Question

Draw a diagram where you display output Y on the y-axis and physical capital K in the x-axis. Draw all the relevant curves for analyzing the Solow-Swan model and explain in words what each of those describes. Assume that the economy starts at steady state and is then hit by a shock that increases the saving rate. Point out what the new steady state levels of capital and output are. Do they increase or decrease? Why? Explain in words the process that leads to the new steady state.

Answer 1

Draw a diagram where you display output Y on the y-axis and physical capital K in the x-axis. Draw all the relevant curves for analyzing the Solow-Swan model and explain in words what each of those describes. Assume that the economy starts at steady-state and is then hit by a shock that increases the saving rate. Point out what the new steady-state levels of capital and output are. Do they increase or decrease? Why? Explain in words the process that leads to the new steady state.

Solow - Swan Diagram:

We assume a closed economy with no government intervention

output per worker, y = c + i

c = consumption per worker

i = investment per worker

Also, c = (1-s)y

So, y = (1-s)y + i

i = sy > i = sf(k) : concave-shaped investment curve below output curve

Depreciation is directly proportional to capital per worker k

So, depreciation = k

It is the straight line drawn from origin.

y = f(k) is a concave-shaped curve representing the production function exhibiting diminishing returns to capital.

The depreciation line intersects the investment curve at point A which is called the steady-state point. corresponding k* and y* are the steady-state capital an output per worker.

Impact of the Shock:

Old steady state occurs at point A with k1* and y1*.

The savings rate is the key determinant of k*. If savings are high, then the economy will have large k and y at steady state. In the below graph, due to an increase in savings from s1 to s2, the investment curve which is a function savings, shifts upward from s1f(k) to s2f(k).

We know that, change in k = i - k

Now, higher savings will increase i so much so that i > k. The investment will exceed depreciation and the change in k is positive. So, capital per worker will increase till the point the new investment curve intersects the depreciation line at point B.

New Steady-state levels of y and k are: y2* and k2*. both are higher than previous levels due to an increase in savings.

So, higher savings rate increases steady-state y and k as it increases the investment and to maintain the capital accumulation equation, capital per worker has to rise to balance the equation

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