Y and C will decrease if t increases.