Marshall attempted to derive consumer's equilibrium in a one commodity framework. For this purpose he assumes (a) Utility is cardinally measurable. (b) Marginal utility of money remains constant. (c) Law of diminishing marginal utility (DMU) for every goods i.e. Demand for any single commodity is satiable and two different commodities can never be perfect substitute of each other. (d) Utility functions are independent. (e) Consumer is a price taker in the market. (f) Consumer must be rational in nature. Marshall considered that the buyer consumes only one commodity X, whose price is P(x). He consumes x1 amount of X out of his money income M. By consuming x1 units of X consumer gets you(x1) units of utility for which he sacrifices monetary utility of λP(x1)x1, where λ = dU/dM i.e. Marginal utility of money). So, consumer's net utility is N(x1) = you(x1) – λP(x1)x1 Limitations: In spite of some good attempts, Marshallian theory is not free from criticism. These are: (a) Cardinal measurement of utility is unrealistic. (b) As the assumption of constancy of MU money is impractical, it is difficult to derive law of demand from Marshallian analysis. (c) Law of DMU may not hold good for everything like intoxicants, stamp collection. (d) As it ignores the interdependent utility function it can't explain substitutes and complements. (e) Giffen Paradox can't be explained by Marshallian theory as it considers zero income effect (f) This theory is only applicable for a one-commodity framework.
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A consumer of two goods faces positive prices and has a positive income. His utility function is you = (x1,x2) = max [ax1, ax2 ] +min [x1,x2] where o