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M = Σ xi pi
i =1
This is a mathematical problem that can be solved using a technique called LaGrange
Multipliers. Solving this problem is equivalent to finding the appropriate levels of each xi to
maximize happiness given the prices of the goods and the amount of money available. In
simple terms, the consumer has a fixed amount of money to allocate among many different
products in a way that gets the greatest level of happiness from the expenditure. The
mathematical conditions necessary to maximize U, subject to the budget constraint M are
Ui / Uj = P i/ Pj for all i and j
Where Ui is ∂ U/ ∂xi , the marginal utility of all the ith good. The marginal utility of every
good divided by the marginal utility of each other good is equal to the relative price ratio of
the goods. Alternatively, Ui / Pi = Uj / Pj By dividing both sides by Pi and multiplying both
sides by Uj. The second expression is analytically equivalent to the first but the interpretation
is slightly different; the extra happiness a consumer gets from every unit of money spent must
be the same for all goods. Regardless of the equation, to maximise utility subject to a budget
constraint, the consumer purchases an amount of each good such that the ratio of the marginal
utilities is equal to the ratio of their prices. The ratio of the marginal utilities of the two
products is the consumers’ personal evaluation of one product versus the other, the
consumers’ own feelings about the merits of one good compared to the other. The price of the
first product p1 divided by the price of the second p2, is the price of the first good in the
market place in terms of the second good. It represents the sellers’ relative evaluation of one
good versus the other. Since the consumer can choose the quantities to buy, equilibrium is
only achieved when the consumer chooses goods in proportion that makes the consumer’s
evaluation equal to the seller’s posted evaluation. The ratio of the marginal utilities of the two
goods must equal the ratio of the prices. In essence, to maximise utility the consumer must
select goods from a limited budget in such a way that the personal evaluation of the products
is the same as the market evaluation. Otherwise there is a profit opportunity, a chance for the
buyer to increase happiness. The ratio of the marginal utilities of any two goods is called
marginal rate of substitution. Utility maximisation requires that the consumer arrange
expenditures so the marginal rate of substitution is equal to the ratio of prices for all goods.
Transaction Utility Theory
The basic tenet of the theory is that a consumer’s notion of value depends not only on the
value of goods and services available relative to the respective prices, but also on the
perception of the quality of the financial deal. 92 This theory was developed based on the
Prospect Theory as explained by Khanmen and Tversky. 93 Later the concept of Transaction
Utility was modelled depending on the difference between the selling price and reference
price. 94 To explain this he postulated reference price, which is the amount of money that a
customer expects to pay for a good or service. It is suggested that any purchase occasion is
associated with two utilities: acquisition utility and transaction utility. Acquisition utility
represents the economic gain or loss from the transaction. Where as transaction utility is
associated with purchase or (sale) and represents the pleasure (or displeasure) of the financial
deal per se and is function of the difference between the selling price (p) and the reference
92
Thaler, Richard (1983), “Transaction Utility Theory”, Advances in Consumer Research, Vol. 10, pp.
229 – 232.
93
Khanmen, Daniel and Tversky, Amos (1979), “ Prospect Theory: An Analysis of Decision Under
Risk”, Econometrica, Vol. 47, March, pp. 263 – 291.
94
Thaler, Richard (1985), “Mental Accounting and Consumer Choice”, Marketing Science, Vol. 4,
No.3, pp 199-214.