SOLOW GROWTH MODEL

Per Capita Variables

kt = Kt/Lt, yt= Yt/Lt, it = It/Lt, ct = Ct/Lt

Parameters (exogenous, constant)

S: savings rate (between 0 and 1)) d : depreciations (between 0 and 1) g= gA = growth rate of technology n= gl population growth rate

Might a policymaker choose a steady state with more capital than the golden rule state?

When the economy begins above the Golden Rule level of capital, reaching the Golden Rule level leads to higher consumption at all points in time. Therefore, the policymaker would always want to choose the Golden Rule level, because consumption is increased for all periods of time.

Variables (endogenous, dynamic)

Yt : output, income Kt = capital Lt = labor, population, workers It= Investment, savings Ct= consumption

Why might an economic policymaker choose the golden rule level of capital?

1. It is reasonable to assume that the objective of an economic policymaker is to maximize the economic well-being of the individual members of society. 2. Since economic well-being depends on the amount of consumption, the policymaker should choose the steady state with the highest level of consumption. 3. The Golden Rule level of capital represents the level that maximizes consumption in the steady state. 4. Suppose, for example, that there is no population growth or technological change. If the steady-state capital stock increases by one unit, then output increases by the marginal product of capital MPK; depreciation, however, increases by an amount δ, so that the net amount of extra output available for consumption is MPK - δ. 5. The Golden Rule capital stock is the level at which MPK = δ, so that the marginal product of capital equals the depreciation rate.

In the Solow model, how does the savings rate affect the steady state level of income? How does it affect the steady-state rate of growth?

1. high saving rate = a large steady-state capital stock and a high level of steady-state output. 2. low saving rate = a small steady- state capital stock and a low level of steady-state output. 3. Higher saving leads to faster economic growth only in the short run. An increase in the saving rate raises growth until the economy reaches the new steady state. 4. That is, if the economy maintains a high saving rate, it will also maintain a large capital stock and a high level of output, but it will not maintain a high rate of growth forever. 5. In the steady state, the growth rate of output (or income) is independent of the saving rate. 6. Affects the investment curve = i= sf(k)

Might a policy maker choose a steady state with less capital than the golden rule steady state?

On the other hand, when the economy begins below the Golden Rule level of capital, reaching the Golden Rule level means reducing consumption today to increase consumption in the future. In this case, the policymaker's decision is not as clear. If the policymaker cares more about current generations than about future generations, he or she may decide not to pursue policies to reach the Golden Rule steady state. If the policymaker cares equally about all generations, then he or she chooses to reach the Golden Rule. Even though the current generation will have to consume less, an infinite number of future generations will benefit from increased consumption by moving to the Golden Rule.

In the Solow Model, how does population growth affect the steady-state level of income? How does it affect the steady state rate of growth?

The higher the population growth rate is, the lower the steady-state level of capital per worker, and therefore there is a lower level of steady-state income per worker. For example, Figure 8-1 shows the steady state for two levels of population growth, a low level n1 and a higher level n2. The higher population growth n2 means that the line rep- resenting population growth and depreciation is higher, so the steady-state level of cap- ital per worker is lower. In a model with no technological change, the steady-state growth rate of total income is n: the higher the population growth rate n is, the higher the growth rate of total income. Income per worker, however, grows at rate zero in steady state and, thus, is not affected by population growth.