Question

An economy is defined by
C= 400+0.4(Y-T)
IP= 200
NX= 40
T=0
Y*=1500
Calculate autonomous expenditure, multiplier, short run equilibrium and output gap.

Answer 1

Given; C = (consumption)$C = 400 + 0.4 (Y-T)$

IP = 200(investment)

NX = 40 (net exports)

T = 0(taxes)

Y* = 1500(potential output)

To get the actual output we use the formula;$Y = C+I+G+N$ .

Substituting we get: Y=400+0.4Y-0.4T+I+G+NX

0.6Y=400-0.4T+I+G+NX; Divide everything with 0.6 to get value of Y.

Y=667.67+0.67T+1.67I+1.67G+1.67NX

Now replace with the values of T, I, G and NX to get;

Y=667.67+0.67+334+1.67+66.8

Y=1069.81

Output gap is given by;$Y-Y*$ . Which is 1069.81-1500 =-430.19

Tax multiplier is the value of T in the above equation which is =0.67

Autonomous expenditure, $AE=C$  which is (400+0.4*1069.81) =827.92