Mathematically, the value of the tax multiplier in terms of the marginal propensity to consume \((M P C)\) is given by the formula a. \(M P C-1\) b. \((M P C-1) / M P C\) c. \(1 / M P C\) d. \(1-[1 /(1-M P C)]\)

The marginal propensity to consume (MPC) is the increase in consumption that results from an increase in income. It represents the proportion of an additional dollar of disposable income that is spent on consumer goods and services. Mathematically, it is the change in consumption over the change in income: \(MPC = \frac{\Delta C}{\Delta Y}\).

The tax multiplier is a measure of how a change in taxes affects the overall economy, specifically the change in GDP due to a change in taxes. It represents the ratio of the change in GDP to the change in taxes. In our context, we are looking for the relationship between the tax multiplier and the marginal propensity to consume.

In the context of the multiplier effect, the tax multiplier can be derived from the government spending multiplier. The government spending multiplier is given by the formula: \(GSM = \frac{1}{1 - MPC}\). Now, to derive the tax multiplier (TM) from the government spending multiplier (GSM), we just need to account for the fact that a change in taxes has a less direct effect on GDP than a change in government spending. Specifically, the tax multiplier has a negative sign in front of the MPC term because an increase in taxes leads to a decrease in disposable income and thus a decrease in consumption, given the MPC. Therefore, the formula for the tax multiplier will be: \(TM = -MPC \times GSM\) Substitute the formula for GSM into this equation: \(TM = -MPC \times \frac{1}{1 - MPC}\)

Now simplify the tax multiplier formula: \(TM = -\frac{MPC}{1 - MPC}\) By analyzing the given options, we see that none of them matches the simplified formula. However, option d can be simplified to match our derived tax multiplier formula: Option d: \(1-\frac{1}{(1-MPC)} = \frac{1 - (1 - MPC)}{1 - MPC} = \frac{MPC}{1 - MPC}\) However, we need to account for the negative sign in the derived tax multiplier formula. Thus, the correct answer should be: \(-\frac{MPC}{1 - MPC}\) Since none of the given options match this formula, it seems none of the options provided are the correct formula for the tax multiplier in terms of the marginal propensity to consume.