Utility Function - How to test if "more is better" is satisfied?u(x,y) = 2x^.2 y^.8MUx = .4...

Question

Utility Function - How to test if "more is better" is satisfied?
u(x,y) = 2x^.2 y^.8
MUx = .4 (y^.8)/(x^.8)
MUy = 1.6 (x^.2)/(y^.2)

what is MRS of x for y
and
is mrs diminishing constant or increasing as the consumer substitutes x for y along an indifference curve

Robert · Accepted Answer

Answer: 
Income: M 
Price of textbook (x): px 
Price of ski lift (y):py 
U(x, y) = xy+3x 
MUx = y+3 and MUy = x 
a) 
Budget line: pxx+ pyy = M 
Budget set has been given in the figure below:
b)
c) 
MRSxy = MUx/MUy = (y+3)/ x 
Marginal rate of substitution is defined as the amount of y which the consumer is 
willing to give up for one extra unit of x. 
Slope of budget line in the above figure represents the marginal rate of 
substitution. At optimal point, MRS = slope budget line = price ratio = px/py 
d)  
Indifference curve by definition is defined as the locus of different consumption 
bundle along with utility remains constant. In other words, along indifference curve 
Utility remain consumption but consumption bundle changes. 
Given this definition, for a fixed utility level of  ̅,

Utility Function - How to test if "more is better" is satisfied? u(x,y) = 2x^.2 y^.8 MUx = .4 (y^.8)/(x^.8) MUy = 1.6 (x^.2)/(y^.2) what is MRS of x for y and is mrs diminishing constant or increasing...

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