Maria derives 288 utils from buying two pairs of hiking boots and four saws.She gets 313 utils from buying one pair of hiking boots and seven saws.Maria is indifferent between these two combinations of hiking boots and saws.True

Question

Quizplus · Accepted Answer

To solve this problem, we need to use the concept of marginal utility. Marginal utility refers to the additional utility or satisfaction that a person receives from consuming one more unit of a good.

Let's assume that the utility of one pair of hiking boots is X, and the utility of one saw is Y. We can use this information to create two equations:

2X + 4Y = 288  (equation 1)
1X + 7Y = 313  (equation 2)

We want to determine if Maria is indifferent between these two combinations of hiking boots and saws. In other words, does she derive the same level of satisfaction from both?

We can start by solving for X in equation 2:

1X = 313 - 7Y 
X = 313/1 - 7Y/1

Now we can substitute this expression for X into equation 1 and simplify:

2(313/1 - 7Y/1) + 4Y = 288 
626/1 - 14Y/1 + 4Y = 288 
-10Y = -338 
Y = 33.8

We can now plug Y=33.8 into either equation to solve for X:

2X + 4(33.8) = 288 
2X = 118.4 
X = 59.2

Therefore, the utility of one pair of hiking boots is 59.2 and the utility of one saw is 33.8.

Now we can calculate the total utility of each combination of hiking boots and saws:

Combination 1: 
2 pairs of hiking boots = 2X = 118.4 
4 saws = 4Y = 135.2 
Total utility = 253.6

Combination 2: 
1 pair of hiking boots = 1X = 59.2 
7 saws = 7Y = 236.6 
Total utility = 295.8

Since the total utility of Combination 2 is higher than Combination 1, Maria prefers Combination 2. Therefore, the statement "Maria is indifferent between these two combinations of hiking boots and saws" is false.

Maria Derives 288 Utils from Buying Two Pairs of Hiking