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Topic_1_-_Production_Technology_Basics

Topic_1_-_Production_Technology_Basics - macro In this...

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Production Technology Basics macro Topic 1 Topic 1 – Production Technology Production Technology slide 1 In this topic you will learn: In this topic you will learn: The Cobb-Douglas production technology What determines the economy’s total output/income How the prices of the factors of production are determined How total income is distributed Topic 1 Topic 1 – Production Technology slide 2 Technologies A technology is a process by which inputs are converted to an output. E.g. labour, a computer, a projector, electricity, and software are being combined to produce this lecture. Topic 1 Topic 1 – Production Technology slide 3 Technologies Usually several technologies will produce the same product -- a blackboard and chalk can be used instead of a computer and a projector. Which technology is “best”? How do we compare technologies? Topic 1 Topic 1 – Production Technology slide 4 Input Bundles Input Bundles x i denotes the amount used of input i ; i.e. the level of input i. An input bundle is a vector of the input levels; (x 1 , x 2 , … , x n ). E.g. (x 1 , x 2 , x 3 ) = (6, 0, 9 3). Topic 1 Topic 1 – Production Technology slide 5 Production Functions Production Functions Y denotes the output level. The technology’s production function states the maximum amount of output possible from an input bundle. 1 ( , , ) n Y f X X = "
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Topic 1 Topic 1 – Production Technology Production Technology slide 6 Cobb Cobb- Douglas Technologies Douglas Technologies A Cobb-Douglas production function is of the form E.g. with 1 2 1 2 . n a a a n Y AX X X = × × " 1/ 3 1/ 3 1 2 Y X X = 1 2 1 1 2, 1, 3 3 . n A a and a = = = = Topic 1 Topic 1 – Production Technology Production Technology slide 7 x 2 x 1 All isoquants are hyperbolic, asymptoting to, but never touching any axis. Cobb Cobb- Douglas Technologies Douglas Technologies 1 2 1 2 a a Y X X = Topic 1 Topic 1 – Production Technology slide 8 Marginal (Physical) Products Marginal (Physical) Products The marginal product of input i is the rate- of-change of the output level as the level of input i changes, holding all other input levels fixed . That is, 1 ( , , ) n Y f X X = " i i Y MP X = Topic 1 Topic 1 – Production Technology slide 9 Marginal (Physical) Products Marginal (Physical) Products 2 / 3 2 / 3 1 1 2 1 1 3 Y MP X X X = = E.g. if 1/3 2/3 1 2 1 2 ( , ) Y f X X X X = = then the marginal product of inputs 1 and 2 are: 1/3 1/3 2 1 2 2 2 . 3 Y MP X X X = = Topic 1 Topic 1 – Production Technology slide 10 Marginal (Physical) Products Marginal (Physical) Products Typically the marginal product of one input depends upon the amount used of other inputs. E.g. if 2/3 2/3 1 1 2 1 3 MP X X = then, 2/3 2/3 2/3 1 1 1 1 4 8 3 3 MP X X = = and if x 2 = 27 then if x 2 = 8, 2 / 3 2 / 3 2 / 3 1 1 1 1 27 3 . 3 MP X X = = Topic 1 Topic 1 – Production Technology slide 11 Marginal (Physical) Products Marginal (Physical) Products The marginal product of input i is diminishing if it becomes smaller as the level of input i increases. That is, if 2 2 0.
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