Lagrange's method and Hicksian demand functions
The formulae for the Hicksian demand functions for goods 1 and 2 derived in
Q1 by using Lagrange’s Method are not valid for very small values of utility u. What are the Hicksian demand functions that are applicable for small values of utility and draw the correct Hicksian demand curves for both goods on a diagram.
Matilda loves sushi (good 1) and miso soup (good 2). Her utility function is given by u(q1,q2) = sqrt(q1) + sqrt(q2). This type of utility function is called the quasilinear utility function. The prices of the goods are p1 and p2.
2a) Draw one indifference curve and several isoexpenditure lines. Show the optimal bundle on the diagram.
2b) Write down the expenditure minimisation problem and solve for the Hicksian (compensated) demand functions q1(p1,p2,u) and q2(p1,p2,u) by using Lagrange’s method.
2c) Is the Hicksian demand curve for good 1 downward slopping or upward slopping?
2d) Is the Hicksian demand for good 1 increasing in utility u? In the price p2 of good 2?