Quasi-linear utility (revisited)

Consider a simple quasi-linear utility function of the form U 1x, y2 5 x 1 ln y.

a. Calculate the income effect for each good. Also calculate the income elasticity of demand for each good.

b. Calculate the substitution effect for each good. Also calculate the compensated own-price elasticity of demand for each good.

c. Show that the Slutsky equation applies to this function.

d. Show that the elasticity form of the Slutsky equation also applies to this function. Describe any special features you observe.

e. A modest generalization of this quasi-linear utility function is given by U 1x, y2 5 x 1 f 1y2, where fr . 0, fs , 0. How, if at all, would the results from parts a–d differ if this general function were used instead of ln y in the utility function?