(Solved):   NOTE: please disregard the strike-through, I still need 1.1 answered 1. Exercise 1 (3,5 poi ...

 

NOTE: please disregard the strike-through, I still need 1.1 answered

1. Exercise 1 (3,5 points). An individual consumes two goods X and Y and his/her utility is given by the following function: U (x, y) = ln(1 + x) + ln(1 + y) where x is quantity of good X and y is quantity of good Y. Good X has a price pa = 5 and good Y has a price pye. The total budget that the consumer is willing to spend is exactly 50 monetary units. 1.1 (1 point) Is the consumer's utility function homogeneous? Prove/argument your answer. 1.2 (0,25 points). Formulate the utility maximization problem subject to a budget constraint and write the Lagrangian function for this problem. You may ignore non-negativity constraints and treat the problem as with one equality constraint. 1.3. (1 points). Find the values of x, y, and of the Lagrange multiplier (A) that solves the problem formulated in (1.2) (Use the Lagrange multiplier method). 1.4. (0,75 points). Verify that the critical point you have found is a maximum and not a minimum. 1.5. (0,5 points). How much the consumer's utility will increase if consumer's budget increases by 1 monetary unit?