What is the form of the expenditure function for this

Question

1. Consider preferences defined over the nonnegative orthant by (x₁, x₂) >- (y₁, y₂) if x₁ + x₂ < y₁ + y₂. Do these preferences exhibit local nonsatiation? If these are the only two consumption goods and the consumer faces positive prices, will the consumer spend all of his income? Explain.

2. A consumer has a utility function u(x₁, x₂) = max{x₁, x₂}. What is the consumer's demand function for good 1? What is his indirect utility function? What is his expenditure function?

3. A consumer has an indirect utility function of the form

v(p₁, p₂, m) = m/min{p₁, p₂}

What is the form of the expenditure function for this consumer? What is the form of a (quasiconcave) utility function for this consumer? What is the form of the demand function for good 1?

4. Consider the indirect utility function given by

v(p₁, p₂, m) = m/p₁+p₂

(a) What are the demand functions?

(b) What is the expenditure function?

(c) What is the direct utility function?