a) The formula for income is Y = C+I+G.
There is no G, so this reduces to Y = C+I.
Output is equal to income, so GDP = Y = 100+0.5Y+I
By algebra and substitution,
.5Y = 100+50
Y =300

b) What is the multiplier for consumption spending for this economy?
This is determined by the MPC (marginal propensity to consume) which is the percentage of income that is spent and is given by the coefficient of Y in the consumption term.
The formula is 1/(1-MPC).
So in this problem, the multiplier = 1/(1-.5) =1/.5 =2
The inverse of this multiplier is the marginal propensity to save (MPS).

b)What is the multiplier for investment spending for this economy?
The investment spending multiplier is 1/MPS = 1/(.5) = 2
This multiplies the effects of investment spending in terms of total income. An investment in a small facility, for example, increases the incomes of the workers who build it, the storekeepers who provide supplies, the distributors who supply the merchants, and the manufacturers who supply the distributors. Each recipient spends a portion of the income and saves the rest.

d) What is the marginal propensity to save?
It indicates the change in saving resulting from a change in income. In fact, if the MPC and MPS are calculated based on after-tax disposable income, they equal one: MPC + MPS = 1. Because MPC = .5, in this example MPC= MPS.