Question

Solow model without ideas accumulation

Q. Let's consider some comparative statics

(change in one exogenous variable while keeping the other exogenous variables constant).

What is the long run (steady-state) effect of a permanent reduction in the depreciation rate on the stock of capital, capital per worker, GDP, and economic growth?

Explain your reasoning using the relevant diagram

Answer 1

Answer

Solow's exemplary model is a magnificent bit of work, all that you could ask of a hypothesis. It

takes on the greatest inquiries—e.g., what decides ways of life, why a few

nations are rich and others poor. The contention depends on standard presumptions, yet it

shows up at not in the least clear ramifications. It fits the realities well. To such an extent that Solow's

model sets the structure for all genuine experimental investigations of development and efficiency.

Solow features specialized change—for example efficiency development—as the way to since quite a while ago run

development of per capita salary and yield. Amassing of capital makes development in the

since quite a while ago run distinctly to the degree that it encapsulates improved innovation.

To build up the model, we start with the fake circumstance of steady populace and

consistent innovation, and afterward, in steps, permit populace to develop, and innovation to improve.

Production function

The aggregate production function is:

  Y = F(K,L)

With steady comes back to scale we can change this into a capacity relating yield for each

laborer to capital per specialist.

  y = f(k)

where y = Y/L, and k = K/L.

Accumulation of capital

The adjustment in the capital stock per laborer (known as capital extending) is equivalent to per specialist net venture short devaluation:

∆k = i - δk.

Overlook government for present purposes, with the goal that speculation is equivalent to private division sparing:

  i = S/L = s Y/L = sy.

where s is the sparing proportion (the MPS is for effortlessness equivalent to the APS). This we can write as far as the creation work:

i = s f(k).

The corresponding sparing salary relationship infers that this speculation work resembles a downsized creation work.

Along these lines, both yield per specialist and speculation per laborer are an expanding capacity (at a diminishing rate, on account of decreasing MPK) of capital per specialist.

To show capital amassing on the chart, we center around the I = s f(k) bend, and
present deterioration.

Deterioration is a straight-line capacity of k. Sooner or later, call it k*, the deterioration line cuts through the leveling speculation bend. To one side of k*, net speculation is certain (net more noteworthy than deterioration), to the correct negative. Venture along the straight line just keeps capital laborer steady, so we can see the line as an equal the initial investment venture plan.

At the end of the day, to one side of k*, k is expanding, to one side, k is diminishing. In this manner k* is the consistent state level of capital per specialist—the since a long time ago run balance of the economy.

Capital per powerful laborer is in balance at k*, for indistinguishable reasons from in the steady innovation case. An expansion in g, much the same as an increment in δ or n, pivots the equal the initial investment line upward.

Capital per real specialist develops at rate g, as outputs per laborer (the capital/yield
proportion is along these lines stable).

Steady state with technological progress

		Growth rate
Capital per effective worker	k = K/ (E × L)	0
Output per effective worker	y = Y/ (E × L) = f(k)	0
Capital & output per worker	Y/L & K/L	g
Total output	Y	n + g

The dispersion of salary among capital and work stays consistent along the steadystate development way. The arrival on capital (in this model, the loan cost) is steady, while
the stock develops at rate n+g. The pay rate develops at g, the work power at n, so the compensation bill likewise develops at n+g

Steady-state distribution of income

	Golden Rule Level	Growth rate
Total income	Y	n + g
Return on capital (interest rate)	MPK = n + g	0
Total return to capital	MPK K	n + g
Wage rate	MP L	g
Total return to labour	MPL L	n + g
Capital share	α = MPK K / Y	0
Labour share	1 − α	0

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