Question

Shelly, a homemaker, spends \(\$ 70\) twice a year on 10 grams of saffron and \(\$ 140\) a year on 28,000 gallons of tap water. a. Out of saffron and water, which is more valuable to Shelly? b. Explain how Shelly's expenditure on saffron and water illustrates the paradox of value.

Short answer

Saffron is more valuable to Shelly. The paradox of value shows that essentials like water cost less despite high utility compared to non-essentials like saffron which cost more.

Step-by-step solution

Calculate Annual Expenditure on Saffron

Shelly spends \(\$ 70\) twice a year on saffron. To find the annual expenditure, multiply \(\$ 70\) by 2.\[\$70 \times 2 = \$140\]So, annually Shelly spends \(\$ 140\) on saffron.

Calculate the Cost Per Gram of Saffron

Shelly buys 10 grams of saffron for \(\$ 70\). To find the cost per gram, divide \(\$ 70\) by 10.\[\$70 \div 10 = \$7 \text{per gram}\]Thus, saffron costs \(\$ 7\) per gram.

Calculate the Cost Per Gallon of Water

Shelly spends \(\$ 140\) annually on 28,000 gallons of tap water. To find the cost per gallon, divide \(\$ 140\) by 28,000.\[\$140 \div 28,000 = 0.005 \text{per gallon}\]Thus, water costs \(0.005\) per gallon.

Compare the Value of Saffron and Water

Comparing the costs calculated, saffron costs \(\$ 7\) per gram versus water's \(0.005\) per gallon. Hence, per unit cost, saffron is more valuable to Shelly than water.

Explain the Paradox of Value

The paradox of value, also known as the diamond-water paradox, observes that necessities like water (having high utility) are cheaper than luxuries like saffron (having low utility). Shelly's expenditure showcases this as she spends much less per gallon on water, a necessity, than on saffron, a luxury.

Key concepts

Value Comparison

Value comparison is the process of comparing the worth or cost of different items. In Shelly's case, she spends \(\text{\LaTeX\textbackslash\)\text{{\$140\}} annually on saffron and \(\text{\LaTeX\textbackslash\)\text{{\$140\}} annually on water. However, a closer look at the cost per unit reveals a significant difference. Each gram of saffron costs her \(\text{\LaTeX\textbackslash\)\text{{\$7\}} while each gallon of water costs \(\text{\LaTeX\textbackslash\)\text{{\0.005\}}. This comparison shows that saffron is much more costly per unit than water, even though the overall annual expenditure is the same.

Utility

Utility refers to the satisfaction or benefit derived from consuming a good or service. Water has high utility because it is essential for survival, while saffron has lower utility as it is a luxury spice. Despite its high utility, water is cheaper per unit than saffron. Therefore, utility does not always directly correlate with the monetary value of an item. Shelly benefits greatly from the large amount of water she consumes, even though it costs very little per gallon.

Cost Analysis

Cost analysis involves examining the cost of different goods and services to understand their value and impact on budget. For Shelly, spending \(\text{\LaTeX\textbackslash\)\text{{\$140\}} annually on water for 28,000 gallons results in a minimal cost per unit, making it affordable. Conversely, saffron, costing \(\text{\textbackslash\)\text{{\$7\}} per gram, represents a more considerable expense per unit. This type of analysis helps in understanding how much one is paying for the utility each item provides and making informed financial decisions.

Economic Paradox

The economic paradox, particularly the paradox of value, demonstrates why some essential goods are inexpensive while luxuries are costly. Known as the diamond-water paradox, it highlights that necessities like water, despite their high utility, are cheaper per unit compared to non-essentials like diamonds or saffron with lower utility. Shelly's spending pattern exemplifies this paradox as she pays considerably less per gallon for water, a necessity, than per gram of saffron, a luxury.