In what follows, we provide the demand analysis associated with budget-constrained linear utility maximization for each of several categories of goods, with the marginal rate of consumption expenditure-as a share of wealth- being a positive constant less than or equal to one. The marginal rate of consumption expenditure is endogenously determined, by a budget-constrained “Cobb-Douglas with Linear Components” utility function maximization problem, where the utility function includes the possibility of savings as a variable, and which reduces to the category specific budget-constrained linear utility maximization problems we are concerned with here. We also show that the budget-constrained Cobb-Douglas with Linear Components utility function maximization problem of a single consumer can be reduced to a finite number of budget-constrained linear utility maximizations problems all having the same number of variables, where the number of such budget-constrained linear utility maximizations problems is equal to the number of “categories” of the non-monetary goods that are consumed.
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