Demonstrate How The Concept Of Utility Affects Purchasing De
Demonstrate How The Concept Of Utility Affects Purchasing Decisions By
Demonstrate how the concept of utility affects purchasing decisions by individuals and consumer surplus.
Questions:
1. The accompanying table shows the price and monthly demand for barrels of gosum berries in Gondwanaland. Price of gosum berries per barrel and native demand per month are as follows:
- $100: 0 barrels
- $90: 100 barrels
- $80: 200 barrels
- $70: 300 barrels
- $60: 400 barrels
- $50: 500 barrels
- $40: 600 barrels
- $30: 700 barrels
- $20: 800 barrels
- $10: 900 barrels
- $0: 1000 barrels
Using the midpoint method, calculate the price elasticity of demand when the price rises from $10 to $20, showing your work. Interpret what this estimate implies about the price elasticity of demand for gosum berries.
Similarly, using the same method, calculate the elasticity when the price rises from $70 to $80, showing your work, and interpret the result.
Notice that the estimates differ. Explain why price elasticity estimates change along the demand curve.
2. Matilda is downloading music and videos from an online site. She is purchasing three music downloads and two video downloads, each costing $3. Her reported marginal utilities are:
- Music downloads: MU of the third download = 60
- Video downloads: MU of the second download = 45
Assess whether Matilda is maximizing her utility based on these values:
a. Determine if she is maximizing utility and explain.
b. Should she consume one more video download? Justify.
c. Should she consume one less music download and one more video? Justify.
d. Should she consume one more music download? Justify.
3. Brandon and his family rent movies from Xanadu, an internet streaming service. His demand schedule and willingness to pay are:
- 1st rental: $7
- 2nd rental: $6
- 3rd rental: $5
- 4th rental: $4
- 5th rental: $3
- 6th rental: $2
- 7th rental: $1
- 8th rental: $0
a. If the price per rental is $3, how many rentals will Brandon buy, and what is his consumer surplus? Explain.
b. At a $5 rental price, how many rentals will he buy and what is his consumer surplus? Explain.
c. With an unlimited subscription for $25 annually, how many rentals will Brandon take, and what surplus will he get? Explain.
d. With a $35 subscription fee, how many rentals will Brandon download, and what consumer surplus does he get? Explain.
e. If Xanadu's market research indicates Brandon’s demand reflects most customers’, what is the maximum one-time annual fee they could charge for unlimited downloads? Justify.
4. Explain why newspaper vending machines differ from soda or snack vending machines using the concept of marginal utility, considering that the former provides access to multiple papers once paid, while the latter dispense only a single item.
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Paper For Above instruction
Introduction
The concept of utility is foundational in understanding consumer decision-making and demand within microeconomics. Utility, defined as the satisfaction or benefit derived from consuming goods and services, influences individual purchasing choices and overall market dynamics. This essay explores how utility affects purchasing decisions through various scenarios—demand elasticity, consumer utility maximization, and consumer surplus—highlighting the significance of marginal utility, consumer preferences, and substitutes. It also discusses real-world examples such as demand for berries, digital downloads, movie rentals, and vending machines to demonstrate the practical applications of utility theory.
Utility and Demand: Elasticity of Gosum Berries
Demand elasticity measures how consumers alter their quantity demanded in response to price changes. The midpoint method provides a reliable calculation by averaging initial and final quantities and prices. For the case of gosum berries, when the price rises from $10 to $20, demand drops from 900 to 800 barrels. The midpoint quantities and prices are (900 + 800)/2 = 850 and ($10 + $20)/2 = $15 respectively.
The elasticity formula:
\[
E_d = \frac{\% \text{Change in Quantity Demanded}}{\% \text{Change in Price}}
= \frac{\frac{\Delta Q}{Q_{avg}}}{\frac{\Delta P}{P_{avg}}}
\]
Calculating:
\[
\Delta Q = 800 - 900 = -100
\]
\[
Q_{avg} = \frac{900 + 800}{2} = 850
\]
\[
\Delta P = 20 - 10 = 10
\]
\[
P_{avg} = \frac{10 + 20}{2} = 15
\]
\[
E_d = \frac{-100/850}{10/15} = \frac{-0.1176}{0.6667} \approx -0.176
\]
The absolute value is approximately 0.176, indicating demand is inelastic in this range, meaning a price increase leads to a less-than-proportionate decrease in quantity demanded.
When the price increases from $70 to $80, demand decreases from 300 to 200. The midpoint calculations:
\[
Q_{avg} = \frac{300 + 200}{2} = 250
\]
\[
P_{avg} = \frac{70 + 80}{2} = 75
\]
\[
\Delta Q = 200 - 300 = -100
\]
\[
\Delta P = 80 - 70 = 10
\]
Calculating elasticity:
\[
E_d = \frac{-100/250}{10/75} = \frac{-0.4}{0.1333} \approx -3.0
\]
The absolute elasticity is 3.0, indicating demand is elastic in this higher price range, where demand is highly responsive to price changes.
