Download SPECIFIC Factors and Income Distribution – See ALSO HANDOUT

SPECIFIC FACTORS AND INCOME DISTRIBUTION
– SEE ALSO HANDOUT OF GRAPHS
1. To analyze the economy's production possibility frontier, consider how the output mix
changes as labor is shifted between the two sectors.
a. Graph the production functions for M and F: The production functions for goods
M and F are standard plots with quantities on the vertical axis, labor on the
horizontal axis, and QM= f(KM,LM) with slope equal to the MPLM, and on
another graph, QF= f(KF,LF) with slope equal to the MPLF.
b. Graph the production possibility frontier. Why is it curved? To graph the
production possibilities frontier, combine the production function diagrams with
the economy's allocation of labor in a four quadrant diagram. The economy's PPF
is in the upper right hand corner, as is illustrated in the four quadrant diagram one
the handout. The PPF is curved due to declining marginal product of labor in each
good. The concave (to the origin) shape illustrates increasing opportunity cost as
the country devotes more labor to the production of one good.
c. Express the slope of the production possibility frontier as a ratio of the Marginal
Product of Labor in the two goods. The slope of the PPF equals –MPL /MPL .
2.
a. Let P /P = 2 (M/F). Determine graphically the wage rate and the allocation of
labor between the two sectors. To solve this problem, one can graph the demand
curve for labor in M as
W= VMPLM = PM MPLM, and the demand curve for labor in F as
W = VMPLF = PF MPLF. Since the total supply of labor is given by the horizontal
axis, the labor allocation between the sectors is approximately LM=29 and LF=71.
The wage rate is about $0.98 or $1/hour.
b. Using the graph drawn for problem 1, determine the output of each sector. Then
confirm graphically that the slope of the PPF at the point equals the relative
price. Use the graph drawn for problem 1b (or the table given in problem 1) to
show that the M sector’s output is QM=48 and F sector’s is QF=88 (but the last
digit is uncertain). (This involves combining the production function diagrams
with the economy's allocation of labor in a four quadrant diagram; please see the
handout.) Using the one we drew, it appears that the slope of the PPF = - MPLF /
MPLM = -PM/PF = -0.5
First, note that PF/PM = 2 was given; it follows that PM/PF = 0.5. Since
labor is mobile, in equilibrium, the wages rates in both industries will be the same.
The wage is determined by the demand and supply of labor. Each industry is
willing to pay a wage up to the Value of the Marginal Product of Labor (VMPL).
Equilibrium occurs at the intersection of the two labor demand curves, where WF
= WM and VMPLF = VMPLM. Next, PF MPLF = PM MPLM, by substitution. Now
1
multiply both sides by -1/(PF MPLM). The result, -MPLF / MPLM = -PM/PF,
shows that at the production point, the slope of the PPF equals the relative price of
the x-axis good, M.
c. Let P /P = 1 (M/F). Repeat parts a and b.
Use a graph of labor demands, as in part a, to show that the intersection of the
demand curves for labor occurs at a wage rate close to $0.72. The decline in the
price of good F caused labor to be reallocated; labor is drawn out of production of
good F and enters production of good M (LM=63, LF=37). This also leads to an
output adjustment, whereby production of good F falls to about 68 units and
production of good M rises to about 76 units.
At the new equilibrium, the slope of the PPF = - MPLF / MPLM = -PM/PF = -1
Remember that PF/PM =1 was given; it follows that PM/PF = 1 also. Labor moves
out of Food and into Manufacturing until WF = WM and VMPLF = VMPLM.
Next, PF MPLF = PM MPLM, by substitution. Given PF = PM =1, it follows that
MPLF = MPLM. Hence, the slope of the PPF = - MPLF / MPLM = -PM/PF = -1
d. Calculate the effects of the price change on the incomes of the specific factors in
M and F. With the relative price change from PF/PM=2 to PF/PM =1, the money
price of good F has fallen by 50 percent (from $2 to $1/unit F), while the money
price of good M has stayed the same ($1/unit M). Wages have fallen, but by less
than the fall in PF (wages fell approximately 27 percent, from 0.98 to 0.72
$/hour). Thus, the real wage in terms of Food (w / PF) actually rises from (0.98/2
=) 0.49 to 0.72 units F/hour) while to real wage in terms of M (w / PM) falls (from
0.98 to 0.72 units M/hour; given PM = $1).
