LINEAR PRODUCTION POSSIBILITIES CURVES.doc

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Department
Business and Environment
Course
BSEN 401
Professor
William Huddleston
Semester
Fall

Description
. LINEAR PRODUCTION POSSIBILITIES CURVES We can express a Production Possibilities Curve with constant Opportunity Cost as a linear equation. e.g. Suppose that the equation for production of Y and X is Y = 150 – 2X where Y is the quantity of Y and X is the quantity of X. We will graph this with Y on the vertical axis and X on the horizontal axis (as usual). i) What is the maximum output of Y if no X is produced, i.e., X = 0? X = 0, => Y = 150 – 2(0) = 150 This gives the ‘vertical intercept’ of the diagram, i.e., the amount of Y when X = 0. ii) What is the maximum output of X if no Y is produced (Y = 0)? Y = 0, => 0 = 150 – 2X => X = 150/2 = 75 This gives the ‘horizontal intercept’ of the diagram, i.e., the amount of X when Y = 0 These two pieces of information are sufficient to draw the Production Possibilities Curve because the function is linear, i.e., a straight line between two points. Quantity of Y 150 75 Quantity of X iii) What is the slope of the Production Possibilities Curve? - 1 - The slope of this line = rise/run = ΔY/ΔX = -150/75 = -2. The coefficient of X in the linear equation gives us the slope directly as –2 since an increase in X of 1 causes a decrease in Y of 2. iv)What is the Opportunity Cost of an increase of one unit of X given full employment? The opportunity cost of a one unit increase in X is 2 units of Y. Opportunity Cost = - ΔX/ΔY = -(-2) = 2 The Opportunity Cost is constant so the function is linear. v) What is the Opportunity Cost of an increase of one unit of Y given full employment? One unit of Y costs 75/150 = ½ unit of X. We could also find this by expressing our equation in terms of X to get X = 75 – Y/2. This would also show that opportunity cost of Y is X/2. The simplest way to find the Opportunity Cost of X is to realize that ΔY/ΔX = 1/(ΔX/ΔY). The opportunity cost of one unit of X is 1/-(ΔX/ΔY) = ½. vi)Suppose that the economy presently produces 40 units of X and 50 units of Y. What is the opportunity cost of increasing X to 50 units? Of increasing X to 60 units? The combination 40X and 100Y are below the production possibilities curve because production of 50Y would allow production of 50X at full employment. An increase in the production of X to 50 units would have 0 opportunity cost therefore. Production of 60 units of X would allow production of a maximum of 30 units of Y. The opportunity cost of moving from (50, 50) to (60, 30) is 20 units of Y. Sources of Growth: Growth of the output possibilities of an economy implies increased productive capacity. This can occur in two ways. 1. An increase in resources - 2 - The increase in res
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