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EC2066 Assignment 1
Deadline: 4
th November
1) A consumer spends his income on X and Y. His preferences are represented by the utility function
Suppose the price of Y is 1, the price of X is p and the consumer’s income is M.
a) Does the consumer’s preferences exhibit diminishing MRS? Derive the consumer’s demand for X and Y.
b) Suppose M = 10. The initial price of X is 0.5, and then the price falls to 0.2. How much does the consumer’s demand for X change? How much of this change in demand can be attributed to income effect and how much to substitution effect?
c) Consider the change in price of X from 0.5 to 0.2. Calculate the CV and the EV.
2) Jean spends her income on fuel for heating her house and other goods (“other goods” represents a composite of all other goods). The price of the composite of other goods is 1, and the price of heating fuel is p. The government decides to put a tax of t per unit on heating fuel.
i) Suppose the government asked for a lump-sum tax that would leave Jean with the same level of utility as after the per-unit tax. Would Jean pay more or less tax under the lumpsum tax scheme compared to the per-unit tax scheme? Explain using a diagram.
ii) Suppose the per-unit tax has been imposed. The local council starts a scheme to help certain residents with their fuel tax bill. Jean qualifies for the scheme, and she receives extra income equal to the amount of tax she pays. Would this make Jean’s utility as high as her pre-tax level of utility? Explain using a diagram.