The correct answer is (a) 10.00.
The multiplier is a measure of the total change in income that results from an initial change in spending. It is calculated by dividing the change in income by the initial change in spending.
In a closed economy with no taxes, the multiplier is equal to 1/(1-MPC), where MPC is the marginal propensity to consume. The marginal propensity to consume is the fraction of an additional dollar of income that is spent on consumption.
If the marginal propensity to consume is 0.90, then the multiplier is 1/(1-0.90) = 10.00. This means that an initial increase in spending of $1 will lead to a total increase in income of $10.
The other options are incorrect because they do not represent the correct value of the multiplier. Option (b), 1.00, is the value of the multiplier when the marginal propensity to consume is 1. Option (c), 0.90, is the value of the marginal propensity to consume. Option (d), 0.10, is the value of the multiplier when the marginal propensity to consume is 0.10.