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  3. 2 20 marks consider the model of lecture note 1...

Question: 2 20 marks consider the model of lecture note 1...

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2. (20 marks) Consider the model of Lecture Note 1, and for simplicity assume theres no go- vernment,so that g -0. For each of the following utility functions U(c,l) (we are ignoring public goods g here), verify that it satisfies the conditions (on the first and second derivatives) for strict increasingness, preference for variety, and normality of c and Next, ignoring the NNCs (i.e., the constraints that c20 and0S1), solve the household pro- blem of maximizing U subject to the budget constraint c = u (1-1) +r. Finally, recall that the NNCs are non-binding if, when we solve the households problem ignoring them, they are nonetheless satisfied. Under what conditions (if any) on the exogenous variables (ie, w, π, and any preference parameters) are the NNCs non-binding? (a) (10 marks) U(el)-1-σ + a-, where a, σ > 0 are parameters. (b) (10 marks) U(c,l)---e-, where e is the mathematical constant, and a,b>0

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