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3 . Preference Shock in a RBC Model ( 3 0 points ) Assume in a two - period real inter - temporal model, the

3. Preference Shock in a RBC Model (30 points) Assume in a two-period real inter-temporal model, the utility function has the following separable form:
U(C, C^', N, N^')=[log (C)+\eta log (1-N)]_Period 1+\beta [log(C^')+\eta ^'log(1-N^')]_Period 2
where C, C^' are consumption and N, N^' are labor. Parameter \eta (or \eta ^') indicates consumer's preference for leisure (or dislike for labor) while \beta indicates the degree of impatience. Now, analyze the general equilibrium effects of a decrease in \eta and an increase in \beta in the real business cycle model. First, consider the effects of a decrease in \eta . a Explain how it changes the consumer's problem intuitively. How does that affect the labor supply N^s.(5 points) b How does that change affect the good market (supply and demand). Using these results, can you determine the effects of the change on the current output Y, employment N, consumption C, investment I, wage w and interest rate r. Use graphs to illustrate. (5 points) c Consider the effects of this change on the credit market. Suppose after \eta decreases, consumers are smoothing consumption and increasing their savings. Determine the effect on interest rate r and investment I. Use graphs to illustrate. (5 points) Second, consider the effects of an increase in \beta . d Explain how it changes consumer's problem intuitively. How does that affect the labor supply N^s and the consumption demand C^d. Write the related first order conditions to support your argument. (7 points) e How does the increase of \beta influence the labor market and good market (supply and demand). Determine the effects of this change on all equilibrium quantities and prices as above (N, Y, C, I, r, w). Use appropriate graphs to illustrate. (8 points)

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