Assume that Sam has following utility function: U(x,y) = 2√x+y.
Assume px = 1/5, py = 1 and her income I = 10.
(e) Draw an optimal bundle which is the result of utility maximization under given budget set. (Hint: Assume interior solution). Deﬁne corresponding expenditure minimization problem (note the elements for expenditure minimization problem are (i) objective function, (ii) constraint, (iii) what to choose).
(f)Describeaboutwhatthedualityproblemis. Deﬁnemarshalliandemandfuction andhicksiandemandfunction. (Hint: identifytheinputfactorsofthesefunctions.)
(g) Consider a price increase for the good x from px = 1/5 to p0x = 1/2. Find new optimal bundle under new price using a graph that shows the change in budget set and the change in optimal bundle when the price increases.
(h)Following(g),ﬁnd the utility level of optimal bundle under old price. Similarly, ﬁnd the utility level of optimal bundle under new price.
(i)Describe substitution effect and income effect with a graph for the price change from px = 1/5 to p0x = 1/2.
(j) Describe three different measures (from the lecture) to evaluate welfare change from a price change.
(k) Following (g), show that these three measures are the same using a graph (or an algebra).