Consider production in the UK economy. Assume that only two goods can be produced: wheat and education services. The production possibility frontier (PPF) is given by W = 200 – 4E, where W is the bushels of wheat produced and E is the units of education services produced.
Which statement (or statements) is true?
i) The opportunity cost of one bushel of wheat is 4 units of education; the opportunity cost is constant along the PPF.
ii) The opportunity cost changes along the PFF, reflecting the increasing opportunity cost when more of either good is already being produced.
iii) The opportunity cost of one unit of education is giving up 40 bushels of wheat.
iv) The opportunity cost of one bushel of wheat is constant along the PPF and equal to 5 units of education.
v) The opportunity cost of one bushel of wheat is ¼ a unit of education; the opportunity cost is constant along the PPF.
The PPF (production possibility frontier) of an economy describes the maximum output that the economy can produce. Considering this hypothetical structure of the UK economy, where only two goods are produced - bushels of wheat (W) and education services (E) - only certain combinations of W and E can be produced when the economy is running at full capacity. Any point (combination of amounts of output of W and E) below the PPF curve represents the situation where the economy is producing goods at less than full capacity. Any point above the curve represents a combined output of W and E that isn't achievable under current production possibilities (according to resources and available labour), but might be achievable in different conditions.
The PPF in this example is given by a straight line
W = 200 - 4E
This means that if, say, 10 E are produced in a unit of time (perhaps a reasonable amount of time in this scenario is 1 hour), at full production capacity, the economy can also produce 200 - 4(10) = 160 W. Or, if 20 E are produced, at full capacity, 200 - 4(20) = 120 W can also be produced.
The opportunity cost of a particular good produced is expressed in terms of how many units of another good could be produced in the same unit of time (here 1 hour). This can be thought of as, for a given amount produced of one good per unit time, the available labour to produce one extra unit of that good in a unit of time (1 hour) could have been used to produce X amount of units of another good.
So, say 10 E are being produced per hour, increasing this by one unit to 11 E per hour represents an opportunity cost in terms of W of (200 - 4(10)) - (200 - 4(11)) = 160 - 156 = 4 . This is to say that for that extra unit of E produced in an hour, 4 units of W could have been produced, because going from a rate of 11 E down to 10 E results in an increase of 156 W to 160 W.
Because the PPF is a straight line in this set-up for the UK economy (it could be any line, that is, more generally a curve), you will find that whatever amount of E produced per hour, producing an extra unit of E results in a loss of X = 4 units of W. In other words, the opportunity cost of E in terms of W is constant and equal to 4 bushels, whatever the current rate of production per hour of E. Equivalenty, the opportunity cost of W in terms of E is constant and equal to 1/4 of a unit of education. For example if 200 W are produced (the maximum amount), decreasing this by one unit per unit time results in an increase (under full production capacity) of production of E of 1/4 units. Decreasing it again from 199 W to 198 W also results in an increase of E by 1/4.
So it can be seen that the opportunity cost of one good expressed in units of the other is the slope of the PPF curve. If the PPF curve is, as in this case, a straight line, the slope (gradient of the line) is constant. Therefore the opportunity cost is constant. For E in terms of W it is 4, as the slope of the equation W = 200 - 4E is 4. For W in terms of E it is 1/4, since the slope of the rearranged equation E = 50 - 1/4 W is 1/4.
Therefore statement v) is the only one that is true
The Production possibility frontier (PPF) is given by W = 200-4E, which is an equation of a straight line. Here the Y-intercept is 200 and the x-intercept is 50 (for a wheat-education PPF)
In such a scenario, the opportunity cost will be constant along the PPF.
Now, using the equation of this line, consider the following:
For W=0, E = 200/4 = 50
and for W= 200, E= 0.
so the production of 200 units of wheat will require the loss of 50 units of education, i.e. the opportunity cost of wheat bushel is 50/200 or 1/4 of a unit of education.
Hence the last statement "The opportunity cost of one bushel of wheat is 1/4 a unit of education; the opportunity cost is constant along the PPF" is correct.