Question

Consider the Solow growth model in which output (Y) is determined by the production function Y_t = 0.2K_t + 0.8L_t, where K and L denote capital and labour used in the production process, and t depicts time. The depreciation is given by δK_t, where δ = 0.2. Saving is given by sY_t, where s = 0.5. Assume that the population does not grow with time. The steady state capital per unit of labour is ______ (in integer).

Answer 1

Correct Answer: 4

To solve the problem using the Solow growth model, we first need to determine the steady state capital per unit of labour (k*). Given the production function Y_t=0.2K_t+0.8L_t, we express output per labour as y_t=0.2k_t+0.8, where k_t=K_t/L_t is capital per unit of labour.

The steady state condition requires that the change in capital per worker is zero, i.e., Δk=0, implying s(0.2k_t+0.8)=(δ+n)k_t. Given n=0 and δ=0.2, the equation simplifies to 0.5(0.2k_t+0.8)=0.2k_t.

Simplifying, we have:
0.1k_t+0.4=0.2k_t
0.4=0.1k_t
k_t=4
This results in a steady state capital per unit of labour, k*=4, which is expected to be an integer value within the given range of 4,4.

Thus, the steady state capital per unit of labour is 4.