Question

An economy is described by the standard Solow model without technological progress and without population growth. You are given the information that the savings rate dropped to a lower level in this economy, but you don’t know by how much it did so. Suppose that prior to the drop in s the economy was in a steady-state with a capital stock per worker higher than the Golden Rule level.

a. In a graph which should include the production function, the investment function and the depreciation function (all in per-worker terms) show how the economy is affected by this drop in the savings rate. Make sure to label each axis, all curves and steady states clearly!

b. Sketch the relationship between the savings rate and the steady-state consumption per worker. Show in this graph the effect of the drop in the savings rate. Remember that the information given at the beginning of the question still holds!

c. Provide an analysis about how consumption per worker, capital per worker and output per worker behave over time. That is, draw time paths that show the behavior of each of these variables immediately before and then after the drop in the savings rate.

Answer 1

(a) The above diagram shows how the economy is affected by the drop in saving rate and what impact it cause on the investment, production and depriciation function. The X-axis represents Capital per worker while the Y-axis represents Output per worker. The 45 degree line represents the depriciation function. f(k) represents output per worker. Since investment depends on saving and saving depends on output so the investment function will be sf(k). Initially the economy is operating at steady state level of capital when the investment function intersects depriciation function at X, which shows the economy is in an equilibrium. K* is the steady state level of capital.

With drop in saving rate from s1 to s2, the consumption per worker will increase while the investment per worker will decrease. As a result of which, the investment per worker function will go downwards from sf(k) to s'f(k). The equilibrium will form when the investment function will intersect depreciation function at X'. Consequently, the steady state level of capital will move to k1.

(b)

The above diagram shows the relationship between consumption per worker and Investment per worker. The axes and curves are as same as in the previous diagram. The gap between Investment per worker and output per worker represents consumption per worker. Initially, the economy is operating at golden rule level of capital (c*). Therefore the consumption here represents the consumption of golden rule level of capital. There is an inverse relationship between consumption per worker and saving per worker. When saving increases, less resources are left for consumption while more for investment and vice versa. Therefore when saving increaes, consumption per worker decreases and as a result investment increases.

(c) The same diagram drawn in part (a) can be used to explain the relationship between saving per worker and output, consumption and capital per worker. When saving rate drops, less capital can be put into investment as consumption will automatically increase with decrease in saving. As a result, the capital per worker will fall. Consequently, the output per worker will also decrease due to fall in capital and moves towards left. The economy will move leftwards in terms of capital per worker.