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(10pts) In the consumer’s optimization problem, MRSl,c is given by (βC) / (1−β)l. The consumer faces...

(10pts) In the consumer’s optimization problem, MRSl,c is given by (βC) / (1−β)l. The consumer faces a typical budget constraint, C = w(h − l) + π − T. Find algebraically the consumer’s optimal choice in terms of C and l.

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Answer #1

MRS is given by

Differentiate C with respect to l in order to get the slope of the budget line

In equilibrium,

slope of IC = slope of budget line

MRS = w

Put the value of l in the budget equation

From this we can get the optimal value of l.

C* and L* is the optimal choice.

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