What is meant by the term "marginal analysis"? Suppose an individual has to choose between renting four apartments at different distances from his place of work

The individual has to commute to work on five days of the week and as such will require different quantities of gasoline depending on the apartment he decides to rent. The monthly rents and expected gasoline consumption from each of the apartments is shown in the table below. If the price of gasoline is $5 per gallon, using marginal analysis, determine the optimum choice for the individual. Which principal is used for this optimization? What does it state?

Apartment Gasoline Consumption (gallons per month) Rent ($ per month)
1 5 1,100
2 10 1,000
3 15 960
4 20 940

Marginal analysis is a cost-benefit analysis that compares the consequences of doing one step more of something. Hence, it is a cost-benefit calculation that studies the difference between a feasible alternative and the next feasible alternative.
To arrive at the conclusion regarding optimum choice of apartment using marginal analysis, it is essential to calculate the marginal commuting cost and the marginal rent cost for movement between each set of alternatives. This is shown in the table below.

Apartment Gasoline Consumption (gallons per month) Commuting cost ($ per month) Marginal Commuting Cost ($ per month) Rent ($ per month) Marginal Rent Cost ($ per month) Marginal Total Cost ($ per month)
1 5 25 - 1,100 - -
2 10 50 25 1,000 -100 -75
3 15 75 25 960 -40 -15
4 20 100 25 940 -20 5

The marginal total cost of moving from Apartment 1 to Apartment 2 is -$75. This implies that the individual gains $75 if he moves from Apartment 1 to Apartment 2. This move is beneficial.
The second movement—from Apartment 2 to Apartment 3—has a marginal total cost of -$15. This implies that the individual gains $15 if he moves from Apartment 2 to Apartment 3. This move is beneficial too.
The third move—from Apartment 3 to Apartment 4—has a marginal total cost of $5. This implies that the individual loses $5 if he moves from Apartment 3 to Apartment 4. This move is not beneficial.
Hence, from the above inferences it is clear that moving toward Apartment 3 is beneficial, whereas moving away from Apartment 3 is not. This implies Apartment 3 is the optimum choice for the individual. The principle used to arrive at the optimum choice is referred to as the Principal of Optimization at the Margin. It states that an optimal alternative has the property that moving to it makes the decision-maker better off and moving away from it makes the decision maker worse off.