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Budget constraint and offer an intuitive explanation

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An individual has a time endowment equal to T hours. Her time can either be spent in leisure/rest, R, or labour, L, such that T= R+L. She gains utility from rest and from the consumption of other goods, C, as described by a utility function, . For every hour worked, she can obtain a wage rate, w. The price of C equals one. The individual's maximisation problem with respect to consumption and rest, can therefore be represented with the following Lagrangian: La = - (C - w(T-R)).

a) By using the provided Lagrangian, state the individual's budget constraint and offer an intuitive explanation of this constraint.

b) Provide the three associated first order conditions of the consumer's maximisation problem.

c) Solve the consumer's maximisation problem in order to provide an expression for the individual's optimal level of consumption, C*. Show your working.

d) By using your answer to c) also find the individual's optimal number of hours in labour, L*. Show your working.

e) Provide an expression for the individual's utility at her optimal point?

Reference no: EM132526594

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