Mathematical presentation of indifference curve, Macroeconomics

Mathematical Presentation:

Consider the utility function U = U(x1, x2). Differentiating totally, we get the following: dU = U1dx1 + U2dx2 = 0 (as along the indifference curve utility is constant, dU = 0). Therefore, 2242_mathmatical repsentaion.png, which is the slope of the indifference curve. It is negative since U1(x1, x2) >0 and U2(x1, x2) >0 by assumption of non-satiation of all goods. Thus, indifference curve is downward sloping because all goods are non-satiated, choice is continuous, reflexive and complete. Economic meaning All goods are non-satiated i.e., larger  (lower) consumption leads to lager (lower) utility. Hence, for given x2, as x1 increases, utility increases. Thus, to maintain same level, utility must be reduced, which is possible by reducing x2. Hence, as x1 increases, x2 must decreases in order to maintain same level of utility. That is why indifference curve is downward sloping.  

 

Posted Date: 10/26/2012 2:44:54 AM | Location : United States







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