Question 1 (20 points)[10 4+6=20 pts]Sam’s utility function over goods X,and X2 is given by:u(x1,x2)=16(x1)/3+(22)1/3(i)Derive Sam’s Marshallian demands for goods 1 and 2 and show that his indirectutility function is given by:(pm)=m/(+)2/3(ii)Use your results from (i)to derive Sam’s expenditure function and his Hicksiandemand for good 1.(iii)Sam is currently located in a village where his income is S100.and the price ofgood 2 is always p2=1.The supply of good 1 in the village is however rather erratic.Half of the time.its supply is high:at such times its price is pt =4.Rest of the time.its and its nrice at such times is n.1A(iii)Sam is currently located in a village where his income is $100,and the price ofgood 2 is always p2 1.The supply of good 1 in the village is however rather erratic.Half of the time.its supply is high;at such times its price is p1 4.Rest of the time,its supply is low.and consequently its price at such times is p1-16.Before today’s market price (which could be p1 4 with probability 1/2.or p1=16with probability 1/2)is announced.a retailer comes along offering to sell good 1 at afixed price of p.What is the highest price p at which Sam will buy from this retailer rather thanwait to purchase in the market?
