Question

On the "calculations" sheet, I have plotted an indifference curve, derived from the utility function (x*0.5)*(y*0.5).

Follow the instructions, also listed in the "Questions" sheet in the excel file, and answer the following 7 questions.

Instructions: Given the current income and prices, the allocation of x and y is not optimal. You may change any of the boxes that are highlighted (e.g. income, Px, Py, or X). You cannot change the consumption of y. This is found by spending all of the remaining income. As you change variables, observe what happens to consumption of good y, marginal utility per dollar of each good, and total utility. Also, observe what happens to the indifference curve diagram on the "calculations" sheet.

Answer the following questions:

1. Given the initial setup (income = $20, price of X = $1, price of Y = $1, and X = 5), utility is not maximized. How can we tell this by looking at marginal utility per dollar? How can we tell this by looking at the graph?
2. Given the relationship between the marginal utility per dollar of x and y, how should you change the level of x to improve utility? Why?
3. Try improving utility by changing x in the direction you state in question 2. Were you correct? If you were, total utility should increase. If you weren't, try moving x in the other direction.
4. What happened to the marginal utility per dollar of X as you went from 1 to 3? Why?
5. What happened to the marginal utility per dollar of Y as you went from 1 to 3? Why?
6. Keep changing the value of X until a maximum is reached. How do you know when this has occurred?
7. Change the income. What happens to the budget constraint when you do this?
   Calalations Sheet ++ 6 ਨੂੰ + + + + - Budget Line Indifternce curve -Bundle ਸ s 3) ੫੦ 13 Co X Income 20 PX 1 (੧ x = Y 26 A0x / 3 0 2 ੧ |91|y40. 7 Utility 8.66025
   

Answer 1

Solution u= x.s you muxa 054_305 muy so y = 05 (7) 095 MU 0.5 -0.288 1.732 At initial set up ice incerne = $ 20 and X-5 Y=15 mux = 0.5 (5) 305 x 30.5 -0.866 muy: 05 () 05 So - 00532 = 0.288 0.86 Px = Py = $1. At equilibrium mux . I but 0.866 F 0.288 Px Py hence utility is not maximized from the graph, utility is not maximized because budget constraint not tugent to indifference curve. In order to improve utility, mux should decrease and for that level of x should increase. This is due to law of diminishing marginal utility (as x increases mure decreajes). Now suppose x is increased from 5 to 8. Then y will be 12. Initial utility = 50.5x150.5 = 8.66 New utility = 80sx 125 = 9.79 we see that utility is increasing New mus at x=8 is os (12) 0 3 2 0.612 muy at 228, 412 is 0.54%) 0.50.408 • Pc due the mux is boor decreasing and muy is increasing to law of dinning diminishing marginal utility.. maximum utility is reached at x=10 and y= 10 because u= 100 x 100 = 10 and mux = 0.5 muy=0.5 Thus mux pe = open=0.5 which is equilibsium condition. with change in income, budget constraint will shift.