QUESTION ONE (16 pts). Suppose a consumer with income m has a utility function over two goods, u (91, 92) = = In(91) + - In(q2), priced at p1 and p2, respectively. (i) (1 pts). Define the budget constraint of the consumer. (ii) (1 pts). Write the utility maximization problem of the consumer. (iii) (4 pts). Derive first-order necessary conditions for a utility max. (iv) (6 pts). Derive the Marshallian demand functions and indirect utility function of the consumer. X + 14 ptsto Undergraduates only. Draw the indifference curve and budget line associated with these functions at this maximum point. How do the budget line and utility- maximizing indifference curve change with an increase in income m? (vi) (4 pts). Masters students only. Prove that the utility function above as well as all other monotonic, continuously differentiable bivariate utility functions u( q1, q2) exhibit downward-sloping indifference curves