Question

Suppose a country has the production function Y = 2 √?, where Y = output and K = physical capital. People devote 30% of output to producing new capital goods ( = 0.30). Further assume that capital depreciates at the rate of 3 percent per period (δ = 0.03).

a. Suppose that the country invested in 6 units of new capital in the current period. By how many units will output change in the next period?

b. What are the steady-state levels of capital and output in this country? Solve and depict graphically.

c. Explain why this country would tend towards a steady-state equilibrium.

Answer 1

a) since the country invested 6 units of new capital so output for the next period = 30/100*6*0.3=0.054 units

The units-of-output depreciation method is based on the assumption an asset will produce a fixed number of units over its lifetime. It is used to allocate the cost of an asset over its useful life. It's also referred to as a non-cash expense because the cash used to buy the asset left the company when it was purchased.Units of production depreciation can be calculated in two steps. First, you divide the asset's cost basis―less any salvage value―by the total number of units the asset is expected to produce over its estimated useful life. Then, you multiply this unit cost rate by the total number of units produced for the period .The unit of production method is a method of depreciation of the value of an asset over time. It becomes useful when an asset's value is more closely related to the number of units it produces than the number of years it is in use.

b)

The steady state level of capital is an amount of capital per worker that is stable over time - as time progresses there is no accumulation or depletion of capital. It occurs when investment in the per capita capital stock is equal to the depreciation of the capital stock.A steady-state economy is an economy structured to balance growth with environmental integrity. A steady-state economy seeks to find an equilibrium between production growth and population growth .A steady state flow process requires conditions at all points in an apparatus remain constant as time changes. There must be no accumulation of mass or energy over the time period of interest. The same mass flow rate will remain constant in the flow path through each element of the system.

The steady state is defined as a situation in which per capita output is unchanging, which implies that k be constant. This requires that the amount of saved output be exactly what is needed to (1) equip any additional workers and (2) replace any worn out capital.

Population growth causes the steady state level of capital to increase and the steady state level of output per worker to increase. C. Population growth causes the steady state level of capital to decrease and the steady state level of output per worker to decrease.

c) Steady State. A system that is in a steady state remains constant over time, but that constant state requires continual work. This condition is also referred to as a system in dynamic equilibrium. Were the process maintaining the system to cease, the conditions would not remain.

Some ecosystems exist in a steady state, or homeostasis. In steady-state systems, the amount of input and the amount of output are equal. In other words, any matter entering the system is equivalent to the matter exiting the system. Some lakes exist as steady-state systems in terms of their water volume.However, in a metabolic pathway, steady state is maintained by balancing the rate of substrate provided by a previous step and the rate that the substrate is converted into product, keeping substrate concentration relatively constant.

Taking different variables, some of the neo-classical economists have given their interpretations to the concept of steady state growth. To begin with Harrod, an economy is in a state of steady growth when Gw=Gn. Joan Robinson described the conditions of steady state growth as Golden Age of accumulation thus indicating a “mythical state of affairs not likely to obtain in any actual economy.”

But it is a situation of stationary equilibrium. According to Meade, in a state of steady growth, the growth rate of total income and the growth rate of income per head are constant with population growing at a constant proportionate rate, with no change in the rate of technical progress. Solow in his model demonstrates steady growth paths as determined by an expanding labour force and technical progress.