Suppose that the utility function for two commodities is: U(q 1 , q 2 ) = q 1 α q 2 (1-α) Let the prices of the two commodities be p 1 and p 2 and let the consumer’s income be M. (1) Check the...

Suppose that the utility function for two commodities is:

U(q₁, q₂) = q₁
^αq₂
^(1-α)

Let the prices of the two commodities be p₁ and p₂ and let the consumer’s income be M.

(1) Check the properties of marginal utilities. In particular, check whether it satisfies diminishing marginal utilities.

(2) Assuming all income is spent on these two commodities, derive the demand curves for the two commodities.

(3) What happens if U(q₁, q₂) = q₁
^αq₂
^β?