# Implications for Labour after a Productivity Shock, RBC Model

I am trying to understand the implication for labour after a one time productivity shock where $$A_t$$ follows a AR (1) process with persistence $$\rho_A=0.95$$. It is stated the following : labour initially jumps up above st.st. by about 0.35% and after 15 periods falls below st.st. The return to work $$w_t$$ (substitution effect) is not sufficiently offset by the drop in $$C_t^{-\sigma}$$ (wealth/income effect) as a rising interest rate induces households to save. I don’t really understand this paragraph.

After optimisation for the firm, I have the following equations: $$r_t=\alpha(\frac{A_tL_t}{K_t})$$ and $$w_t=(1-\alpha) (\frac{K_t}{A_tL_t})^\alpha A_t$$ and for the household theEuler Equation $$C_t^{-\sigma}=\beta E_tC{t+1}^{-\sigma}[r_{t+1}+(1-\delta)]$$ and labour supply $$\chi L_t^{\gamma-1}=C_t^{-\sigma}w_t$$.

• What is the question? Which part of the paragraph you don’t understand?
– 1muflon1
Apr 25 '20 at 12:37