Question

Consider an economy in which the amount of investment is equal to the amount of saving (i.e., the economy is closed to international flows of capital). Any output that is not saved is consumed. The production function is y=Akα . Find the value of γ, the fraction of income that is invested, that will maximize the steady-state level of consumption per worker. (This is called the "golden rule" level of investment.)

Answer 1

The golden rule level of investment occurs in a closed economy where savings are optimized to match the marginal product of capital in the production function. This maximizes steady-state consumption per worker when the production function is y=Ak^α.

Step-by-step explanation:

The student is asking about the 'golden rule' level of investment in a closed economy where investment is equal to saving. The production function given is y=Akα, which describes how output (y) is produced from capital (k) with constant returns to scale.

To find the fraction of income invested (γ), which maximizes the steady-state level of consumption per worker, we have to consider the relationship between saving, investment, and consumption.

According to the Keynesian consumption function, consumption is a function of national income. A portion of this income is saved, where the marginal propensity to save (MPS) is the ratio of additional saving to additional income. The marginal propensity to consume (MPC) is the ratio of additional consumption to additional income, and together MPC + MPS must equal 1.

In the context of this economy, if all output not saved is consumed, to maximize consumption savings must be adjusted to the optimal investment rate which equates to the marginal product of capital. The golden rule level of investment is reached when the steady-state consumption is maximized, which occurs when the marginal product of capital equals the rate of depreciation.