Consider a consumer who consumes two goods and has utility function u(x1,x2)= x2 +\sqrt(x1)....
Question:
Consider a consumer who consumes two goods and has utility function
{eq}u(x_1,x_2)= x_2 +\sqrt{x_1} {/eq}
Income is m, the price of good 2 is 1, and the price of good 1 changes from p to (1+t)p.
Compute the compensating variation, and the changer in consumer's surplus for a change in the price of good 1, holding income and the price of good 2 fixed.
Compensating variation and Equivalent variation:
Due to a change in prices of the goods consumed, a utility receiver by the consumer from the consumption of these goods can be affected. For example, in a two normal good economy and fixed income with monotonic preferences for both goods, increase in the price of one of the goods would lead to less consumption of that good which may decrease the consumer utility. Similarly, with a decrease in the price of one of the goods, its consumption would increase by the law of demand, which can increase the utility received by the consumer. There are three popular methods to measure these effects of the price change on utility - compensating variation, equivalent variation, and change in consumer surplus. Compensating variation refers to the amount of income adjustment that should be provided to consumer after the price change to give him the same level of utility as he was on before the price change. Equivalent variation is a slightly different concept which suggests the amount of income adjustment that should be made with the consumer before the price change to give him the original level of utility as will be after the change in price. Consumer surplus is defined as the difference between maximum willingness to pay for a good by the consumer and the price that he actually ends up paying for it.
Answer and Explanation: 1
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View this answerIn our question, we are provided with a quasi-linear utility function in good 2 given by:
{eq}u(x_1, x_2) = \sqrt{x_1} + x_2 {/eq}
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Consumer Surplus: Definition, Formula & Examples
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