1. With a Utility U(x1, x2) = x1³x2¹, x1 and x2 are the quantity of good 1 and good 2, measure the marginal rate of substitution (MRS) in functional form. What is MRS(1,1)?
2. Following 1, If p1 (price of good 1) and p2 (price of good 2) are $40 and $20 with a budget of $800, what is the optimum consumption bundle (consumer's choice) if the budget must be finished with no saving?
3. X1 and X2 are perfect complements and these 2 goods must be consumed at the scale of X2 = 5X1 (if he buys 1 X1, he must buy 5 X2) where X1 is located on the x-axis. Plot the indifferent map to show.
4. Following 3, consumption sets (X1, X2) including (5; 1), (10; 10), and (15; 4) have passed through the indifference curves and located on the horizontal section of the curves. Show them in the diagram.
5. Following 4, if the utility function U(X1, X2) = min(5X1, X2), show the utility value of the 3 sets as stated in Q4.
6. Following 5, if the new utility is U(X1, X2) = min(X1, 1/5X2), re-calculate the utility level of the 3 sets as stated in Q4.