# Economics simplification of stochastic transition of capital

I'm taking an macro-econ paper and I can't seem to work out the following simplification. Basically somehow by combining equation 4.14 and 4.15 we get 4.16.

$y_{t-1}$ denotes the previous year's output per capita, so $ln(y_{t-1})$ should be $a*ln(k_{t-1}) + ln(A)$, can't seem to explain the process even though I know the solution!

### Equation 4.14

$$ln(k_{t+1}) = b + a*ln(k_t) + ln(A_t)$$

### Equation 4.15

$$ln(y_t) = a*ln(k_t) + ln(A_t)$$

### Equation 4.16

$$ln(y_t) = ab + a*ln(y_{t-1}) + ln(A)$$

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$$\ln k_{t+1}\stackrel{(4.14)(4.15)}{=}b+\ln(y_t)\implies\ln(y_t)\stackrel{(4.15)}{=}a\cdot(b+\ln(y_{t-1}))+\ln(A_t)$$