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    Northwest Florida State College
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Category > Economics Posted 03 May 2017 My Price 9.00

Exponential utility. Assume that infinite-horizon households maximize a utility function of the form of equation

Exponential utility. Assume that infinite-horizon households maximize a utility function of the form of equation (2.1), where u(c) is now given by the exponential form, u(c) = −(1/θ) · e−θc where θ >0. The behavior of firms is the same as in the Ramsey model, with zero technological progress.

a. Relate θ to the concavity of the utility function and to the desire to smooth consumption over time. Compute the inter temporal elasticity of substitution. How does it relate to the level of per capita consumption, c?

b. Find the first-order conditions for a representative household with preferences given by this form of u(c).

c. Combine the first-order conditions for the representative household with those of firms to describe the behavior of ˆ c and ˆk over time. [Assume that ˆk(0) is below its steady-state value.]

d. How does the transition depend on the parameter θ? Compare this result with the one in the model discussed in the text.

 

 

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Status NEW Posted 03 May 2017 12:05 PM My Price 9.00

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