The variation in elasticity estimates along the demand curve reflects different consumer sensitivities at various price points, known as the "elasticity along a demand curve." High elasticity at higher prices suggests that consumers are more responsive when the good becomes expensive, possibly substituting it with alternatives, whereas demand tends to be more inelastic at lower prices.
Utility Maximization and Consumer Choice: Matilda’s Downloading Behavior
Matilda’s utility maximization condition stipulates that consumers allocate their income so that the marginal utility per dollar spent is equalized across all goods. For her, given her marginal utilities and prices:
- Music downloads MU(3rd) = 60
- Video downloads MU(2nd) = 45
- Price per download = $3
The marginal utility per dollar for the third music download:
\[
MU/P = 60 / 3 = 20
\]
For the second video download:
\[
MU/P = 45 / 3 = 15
\]
Since the marginal utility per dollar spent on music exceeds that of videos, Matilda could increase her overall utility by purchasing one more video download, provided the marginal utilities for additional units remain positive. The current imbalance indicates she is not optimizing her utility because the last dollar spent yields higher satisfaction in music downloads than in videos.
To examine whether she should consume more or fewer downloads, the principle of marginal utility per dollar suggests:
- She should buy more videos until MU per dollar aligns across goods.
- If MU per dollar for videos exceeds that for music, she should consume more videos and fewer music downloads to maximize utility; this aligns with part c's analysis.
Therefore, she should reallocate her spending—reducing some music downloads and increasing video downloads—to reach an equilibrium where MU per dollar is equalized across goods, maximizing her total utility.
Consumer Demand and Surplus in Movie Rentals
Brandon’s demand schedule demonstrates diminishing willingness to pay for each additional rental, which is typical due to decreasing marginal utility. At a rental price of $3, Brandon values the first rental at $7 and the eighth at $0. His consumer surplus (CS) is the sum of the differences between what he is willing to pay and what he actually pays for each rental he chooses.
At $3 per rental:
- Brandon will rent up to the point where his willingness to pay exceeds $3, which is at the sixth rental (willingness to pay $2). But since $2 is less than $3, he will rent only five movies.
- Total consumer surplus:
\[
CS = \text{Sum of }(WTP_i - P) \text{ for all rentals rented}
\]
\[
= (7-3) + (6-3) + (5-3) + (4-3) + (3-3)
= 4 + 3 + 2 + 1 + 0 = \$10
\]
Similarly, at $5 per rental:
- Brandon’s willingness to pay drops below $5 after the third rental.
- He can rent up to three movies because beyond that, his WTP falls below $5.
- Consumer surplus:
\[
CS = (7-5) + (6-5) + (5-5) = 2 + 1 + 0 = \$3
\]
- Brandon rents three movies, with the last rental’s WTP exactly equal to the price, yielding zero surplus on that last rental.
With a flat subscription fee of $25 annually allowing unlimited rentals:
- Brandon will rent as many as his WTP justifies.
- His willingness to pay decreases, but since he can rent unlimited movies at $25, he will rent all 8 possible movies (the maximum segmented by his WTP for each), and his consumer surplus is:
\[
CS = \sum_{i=1}^{8} (WTP_i - \frac{Annual fee}{Number of Rentals})
\]
However, a more accurate approach is to note that the consumer’s total WTP sum is (7+6+5+4+3+2+1+0) = $28, and the total fee is $25. Since he derives utility from each rental worth more than the marginal cost, his consumer surplus is:
\[
CS = \text{Total WTP} - \text{Total Payment} = 28 - 25 = \$3
\]
Similarly, at a $35 subscription fee:
- Brandon’s willingness to pay is capped at $28 of total WTP, which is less than the fee.
- Therefore, he would not subscribe and rent any movies, leading to zero consumer surplus.
The maximum fee that Xanadu could charge per year is equal to the total WTP summed across most customers, which in Brandon's case is $28, reflecting the maximum they can extract as a one-time fee without losing all business.
Utility in Vending Machines: Multiple versus Single Item Dispensing
The difference between newspaper vending machines and soda or snack vending machines stems from utility and marginal utility concepts. Newspaper vending machines provide access to multiple newspapers after a single payment, offering a form of 'bundle utility'—the aggregate satisfaction derived from multiple items purchased simultaneously. This multiplicity of goods in one purchase increases consumer convenience and perceived value, leveraging the concept of total utility—more goods lead to greater total utility.
Conversely, soda and snack machines typically dispense only one item per payment, focusing on marginal utility — the additional satisfaction obtained from consuming one more unit of a good. Each purchase is independent, with no utility gained from sharing or simultaneously accessing multiple goods unless the consumer makes multiple transactions. This design aligns with the principle that marginal utility diminishes with each additional unit, emphasizing efficient allocation of consumer resources per transaction.
Thus, vending machines differ because newspaper machines are designed to maximize perceived total utility by providing access to multiple items at once, leveraging consumers’ preference for convenience and bundle consumption. In contrast, single-item vending machines cater to the marginal utility principle by offering a single, discrete unit, encouraging consumers to evaluate instant satisfaction against their willingness to pay.
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References
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