Question

Sue's monthly budget for bottled water and soft drinks is $\backslash (23$. The price of bottled water is $\backslash )1$per bottle, and the price of soft drinks is$\$2$per bottle. Calculate the slope of Sue's budget constraint. Given this information and the information provided in Problem $F-3$, find the combination of goods that satisfies Sue's utility-maximization problem in light of her budget constraint.

Short answer

A cheeseburger and French fries, the utility maximization combination is four and two, respectively.

Step-by-step solution

    Introduction

The marginal value and total utility of a cheeseburger and French fries are depicted graphically below.

We added two columns of marginal utility per dollar for cheeseburgers and French fries to this table.

The marginal utility per dollar for the first cheese burger is $\$20(20/1=20)$, while the marginal utility per dollar for the first French fries is$\$10(10/1=10)$. Because cheese burgers have a higher marginal utility, they are purchased. This leaves you with $\$5(6-1=5)$ in earnings.

    Explanation

Because the second cheese burger has a higher marginal utility per dollar, namely $16$, it is also purchased, and the remaining income is $\$4(5-1=4)$. The third cheese burger also had a greater marginal utility per dollar, i.e. $12$, therefore it was purchased, and the revenue is now $\$3(4-1=3)$.

The first French fries have a higher marginal utility per dollar$(8versus10)$than the fourth cheese burger, hence the first French fries are ordered. This leaves $\$1(2-1=1)$available for spending.

    Conclusion

The marginal utility of second French fries per dollar is $8$, which is the same as the marginal utility of a cheeseburger per dollar, i.e.$8$, and all revenue is spent equally on consuming. Four cheeseburgers for $\$4$and two French fries for $\$2$, resulting in a total expenditure of $\$6(4+2=6)$.

Thus, for a cheeseburger and French fries, the utility maximization combination is four and two, respectively.