Consider the Utility Function $u \left( x _ { 1 } , x _ { 2 } \right) = \ln x _ { 1 } + x _ { 2 } ^ { 1 / 2 }$

Essay

Consider the utility function $u \left( x _ { 1 } , x _ { 2 } \right) = \ln x _ { 1 } + x _ { 2 } ^ { 1 / 2 }$ .(Explain all your answers.)
a.Derive the function for the marginal rate of substitution.
b.Do the tastes represented by this utility function satisfy diminishing MRS?
c.The marginal utility of a good is defined as the change in utility from additional consumption of that good (holding all else constant).Derive the marginal utility of
$x _ { 1 }$ and
$x _ { 2 }$ .
d.Why does an ordinal approach to utility theory not any attention to what you derived in (c)?
e.Why does an ordinal approach to utility not treat the marginal rate of substitution the way it treats the marginal utility concept?