Suppose that the utility function for two commodities is: U(q1, q2) = q1α q2(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) = q1α q2β?

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Suppose that the utility function for two commodities is:

U(q1, q2) = q1α q2(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) = q1α q2β?

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