Question: Discuss the relationship between compensating variation and equivalent variation
31 Oct 2022,4:55 PM
Question 1: Discuss the relationship between compensating variation and equivalent variation.
Question 2: Assuming all necessary assumptions hold, discuss why every competitive equilibrium allocation is Pareto efficient but not every Pareto efficient allocation is a competitive equilibrium alloca- tion.
Question 3: Consider a two agent two good pure exchange economy. Can we derive the Pareto set directly from agents’ offer curves? Discuss.
Question 4: Discuss the relationship between a firm’s market power and market failure.
Question 5: Explain why voluntary provision of public goods results in an inefficient provision.
Further assume each agent has an equal share of the firm. Compute a competitive equi- librium (if any exists) which has no additional production of good x2 i.e. total availability of good x2 remains equal to the initial endowment. [15 marks]
Question 7: Consider a two-good exchange economy with a population of N, where there are equal number of men (m) and women (w). Each man has an endowment of 300 units of good 1; each woman has an endowment of 200 units of good 2. Each man has a utility function
- Find the competitive equilibrium allocation. [10 marks]
- Prove that the competitive equilibrium is inefficient, i.e. a discussion is not sufficient. [15 marks]
Expert answer
Compensating variation (CV) is a measure of how much a consumer is willing to pay to maintain a given level of consumption when prices change. Equivalent variation (EV) is a measure of how much a consumer is willing to pay to maintain a given level of utility when prices change.
The two measures are related, but they are not the same. CV captures the changes in purchasing power that result from price changes, while EV captures the changes in utility that result from price changes.
CV = ∆Q/∆P
EV = ∆U/∆P
Where:
∆Q = the change in quantity demanded as a result of a price change
∆P = the change in price
∆U = the change in utility as a result of a price change
Thus, CV measures the change in quantity demanded in response to a price change, while EV measures the change in utility in response to a price change.
CV is always equal to or greater than EV. This is because a consumer is willing to pay more to maintain a given level of utility (EV) than they are to maintain a given level of consumption (CV). This is due to the fact that utility is a function of both consumption and prices, while consumption is only a function of prices. Thus, a given price change will have a larger impact on utility than it will on consumption. As such, consumers are willing to pay more to maintain a given level of utility than they are to maintain a given level of consumption.
The relationship between CV and EV can be illustrated with a simple example. Consider a consumer who is initially consuming two units of a good, each unit costing $1. The consumer has a total utility of 10 (this could be due to the fact that the first unit provides 9 units of utility and the second provides 1 unit of utility). Now, assume that the price of the good increases to $2 per unit.
The CV for this price increase is simply the change in quantity demanded divided by the change in price. In this case, theconsumer will demand one fewer unit of the good, so the CV is (-1)/(2-1) = -1. The EV for this price increase is the change in utility divided by the change in price. In this case, the consumer's utility will fall by 9 units (from 10 to 1), so the EV is (-9)/(2-1) = -9.
As can be seen from this example, CV is always equal to or less than EV. This is because a price change has a greater impact on utility than it does on consumption. Thus, consumers are willing to pay more to maintain a given level of utility than they are to maintain a given level of consumption.
It should be noted that the relationship between CV and EV can change depending on the nature of the good being consumed. For example, if a good is a necessity, then consumers may be more likely to reduce their consumption in response to a price increase than if the good is a luxury. In this case, CV would be greater than EV. However, if a good is a luxury, then consumers may be more likely to reduce their utility in response to a price increase than if the good were a necessity. In this case, EV would be greater than CV.