5 Pages
Unlock Document

Business and Environment
BSEN 401
William Huddleston

. 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
More Less

Related notes for BSEN 401

Log In


Join OneClass

Access over 10 million pages of study
documents for 1.3 million courses.

Sign up

Join to view


By registering, I agree to the Terms and Privacy Policies
Already have an account?
Just a few more details

So we can recommend you notes for your school.

Reset Password

Please enter below the email address you registered with and we will send you a link to reset your password.

Add your courses

Get notes from the top students in your class.