Robin has the utility function U ( x1 , x2)= 1/ 5 ln ( x1 )+ 4 /5 ln ( x2 ) .

a) Set up the Lagrangian and derive an expression for the marginal rate of substitution and calculate the Marshallian demand for both goods.

b) What will happen to Robin’s share of expenditures on good x1 if the price of good one, p1 , increases. Verify your conclusion formally!