by Marginal Efficiency of Investment (MEI) is a concept that is related to the Marginal Efficiency of Capital (MEC). Both MEC and MEI are used to evaluate investment decisions, but they focus on different aspects of the investment. MEC measures the expected return on an additional unit of capital investment, while MEI measures the expected increase in output resulting from an additional unit of investment.
MEI is an important concept in macroeconomics because it helps to explain how changes in investment can affect the overall level of economic activity. When firms invest in new capital equipment, it can lead to an increase in output and employment, which can have positive spillover effects throughout the economy. MEI can help policymakers and investors understand the potential impact of changes in investment levels on the overall economy.
To understand MEI, it is helpful to start with the concept of the production function. The production function describes the relationship between inputs (such as capital and labor) and outputs (such as goods and services). It is typically represented by an equation that relates the level of output (Y) to the level of inputs (K and L):
Y = F(K,L)
where K represents the level of capital input and L represents the level of labor input. F is a function that describes the technology and production process used by the firm.
The production function is usually assumed to exhibit diminishing marginal returns to capital and labor. This means that as the level of capital or labor input increases, the increase in output becomes smaller and smaller. In other words, each additional unit of input generates less additional output than the previous unit. This is due to factors such as diminishing returns to scale, congestion effects, and bottlenecks in the production process.
The concept of MEI arises from the idea that the marginal product of capital (MPK) decreases as the level of capital input increases. The MPK is the additional output that is produced by an additional unit of capital input, holding the level of labor input constant. Mathematically, the MPK is defined as:
MPK = ∂Y/∂K
where ∂Y/∂K is the partial derivative of the production function with respect to K.
As the level of capital input increases, the MPK decreases due to diminishing marginal returns to capital. In other words, each additional unit of capital input generates less additional output than the previous unit. This means that the cost of an additional unit of capital (which is equal to the price of the capital equipment) must be less than the additional output that it generates in order for the investment to be profitable.
The MEI is the rate of return that is required for an investment in capital equipment to be profitable, given the current level of technology and production processes. Mathematically, the MEI can be expressed as:
MEI = r + ∂F(K,L)/∂K
where r is the required rate of return on the investment, and ∂F(K,L)/∂K is the partial derivative of the production function with respect to K.
The MEI can be thought of as the rate of return that is required for an investment in capital equipment to generate enough additional output to cover the cost of the investment. If the MEI is greater than the required rate of return on the investment, then the investment is considered profitable. If the MEI is less than the required rate of return, then the investment is not considered profitable.
Example:
Suppose a firm is considering investing in a new machine that costs $100,000. The machine is expected to increase output by 20% and has a useful life of 5 years. The expected annual return on the investment is 10%. The required rate of return on the investment is also 10%. Using the production function Y = F(K,L), where K represents capital input and L represents labor input, the following table summarizes the inputs and outputs of the investment decision:
| Investment Cost | Expected Increase in Capital Input | Expected Increase in Output | Expected Annual Return | Required Rate of Return | MEI |
| $100,000 | 1 | 20% | 10% | 10% | 10% |
In this example, the expected increase in output resulting from an additional unit of investment (i.e., the MEI) is 10%. This means that the investment is expected to generate enough additional output to cover the cost of the investment and earn a rate of return that is equal to the required rate of return on the investment.
Of course, in reality, there are many more factors to consider when evaluating an investment decision, and the expected returns and costs can vary significantly depending on the specific circumstances. Nonetheless, this example illustrates how MEI can be used to guide investment decisions and assess the expected impact of an additional unit of investment on output.
