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Economic Growth and Convergence

# Economic Growth and Convergence - 2 Economic Growth and...

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2. Economic Growth and Convergence 1. The Production Function: Review We begin our theoretical study of economic growth by considering how a country's technology and factors of production–or factor inputs–determine its output of goods and services, measured by real GDP. The relation of output to the technology and the quantities of factor inputs is called a production function . We will build a simplified model that has two factor inputs: capital stock , K , and labor, L . In this model, capital takes a physical form, such as machines and buildings used by businesses. A more complete model would include human capital , which embodies the effects of education and training on workers' skills, and the effects of medical care, nutrition, and sanitation on workers' health. In our simplified model, the amount of labor input, L , is the quantity of work-hours per year for labor of a standard quality and effort. That is, we imagine that, at a point in time, each worker has the same skill. For convenience, we often refer to L as the labor force or the number of workers–these interpretations are satisfactory if we think of each laborer as working a fixed number of hours per year. We use the symbol A to represent the technology level . For given quantities of the factor inputs, K and L , an increase in A raises output. That is, a more technologically advanced economy has a higher level of overall productivity . Higher productivity means that output is higher for given quantities of the factor inputs. Mathematically, we write the production function as Key equation (production function): (1) One way to see how output, Y , responds to the variables in the production function–the technology level, A , and the quantities of capital and labor, K and L –is to change one of the three variables while holding the other two fixed. Looking at the equation, we see that Y is proportional to A . Hence, if A doubles, while K and L do not change, Y doubles. For a given technology level, A , the function F(K, L) determines how additional units of capital and labor, K and L , affect output, Y . We assume that each factor is productive at the margin. Hence, for given A and L , an increase in K –that is, a rise in K at the margin–raises Y . Similarly, for given A and K , an increase in L raises Y . The change in Y from a small increase in K is called the marginal product of capital , which we

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abbreviate as MPK . The MPK tells us how much Y rises when K increases by one unit, while A and L do not change. The corresponding change in Y from a small increase in L is called the marginal product of labor , or MPL . The MPL tells us how much Y rises when L increases by one unit, while A and K do not change. We assume that the two marginal products, MPK and MPL, are greater than zero.
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