1. (Consumer theory)

 

Consider the utility function u(x) = ?x1 + ?x2 ; and a standard budget constraint: p₁x₁+p₂x₂=I.

 

a. Are the preferences convex? (1 pt)

 

b. Are the preferences represented by this function homothetic? (1 pt)

 

c. Formally write the utility maximization problem, derive the first order conditions and find the Marshallian demand function. (2 pt)

 

d. Verify that the demand function is homogeneous of degree 0 in prices and income. (1 pt)

 

e. Find the indirect utility function. (1 pt)

 

f.  Find the expenditure function by inverting the indirect utility function. (1 pt)

 

g. Verify that expenditure function E(p; u) is homogeneous of degree 1 in prices. (1 pt)

 

h. Check if the expenditure function is increasing in each of the prices. (2 pt)