Capital owners are better off due to the lower real wage they must pay and the
lower relative price for the food they buy. Landowners are worse off due to the
higher real wage they must pay and the lower relative price for the food they sell.
One may calculate the real income of capitalists by subtracting what they pay the
workers from their total production, QM – (real wage, w, times units of labor
employed, LM). When PF/PM=2, QM – w(LM) = 48 - .98(29) = 19.6 units of M.
When the relative price of F falls to PF/PM =1, then the real income of capitalists
rises to QM – w(LM) = 76 - .72(63) = 30.6 units of M. By subtracting the old level
of real income from the new, one can see that the capitalists gain (30.6 – 19.6 =)
11 units of M.
Repeating this process, one may calculate the real income of landowners by
subtracting what they pay the workers from their total production, QF – (real
wage, w, times units of labor employed, LF). When PF/PM=2, QF – w(LF) = 88 .49(71) = 53.2 units of F.
When the relative price of F falls to PF/PM =1, then the real income of landowners
2
falls to QF – w(LF) = 68 - .72(37) = 41.4 units of F.
By subtracting the old level of real income from the new, one can see that the
landowners lose (41.4 – 53.2 =) 11.8 units of F.
Remember that the country’s income will equal the value of its production. With
trade, it will increase production of its (more valuable) comparative advantage
good and import some of its disadvantage good. As in the Classical and HO
Models, trade raises the per capita income of participating countries. In the
Specific Factors Model, owners of resources specific to the exporting industry
gain. Owners of resources specific to the import-competing industry lose. In this
example, the capitalists gained and the landowners lost real income. Mobile
factors may gain or lose, as discussed in the answer to part e. You should be
careful to contrast these results with the predictions of the HO Model (see the
Factor-price Equalization and the Stolper-Samuelson Theorems).
e. Discuss the effects of the price change on the income received by labor. To
determine the welfare consequences for workers, we need to know the quantities
of goods M and F that they consume. If workers consume only M, then they are
worse off. If they consume only F, then they are better off.
(Extra) Given the above information, one can construct the budget constraint
faced by labor and show that if workers initially consumed F and M in a ratio of
26/46, then their welfare would not change. If ratio of F to M was higher, then
they would be better off as a result of the decrease in the price of food. However,
the derivation of this ratio is unimportant for our purposes. We do not know the
demands of workers for the two goods(DF, DM). Therefore we do not know
whether they are helped or hurt by the decline in the price of food and the
consequent decline in wages.
3. What if the mobile factor, labor, increases in supply? The box diagram presented below is
a useful tool for showing the effects of increasing the supply of the mobile factor of
production, labor.
a. Analyze the qualitative effects of an increase in the supply of labor in the specific
factors model, holding the prices of both goods constant at P /P = 1 (M/F). For
an economy producing two goods, X and Y, with labor demands reflected by their
marginal revenue product curves, there is an initial wage of W1 and an initial
labor allocation of Lx=OxA and LY=OYA. When the supply of labor increases,
the right boundary of this diagram is pushed out to OY'. The demand for labor in
sector Y is pulled rightward with the boundary. The new intersection of the labor
demand curves shows that labor expands in both sectors, and therefore output of
both X and Y also expand. The relative expansion of output is ambiguous; it
depends on the shapes of the MPL curves. Wages paid to workers fall. The
3
incomes of the capitalists and the landowners both increase. See answer to part b.
PxMPLx
1
w1
w2
2
PyMPLy
Ox
Oy’
A
B Oy
b. Graph the effect on the equilibrium for the numerical example in problems 1 and
2, given P /P = 1 (M/F), when the labor force expands from 100 to 140.
From the shape of the MPL curves, it is clear that labor will continue to exhibit
diminishing returns. Using the numerical example (see graphs on handout), LM
increases to 91 from 63 and LF increases to 49 from 37. Wages decline from
$0.72 to $0.62. This new allocation of labor yields a new output mix of
approximately QM=95 and QF=75. (Again, the last digit is approximate).
Using a four quadrant diagram, you can demonstrate that the new production
possibility frontier shifts out, becomes more concave and is steeper at the x-axis
(flatter at the y-axis
4