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Zorluk: OrtaCardinal Utility Analysis and Consumer Equilibrium

The table below presents the total utility schedule for a consumer consuming successive units of commodity ZZ:

Units of ZZTotal Utility (utils)
118
232
342
448
550

If the market price of commodity ZZ is N6\mathbb{N}6 per unit and 1 util=N11\text{ util} = \mathbb{N}1, what is the consumer surplus at the equilibrium level of consumption?

  1. \mathbb{N}24Cevap
  2. B
    \mathbb{N}48
  3. C
    \mathbb{N}20
  4. D
    \mathbb{N}12

Cevap

\mathbb{N}24
The option specifying \(\mathbb{N}24\) is correct. Marginal utility per unit is derived as: Unit 1 = 18, Unit 2 = 14, Unit 3 = 10, Unit 4 = 6, Unit 5 = 2. With price \(P_Z = \mathbb{N}6\), consumer equilibrium condition \(MU_Z = P_Z\) is satisfied at 4 units of consumption. At 4 units, Total Utility is \(\mathbb{N}48\) and Total Expenditure is \(4 \times \mathbb{N}6 = \mathbb{N}24\). Consumer surplus is \(48 - 24 = \mathbb{N}24\).

Adım Adım Çözüm

1
Calculate Marginal Utility (MU) for each unit consumed
MU1=18MU_1 = 18, MU2=14MU_2 = 14, MU3=10MU_3 = 10, MU4=6MU_4 = 6, MU5=2MU_5 = 2
Marginal utility is the change in total utility resulting from consuming one additional unit (MUn=TUn−TUn−1MU_n = TU_n - TU_{n-1}).
2
Determine the consumer equilibrium quantity
Equilibrium occurs at 4 units because MU4=N6=PZMU_4 = \mathbb{N}6 = P_Z
Under cardinal utility analysis, a consumer maximizes utility for a single commodity when MU=PMU = P (in monetary terms).
3
Calculate Total Expenditure at equilibrium
\text{Total Expenditure} = 4 \times \mathbb{N}6 = \mathbb{N}24
Total expenditure is calculated by multiplying the equilibrium quantity by the unit price.
4
Compute Consumer Surplus
\text{Consumer Surplus} = \text{Total Utility} - \text{Total Expenditure} = \mathbb{N}48 - \mathbb{N}24 = \mathbb{N}24
Consumer surplus is the net monetary gain derived from consumption, calculated as the total utility minus total amount paid.

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Cardinal Consumer Equilibrium and Consumer Surplus Calculation
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Cardinal Utility Analysis and Consumer Equilibrium

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