Suppose thats=.4,δ=.3,gN=.03, and gA=.02. In the Solow Growth model westudied in class, the steady state growth...

Suppose thats=.4,δ=.3,gN=.03, and gA=.02. In the Solow Growth model westudied in class, the steady state growth rate of output (Y) is:

A. 0

B. 2%

C. 3%

d. 5%

Solutions

Expert Solution

Steady state occurs when: Change in k = 0 where k = K/(AN) i.e. Capital per effective worker.

In Solow model y = Y/(AN) depends only on k and thus if change in k = 0 then change in y will also 0 and thus y will be constant where y = Output per effective worker, Y = Output.

Thus according to Solow model y = Y/(AN) if constant.

Formula :

% change in (A/B) = % change in A - % change in B

% change in (A*B) = % change in A + % change in B

Here we have to calculate growth rate of Y i.e. % change in Y

We can write Y as Y = (Y/(AN))*A*N

=> % change in Y = % change in [(Y/(AN))*A*N]

Using above formulas we have :

% change in Y = % change in [(Y/(AN))*A*N] = % change in (Y/(AN)) + % change in A + % change in N

As discussed above that Y/(AN) = y is constant => % change in (Y/(AN)) = 0, Here gA = 0.02 => % change in A = 2%; Also gN = 0.03 => $ change in N = 3%

=> % change in Y = % change in (Y/(AN)) + % change in A + % change in N = 0 + 2% + 3% = 5%

Thus, Growth rate of Output(Y) = 5%.

Hence, the correct answer is (d) 5%

Rahul Sunny answered 1 month ago

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