1. Consider a three-period endowment economy, where the agent has endowments Yt, Yt+1, and Y+2. for...

 

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1. Consider a three-period endowment economy, where the agent has endowments Yt, Yt+1, and Y+2. for each period. Assume that the endowments have two components: a permanent (YP) and a transitory component (Y). For example at time t, the endowment of the agent can be represented as: Y = Y+YN Further assume that the permanent component of endowment grows with a gross rate of Gy. The household has the following utility function at time t: U (Ct) = -(C+ - C) where C is the bliss point of consumption (Caution: It is not the optimal consumption level) and a is a parameter (I let you determine the sign of it). (a) Derive the intertemporal elasticity of substitution for the household. In your answer make sure define it and give proper economic intuition. (b) Derive the intertemporal budget constraint of the household. Give proper economic intuition. (c) Derive the relevant Euler equations. Give proper economic intuition. (d) Now assume that (1+r) = 1 and derive the consumption function. Give proper economic intuition for the function. (e) Derive the MPCs out of permanent income and transitory income. Compare the values, and explain the result economically. 1. Consider a three-period endowment economy, where the agent has endowments Yt, Yt+1, and Y+2. for each period. Assume that the endowments have two components: a permanent (YP) and a transitory component (Y). For example at time t, the endowment of the agent can be represented as: Y = Y+YN Further assume that the permanent component of endowment grows with a gross rate of Gy. The household has the following utility function at time t: U (Ct) = -(C+ - C) where C is the bliss point of consumption (Caution: It is not the optimal consumption level) and a is a parameter (I let you determine the sign of it). (a) Derive the intertemporal elasticity of substitution for the household. In your answer make sure define it and give proper economic intuition. (b) Derive the intertemporal budget constraint of the household. Give proper economic intuition. (c) Derive the relevant Euler equations. Give proper economic intuition. (d) Now assume that (1+r) = 1 and derive the consumption function. Give proper economic intuition for the function. (e) Derive the MPCs out of permanent income and transitory income. Compare the values, and explain the result economically.