At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
20,40 I GUESS BUT I M NOT SURE.
can u explain how did u get dat
since solving utility function we get 2x=y, that means the given consumption is not an optimal consumption. thus you cannot use optimization in this problem. thus you cannot solve it.
Each graph is not meet.
U = min(4x, 2x+y) Your example: x = 15, y = 10 Then, U(15,10) = 40 Question: Whats py = ? in order to satisfy U(x,y) = 40 Solution: We assume that we can find py because we assume that the person is maximizing his utility for given prices. First, you must know that px.x + py.y = budget. You want to know what is the price of the good y that allows the person to buy many combinations of goods with the same utility U(x,y)=40 Let's think about the conditions under x and y that makes U(x,y)=40: 1)There are three cases were Utility is never 40: If x < 10, U < 40 if x > 20, U > 40 if x = 10, y<20, U < 40 2)If x = 10, y>20, U(10, y) = 40 always. We cant use this case to find py. There is no restriction under y that we can use to find py. 3)If 10 <= x <= 20, then we must have 2x + y = 40 in order to make U (x, y) = 40 In this case, 0 <= y <= 20, and we now can make assumptions under py. Lets solve for this case: We want to max: px.x + py.y subject to some conditions: x=>10 x<=20 2x+y=40 So, we have (for px =10): L = 10.x + py.y -l1(2x + y - 40) deriving: dL/dx = 0: 10 - l1.2 = 0 -> l1 = 5 dL/dy = 0: py - l1 = 0 -> py = l1 -> py = 5 Biding condition dL/dl1 = 0: 2x+y-40=0 We find that py = 5 is a condition to make U(x,y)=40, if 10 <= x <= 20, 0 <= y <= 20. Now, we'll have the following budget, price and quantities in your example: x=15 y=10 px=10 py=5 py.y + px.x = 5.10 + 10.15 = 200 You can now test and see if py=5 is ok for the budget 200: Ex1) All these cases U(x,y)=40 For 10 <= x <= 20 and 0 <= y <= 20 x=20 y=0 -> px.x + py.y = 200 x=19 y = 2 -> 10.19 + 5.2 = 200 x=18 y = 4 -> 10.18 + 5.4 = 200 .. x=11 y = 18 -> 10.11 + 5.18 = 110 + 90 = 200 x=10 y = 20 -> 10.10 + 5.20 = 200 Ex2) For x>20 or x<10, or x=10 and y>20, U is different from 40. Ex4) Now, suppose the price was different from py=5, Think that py=20 Then, your budget, for px=10, x=15 and py=20, y=10 would be: budget: 10.15 + 20.10 = 350 But, if you had 350, you could buy only x goods: x=35 y=0 But in this case, your utility would be U(35,0)= min(140, 70) = 70 And you would be in a better position… In the other hand, if py = 5, then your budget is 200, 10.x + 5.y = 200 and if you do the same thing, only buys x: 10.20 + 5.0 = 200 -> U=40 See that from the conditions we have described earlier, the only way this consumer could get more utility would be if he get x>20. But since px=10, and the budget is 200, it is impossible. He can only get x=20. Note that all the cases where py is not 5, you can reorganizer your consumption in order to make more utility than U=40, or maybe you can never get the same utility U=40. But if you could do that, then you would not being rational at first place.. And note that we assumed that the person was maximizing his utility for given prices.
Why is u=40?