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Zorluk: Çok zorConcept and Calculation of Consumer Surplus

A consumer's evaluation of total utility derived from consuming successive tubers of yam in a local Nigerian market (expressed in monetary terms) is presented in the table below:

Quantity of Yam (Tubers)Total Utility (₦)
11,800
23,300
34,500
45,400
56,000
66,300

If the prevailing market price of a tuber of yam is ₦900, what is the total value of consumer surplus (in ₦) enjoyed by the consumer at equilibrium?

Cevap: 1800 ₦

Cevap

The consumer surplus enjoyed by the consumer at equilibrium is ₦1,800.
To find consumer surplus, one must first establish the consumer's profit-maximizing equilibrium quantity where Marginal Utility (MU) equals Price (P). From the Total Utility (TU) values, the MU for successive units is ₦1,800, ₦1,500, ₦1,200, and ₦900. At the 4th unit, MU equals the market price of ₦900. Total utility for 4 units is ₦5,400 and total outlay is 4×900=₦3,6004 \times 900 = \text{₦}3,600. Subtracting total outlay from total utility yields a consumer surplus of ₦1,800.

Adım Adım Çözüm

1
Calculate Marginal Utility (MU) for each unit consumed
MU values are ₦1,800 for the 1st tuber, ₦1,500 for the 2nd, ₦1,200 for the 3rd, ₦900 for the 4th, ₦600 for the 5th, and ₦300 for the 6th tuber.
Consumer equilibrium is reached when the marginal utility of a unit equals its market price.
2
Determine the equilibrium quantity consumed
The consumer purchases 4 tubers of yam.
For the 4th tuber, MU=₦900MU = \text{₦}900, which matches the prevailing market price of ₦900. Consuming a 5th tuber yields MU=₦600<₦900MU = \text{₦}600 < \text{₦}900, which reduces net utility.
3
Calculate the actual total expenditure
Total Expenditure=4×₦900=₦3,600\text{Total Expenditure} = 4 \times \text{₦}900 = \text{₦}3,600.
Total expenditure is equal to the quantity purchased multiplied by the market price per unit.
4
Subtract Total Expenditure from Total Utility to find Consumer Surplus
Consumer Surplus=₦5,400−₦3,600=₦1,800\text{Consumer Surplus} = \text{₦}5,400 - \text{₦}3,600 = \text{₦}1,800.
Consumer surplus measures the difference between total willingness to pay (Total Utility at 4 units) and actual expenditure.

Anahtar Kavram

Calculation of Consumer Surplus from Discrete Utility Schedules
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Konular

Concept and Calculation of Consumer Surplus

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