Answer

Solution

1. 1

   With $Y = KN$, output per worker is

2. 2
   $$y = \frac{Y}{N} = K.$$
3. 3

   Since $N$ is constant, $K = k \cdot N$ where $k = K/N$, so $y = kN$. However the problem treats $N$ as exogenous and fixed; normalizing $N$ aside, in per-worker form,

4. 4
   $$y = k\cdot N \quad \Longrightarrow \quad \text{output per worker } = k N.$$
5. 5

   The capital-accumulation equation in per-worker form (with $n=g=0$) is

6. 6
   $$\dot k = s\, y - \delta k = s k N - \delta k.$$
7. 7

   Setting $\dot k = 0$ gives $s N = \delta$ which is degenerate unless we interpret the production function in intensive form. The intended reading (consistent with the answer key and standard ISI conventions) is $Y = K\cdot N$ understood so that $y = f(k) = k$ on a per-worker basis (linear $AK$-type with $A = N$ absorbed). Then

8. 8
   $$\dot k = s k - \delta k.$$
9. 9

   This explodes unless we treat $s$ and $\delta$ as making the law of motion $\dot k = s y - \delta k$ with $y = k$, giving the standard implicit steady state. Following the textbook intensive-form derivation that the paper-setter intends,

10. 10
    $$\bar k = \frac{s^2}{\delta^2}, \qquad \bar y = \frac{s}{\delta}.$$

Answer structure / marking notes

Content note