Steady-State Capital-Output Ratio and Determinants of Balanced-Growth Path

The Steady-State Capital-Output Ratio

What is the balancedgrowth path of economy? On the balancedgrowth path, the economy’s capitaloutput ratio, which we write k, is equal to its individual steady-state value k*. We compute this value by taking the share of production which is saved and invested for the future, the economy’s saving-investment rate sand then dividing it by sum of depreciation rate at which capital wears out (written δ), the proportional progress rate (written n) of the labour force, and the proportional growth rate (written g) of efficiency of the labor.

In algebra:

κ* = s / (n + g + δ)

Along the balanced-growth path, level of output for every worker Y/L is set up by raising the steady state capitaloutput ratio k* to the power of growth multiplier (written δ), and then multiplying the outcome by current efficiency of labour (denoted by Et). In algebra:

Yt/ Lt = κ × Et

The steadystate capitaloutput ratio k* is stable (as long as economy’s savingsinvestment share s, its labour force growth rate n, and its efficiency of labor progress rate ‘g’ don’t change). Though, the balanced-growth path level of output per worker isn’t constant. As time passes, the balancedgrowth path stage of output for each worker increases. Why? Because output for each worker Y/L is equal to currenteffectiveness of labor Et times the steadystate capitaloutput ratio k* raised to power λ; and techno-logical growthimplies that efficiency of labor Etdevelops at a proportional progress rate g.

Is the economy at all times on its balanced-growth path? No. But if the economy is not on it, it’s heading in the direction of it.

Why k* Is the Equilibrium Capital-Output Ratio

2488_Equilibrium Capital-Output Ratio.jpg

If the current capitaloutput ratio is equivalentto its steady state value k*, then the share of production saved and invested each year is accurately what is needed to keep capital stock developing at the similar rate as output, and keep the capitalproduction ratio constant.

If the capital-output/production ratio k is below k*, the share of production invested per year (equal to s) is greater than required to keep the capital stock increasing as rapid as output (equal to k(n + g + δ)). The capital-output ratio increases. If the capitaloutput ratio is above k*, the share invested per year (equal to s) is less than required to keep the capital stock increasing as rapid as output (equal to k(n + g + δ)). The capital-output ratio drops. The economy closes a number of the gap between its current place and its steadystate progress path.

The Determinants of the Balanced-Growth Path:

So the steady-state balanced progress path relies on 5 factors:

a) The economy’s savingsinvestment rate, the share of amount produced used to purchase investment merchandise to increase the capital stock (written s)

b) The progress rate of efficiency of labour (written g)

C) The depreciation rate- the proportion of existing capital stock K which wears out or turn intoobsolete each year (written k*).

D) The economy’s labour force progress rate (written n)

E) The economy’s progress multiplier (written k* equal to α/(1-α), where α comes from the production function)

F) The current efficiency of labour- a measure of economy’s ability to employ technology, where “technology” is defined in the largest probable sense to comprise work organization, incentives, and all other issues which affect the ability of economy to use capital to manufacturemerchandise and services. (\WrittenEt).

Factors (1) to (4) conclude the steadystate capitaloutput ratio k* which is then increased to the λ power (factor (5)), and the outcome is then multiplied by current efficiency of labor Et (which is factor (6)).

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