Final answer:
The correct steady-state expression in the Solow model with a government budget surplus is sf(k) = (n + d + g)k, where s is the saving rate, f(k) is the production function, d is the depreciation rate, n is the population growth rate, and g is the government budget surplus.
Step-by-step explanation:
The question pertains to identifying the correct expression for the steady-state capital-labor ratio when a government budget surplus is considered within the Solow growth model. In the Solow model, the steady state is when the economy's capital stock is unchanging over time, meaning investment is exactly enough to cover depreciation and the expanding labor force. Let's denote saving rate by s, the production function as f(k), the depreciation rate as d, population growth rate as n, and government budget surplus as g. The steady state condition in this augmented Solow model with government budget surplus can be expressed as (1), which reflects that savings plus the government surplus finance investment needed for maintaining a constant capital-labor ratio in the face of depreciation and population growth.
The correct steady-state expression that accounts for the government surplus in the Solow model is:
sf(k) = (n + d + g)k
This equation states that the amount of saving multiplied by the output per capital, sf(k), is used to cover the losses from depreciation and population growth (n + d), as well as the government's budget surplus g, times the capital per worker (k). If the amount saved and the government surplus is exactly equal to what's needed for those purposes, the economy is in a steady state. Therefore, the correct expression for the steady state capital-labor ratio including a government budget surplus is option B: sf(k) = (n + d + g)k.