Advanced Mathematical Methods for Economics, Economics (H) Sem 3, Paper Solution 2023 Q13,

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Topic Discussed : Advanced MME 2023 Paper Solutions Q13
Q. An individual purchases quantities a, b and c of three different commodities whose prices are p, q, r respectively. The consumer’s exogeneous income given is M where M greater than 2p. The utility function is defined as U(a, b, c) = a + ln(bc).
(a) Using the Lagrangean method, find the consumer’s demand for each good as function of prices and income.
(b) Show that the ratio between marginal utility of a commodity and its prices per unit must be same for all the commodities.
(c) Show that the expenditure on second and third good are always equal.

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