Comparative Advantage Production Possibilities Frontiers and the Gains From Trade 1 Opportunity Cost De cid 133 nition 1 The opportunity cost of something is what is given up to attain that item both explicitly and implicitly Example 2 The cost of using cid 135 atboats for river travel What is the cost of going to college The cost to o ering a scholarship to a football player In each of these examples there is a non explicit cost that is part of the opportunity cost For the cid 135 atboats there was the time cost of travelling back up river Going to college means that you are not earning income and expe rience doing something else A scholarship to a football player precludes that scholarship from going to someone else Example 3 Each day Robinson can either collect 20 coconuts or catch 5 cid 133 sh What is the opportunity cost to Robinson for a cid 133 sh We calculate the opportunity cost as the number of coconuts that one must give up per cid 133 sh Numerically we put the production of cid 133 sh on the denominator and the coconuts in the numerator opportunity cost of cid 133 sh 20C 5F 4 C F To calculate the opportunity cost of coconuts we cid 135 ip the fraction i e 1 4 2 Production Possibilities Frontiers De cid 133 nition 4 A Production Possibility Frontier represents all the combinations of output that can be produced Points within the frontier are attainable but ine cient Points along the frontier are attainable and e cient Points beyond the frontier are unattainable Example 1 Points A B and C are all attainable However point C is ine ciently using resources Point D is unattainable 2 1 Drawing Production Possibilities Frontiers Example 5 Suppose that we are told that in region W there are 100 units of labor Each unit of labor can produce either 5 units of Butter or 2 units of Guns What does the PPF look like Start by labeling the two points where everyone is employed producing butter 500 0 and where everyone is producing guns 0 200 2 ButterGuns ABDC Now ask what is the opportunity cost of butter 2 Guns 5 Butter Since it is always 2 Guns 5 Butter we know that the PPF is a straight line Note that the absolute value of the slope of the PPF is the opportunity cost of the x axis good Example 6 Suppose that in region A we have 50 units of labor Each unit of labor can produce either 2 units of guns or 2 units of butter Again start with the two points where everyone is producing guns 0 100 and where everyone is used producing butter 100 0 3 ButterGuns200500ButterGuns200500slope 2 5 opportunity cost of butter What is the opportunity cost of butter opportunity cost of butter 2 Guns 2 Butter 1 G B Again this is constant therefore we can just connect the two points with a straight line 2 2 Drawing a PPF with two regions Suppose that now we wish to draw the joint PPF of region A and region W Start by cid 133 guring out how many units of guns can be produced if every unit of labor in A and every unit of labor produces guns 300 and the same for butter 600 4 ButterGuns100100ButterGuns100100 What is the opportunity cost of Butter Well it depends now on which region the unit of labor that we are switching resides in Therefore the PPF is NOT a straight line connecting the two So what do we do Start by thinking about the point 0 300 Everyone in both regions is producing Guns If we wanted someone to produce butter would we have someone in region W or region A switch from guns to butter Since the opportunity cost of butter in region W is 2 5 and the cost is 1 in region A it is clearly cheaper to produce in W So at cid 133 rst the slope of the ppf will be 2 5 i e the opportunity cost in W However eventually everyone in Wisconsin has switched from Guns to Butter Lets label this point on our graph 5 ButterGuns300600ButterGuns300600 At point A everyone in W is producing Butter and everyone in region A is producing Guns I cid 146 ve connected A to the vertical axis with a straight line because the opportunity cost of butter in W is constant Thus the line seg ment that connects A to the vertical axis has a slope of cid 0 2 5 Again this is the opportunity cost of the cid 133 rst 500 units of Butter What is happening at a point between A and the vertical intercept along that line segment At those points everyone in region A is producing guns but in region W some people produce guns and some people produce butter What happens if we go past point A Now workers in region A must be switched from guns to butter The cost of this in region A is constant and equal to 1 So our PPF looks like this How can we produce points along the segment to the right of point A At those points everyone in W is producing Butter while some people in A produce guns and some produce butter Note that the opportunity cost of butter is 2 5 6 ButterGuns300600100500AButterGuns300600100500Aslope 2 5slope 1 for the cid 133 rst 500 units of butter and 1 for the next 100 units 2 3 A PPF with 3 or more regions Ok now lets add to the joint PPF of A and W a third region N In region N there are 100 units of labor each unit of labor can produce either 1 gun or 3 units of butter What does the joint PPF look like Again start by cid 133 nding the total number of guns if everyone in all three regions produces guns 0 400 and the same for butter 900 0 Now if ANW is currently producing 400 guns and wanted to produce some butter in which region would we cid 133 rst switch a worker from guns to butter Look cid 133 rst at the opportunity cost of butter in each region Since butter is cheapest in region N that is the cid 133 rst region to switch Plot the point in the graph where region N is completely specialized in butter while A W are producing guns W A N 2 5 1 1 3 7 ButterGuns400900 Notice that along the line segment connecting A to the vertical axis every one in A W is producing guns while some in N are producing guns and some are producing butter The slope of that line segment is 1 3 the oppor tunity cost in region N of butter After 300 units of butter are produced there is no one left in region N to switch If more butter is produced it must come from a di erent region W Next plot the point where everyone in W and N is producing butter while everyone in region …