Suppose the Planned Aggregate Expenditures curve is given by

Suppose the Planned Aggregate Expenditures curve is given by PAE-Ab(Y-tY) where A is autonomous expenditures, b is the marginal propensity to consume, t is the proportional tax rate and Y is total output. Suppose the government increases t from O to 0.5 and the multiplier halves. Then, b is equal to: O 1/4 1/2 2/3 None of the above.

Solution

With t=0 multiplier = 1/(1-b)

With t= 0.5 multiplier = 1/2(1-b)

Also multiplier = 1/(1-b+tb)

=> 1/{2(1-b)}= 1/(1-b+tb)

2-2b= 1-b+tb

1= 2b-b + 0.5b

b= 1/1.5= 10/15= 2/3

2/3 is correct