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4. Assume that the utility function is U(x, y) = y + B Inx (B>0) x>0;y>0 a. Explain if the commodity x is a good or a bad. If the B was negative, will the type of commodity x be different? Why? (HINT: Considering the sign of the coefficients will guide.) (3 pts) b. Compute the du/ox and dzu/02x. Is the utility function increasing or decreasing in x? Determine the curvature of the utility function in x. (4 pts) c. Assume the consumer maximizes utility subject to a budget constrain. i. Write down the Lagrangean function. (3 pts) ii. Write down the first order conditions for this problem with respect to x, y, and 2. (HINT: Remember the partial derivative) (Do not forget the B is only a kind of a number and, a coefficient) (6 pts) iii. Derive the Marshallian demand functions for good x and good y. Explain how the quantity demanded is related to changes in price and income. (10 pts) iv. Under the assumption of Px =1; determine the income-consumption curve's equation, parametrically. (HINT: You can use the result found in the option above, ni) (4 pts)