The Engel expenditure curve relates a consumer's expenditure on a com- modity to his or her total income. Letting Y = consumption expenditure on a commodity and X = consumer income, consider the following models:
Yi = β1 + β2 Xi + ui
Yi = β1 + β2 (1/Xi ) + ui
ln Yi = ln β1 + β2 ln Xi + ui ln Yi = ln β1 + β2 (1/Xi ) + ui Yi = β1 + β2 ln Xi + ui
Which of these model(s) would you choose for the Engel expenditure curve and why?
(Hint: Interpret the various slope coefficients, find out the expressions for elasticity of expenditure with respect to income, etc.)