Show that the share of income spent on a good x is where E is total expenditure. Empirical work in demand theory focuses on income shares. For any good, x, the income share is defined asIn this problem we show that most demand elasticities can be derived from corresponding share elasticities. a. Show that the elasticity of a good’s budget share with respect to incomeis equal toInterpret this conclusion with a few numerical examples. b. Show that the elasticity of a good’s budget share with respect to its own priceis equal toAgain, interpret this finding with a few numerical examples. c. Use your results from part (b) to show that the ‘expenditure elasticity’ of good x with respect to its own price is also equal to d. Show that the elasticity of a good’s budget share with respect to a change in the price of some other goodis equal to e. With a CES utility function, the share of income devoted to good x is given bywhere k= δ/(δ −1)=1− σ. Use this share equation to prove Equation 5.56: Hint: This problem can be simplified by assuming

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