In Marshillian surplus analysis, we assumed the marginal utility of money constant which was MUm=1. But in the alternative method we will not keep the marginal utility of money constant due to which we will get a comparatively low consumers surplus than the Marshillian theory of cardinal utility. Hence, we will take Money Income on Y-axis and Quantity of X on X-axis. As a result we will get a budget line MM’ and we will then make an indifference curve tangent to MM’ with the equilibrium point E. In this case AM is the total expenditure of the consumer for the Quantity OQ1.
To find out the maximum quantity the consumer will be willing to pay for OQ1, We draw an indifference curve I0 passing through the point M. This curve is flatter for any given quantity of X, it shows that when the money income increases Marginal utility for money falls .
Money (Y) = MUm
Now the consumer will be willing to pay BM for the Quantity OQ1 rather than do without it and the consumer surplus is the difference B’E.
To compare Marshillian analysis and the alternative measure, we will now make a new indifferenc curve I0’ parallel to I0,where we will keep marginal utility of money constant. Under these assumptions Marshillian consumer surplus is EA”which is larger than E’B(where Money income is inversely proportional to MUm)
the quantity of X is same for both the analysis, hence MUx is same or constant for both at these two points. However the income left to spent on other goods OA is larger than OB at point B’.
hence the marginal utility of money is higher at point B’ then at point E. So we will conclude that slope of I0 is smaller than I1
Slope I0 at B’ = MUx < MUx = slope of I1 at E
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