Question

3. Suppose the utility function for two goods, x and y, is: U = U(x,y) = xłyż. a. Graph the indifference curve for U = 10. b. If x = 5, what must y equal to be on the U = 10 indifference curve? What is the MRS at this point? c. Derive a general expression for the MRS for this utility function. Show how it can be interpreted as the ratio of the marginal utilities. d. Does this individual have convex preferences? e. Consider the transformation V(x,y) = [U(x,y)]3. Show that for this transformation, the V = 1000 indifference curve has the same properties as the U = 10 curve calculated in parts a and b. What is the general expression of the MRS of this transformed utility function?

Answer 1

X and yes 700h e - 011 i sitt EXY24/ 2 D Y a I of utility U=ION AN Utility function for two goods U = V(x, y) x 2 y ² Now, when level of utility - 1 then, 10= x/2 g / acond When, X= 1, y = 10210 When X=2, 10=21²4 / =) 10 = 1.414/2 ) y = 50.. Now we can Placing x on yutical anis graph the indiffuance Canuc for U = 10 the horizontal anis and. Y on the 5070 -U-10 Scanned CamScanner

2 It azs, and 1= 10, whaN NHA Utility fruction, U= x/y / marginal utility of n = au £x /4/2=mUX and marginal utility of y d 2 x 22 y=/.. rot ay 3 V- bu NAM - Moy!. ..Huce MRS - MUX. xi-th y/2AM moy Thyla NOW, when n=5, and U=10, then y will be? 10 = (5 292 y 12. Det - y - 19.98 Now MRS at x-5 and y= 19.98 will be? - MRS. Y 19.98 - 3.99 S NAVN) 2 Now, U = x ² y ½ h taking total differentiation & du at x ²4% d x t £u/y / dy Now, along an inditfuence cmic change in utility do=o. Hace Scanned with CamScanner

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