191T4 - ECON191 (Spring 2010) 11, 12 & 15.3.2010...

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1 ECON191 (Spring 2010) 11, 12 & 15.3.2010 (Tutorial 4) Chapter 3 Production and Technology (Chapter 6 & 7 of textbook) Production function A production function shows the maximum amount of any output a producer in our economy can get most efficiently, given a certain level of inputs. It summarizes the technology a producer faces in the economy by describing the technology as a constraint on the producer’s ability to produce. A production function can be represented as Y = f ( K , L ), assuming there are two inputs: K and L in our production. One input case: Total production and marginal product Two input case Isoquant Total product curve: It shows the relationship between labor and output when the amount of capital is constant. Marginal product curve: It shows the changed in output level resulting from increasing labor by 1 unit. It is the slope of SR TP curve at any point. The shape of the TP curve and MP can be explained by the diminishing returns. Law of diminishing returns: when more of an input is added with all other inputs constant, marginal product will decrease eventually. K L 1 1 4 4 IQ 20 A production function can be depicted by a set of isoquants. Isoquant : it shows the different combinations of inputs ( K and L ) that are required to produce a given level of output. Isoquants are strictly cardinal, each IQ represents a level of real output and the space between IQs are meaningful. If we consider a very small increase in labor, then the slope of the isoquant will be marginal rate of technical substitution.
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2 Marginal rate of technical substitution (MRTS) MRTS is the rate at which one input can be substituted for another while keeping output produced constant. MRST is decreasing L K K Y L Y MP MP MRTS K L LK ) , ( L K Y Y K K Y L L Y Y ( L MP Y L Y MP L L and K MP Y K Y MP K K ) 0 K MP L MP Y K L K MU L MP K L K L MP MP L K and L K MRTS KL K L KL MP MP MRTS Isocost line Isocost line : it shows the various combinations of two inputs that can be purchased with a certain amount of money. Slope of isocost curve: relative factor price K L w w Suppose w L = 2, w K = 2, then the slope of the isocost curve is –1. [Total cost for (4K, 1L) and (1K, 4L) will be the same, and is $10] The equation for the isocost curve is C K w L w K L L K 1 1 4 4 Slope = K L w w = –1 Icost = 10
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3 Cost minimization: optimal input combination Cost minimization condition : K L KL w w MRTS , i.e. when isoquant is tangent to isocost curve. K
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191T4 - ECON191 (Spring 2010) 11, 12 & 15.3.2010...

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