Consider a population of households who choose a consumption bundle q1, . . . , qJ to maximize preferences, represented by a utility function of the form

4 Consider a population of households who choose a consumption bundle q1,.. . ,qj to maximize their preferences, represented by a utility function of the form (called a Stone-Geary utility function), subject to the budget constraint 3-1 where p denotes the market price of the jth good and x denotes money income. (a) Show that treating money income as a random variable X, the h as random variables such that Ebh X-lih, and letting yh = Phqh gives a linear model for the conditional mean of y, given X = of the form (b) Interpret the model parameters and the random error in this model c)Comment on your results 4 Consider a population of households who choose a consumption bundle q1,.. . ,qj to maximize their preferences, represented by a utility function of the form (called a Stone-Geary utility function), subject to the budget constraint 3-1 where p denotes the market price of the jth good and x denotes money income. (a) Show that treating money income as a random variable X, the h as random variables such that Ebh X-lih, and letting yh = Phqh gives a linear model for the conditional mean of y, given X = of the form (b) Interpret the model parameters and the random error in this model c)Comment on your results