Lecture_5

# Lecture_5 - INTERMEDIATE MACRO THEORY Fall 2011 UC Davis...

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INTERMEDIATE MACRO THEORY Fall, 2011, UC Davis Giovanni Peri, Professor of Economics, [email protected]

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2 4.1 Introduction In this chapter, we learn: how to set up and solve a macroeconomic model. how a production function can help us understand differences in per capita GDP across countries. the relative importance of capital per person versus total factor productivity in accounting for these differences. the relevance of “returns to scale” and “diminishing marginal products.” how to look at economic data through the lens of a macroeconomic model.
3 A model is a mathematical representation of a hypothetical world that we use to study economic phenomena. For economists it consists of equations and unknowns with real world interpretations. Macroeconomists document facts, build a model to understand the facts, and examine the model to see how effective it is at explaining the facts.

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4 A Model of Production Vast oversimplifications of the real world in a model can still allow it to provide important insights. Consider a single, closed economy, with only one consumption good. We represent the productive capacity of the economy with a production function.
5 Setting Up the Model A certain number of laborers make the consumption good. Indicate them with L. A certain number of machines are used to produce the good. Indicated them with K. In the country there is a total fixed number of potential workers L and machines K. . A production function tells how much output can be produced given any number of inputs, laborers, and machines.

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6 A is a productivity parameter. Higher value of A means that firms can produce more, all else equal. Usually it is associated with better technology or higher efficiency. The Cobb-Douglas production function is the particular production function that takes the form of a product of factors raised to an exponent. We assume α = 1/3. α = 1 t t t L AK Y Production function
7 A production function exhibits constant returns to scale if doubling each input exactly doubles output. If the exponents on the inputs sum to 1, the function has constant returns to scale. This means that doubling (multiplying by x) the inputs the output doubles (is multiplied by x). Production function 3 / 2 3 / 1 ) , ( L K A L K F Y = =

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8 The standard replication argument implies that a firm can build an identical factory, hire identical workers and capital, and can exactly double production. The standard replication argument implies constant returns to scale.
9 Math Assume A=1 Y=K 1/3 L 2/3 Double the inputs produces the following output: (2K) 1/3 (2L) 2/3 =2 (1/3+2/3) K 1/3 L 2/3= 2K 1/3 L 2/3 =2Y recall that product of exponential with the same base equals the base raised to the sum of exponents.

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Returns to Scale If the exponents in the Cobb-Douglas production function sum to 1 we have constant returns to scale, CRS. If the sum to more than one we have increasing returns to
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Lecture_5 - INTERMEDIATE MACRO THEORY Fall 2011 UC Davis...

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