Suppose you want to analyze personal consumption expenditures by using income. However, you also believe that personal consumption expenditures might vary by gender (female-male) and marital status (married-single).

(a) By setting appropriate dummy variables, construct a regression where not only the autonomous consumption but also the marginal propensity to consume are allowed to vary by gender and marital status. In your regression, you should have the assumption that the differential effect of gender (marital status) on autonomous consumption and marginal propensity to consume is the same across two categories of marital status (gender). Once you construct your regression, derive the expected personal consumption expenditures of each group.

(b) Re-construct the regression in (a) by allowing the differential effect of gender (marital status) on autonomous consumption and marginal propensity to consume to vary across two categories of marital status (gender) and derive expected personal consumption expenditures of each group.