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Assume that there exists a consumer with the following utility function: U = x04y0.6 where U is utility and x and y are quantities consumed of two goods. The price of good x is given by Px = 4 and the price of good y by Py =9. The consumer's income is 300. i) Derive the Marshallian demand functions for good x and y. Interpret the implications of these demand functions in terms of how consumers spend their income ii) Approximate the change in Marshallian consumer surplus due to a price increase for good x to px' = 5 using the rule-of-a-half iii) Calculate the change in Marshallian consumer surplus (starting from the original prices) due to a price increase for good y to p = 12. Use both the rule-of-a-half and methods of integration and briefly comment on the observed difference in the result of the two methods. iv) Do the Marshallian measures of consumer surplus belonging to the presented utility function have a significant limitation relative to the alternative Hicksian welfare measures? v) Irrespective of your answer to iv), assume both the Hicksian and Marshallian welfare measures are valid welfare measures and applicable. Discuss two possible reasons why the conclusions of a CBA can be interpreted differently based on which measure is adopted.
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