Question

For each of the following utility functions: Calculate MUx, MUy, MRSx,y; determine whether or not the property of “more is better” is satisfied for both

goods; determine whether or not the marginal utility of x diminishes,
remains constant, or increases as the consumer buys more x; determine whether or not the marginal rate of substitution diminishes, remains constant, or increases as the consumer substitutes x for y along an indifference curve; and sketch the graph of a typical indifference curve.

(a) U(x,y)=(xy)^1/2

I really need help with the indifference curve part of the question!

Answer 1

U = (xy)^1/2 = x^1/2y^1/2

y^1/2 = U / (x^1/2)

Squaring,

y = (U²) / x [Equation of indifference curve]

Utility remains constant along an indifference curve (IC) while x and y varies along it. So, for purpose of drawing the IC, let us (hypothetically) assume that U = 10. Then,

y = 100 / x

We may develop following data table:

x	y
1	100
5	20
10	10
20	5
25	4
50	2
100	1

Graph of IC:

This is the generalized shape of IC for given utility function, which you can draw without any specific U and x-y values.