International Economics 8th Edition Appleyard Solutions Manual
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CHAPTER 5
INTRODUCTION TO NEOCLASSICAL TRADE THEORY: TOOLS TO BE EMPLOYED
Learning Objectives:
■ Review the microeconomic principles of consumer and producer behavior.
■ Explain the concept and limitations of a community indifference curve.
■ Examine the underlying basis for a production-possibilities frontier with increasing opportunity costs.
I. Outline Introduction
The Theory of Consumer Behavior
- Consumer Indifference Curves
- The Budget Constraint
- Consumer Equilibrium Production Theory
- Isoquants
- Isocost Lines
- Producer Equilibrium
The Edgeworth Box Diagram and the Production-Possibilities Frontier
- The Edgeworth Box Diagram
- The Production-Possibilities Frontier
Summary
II. Special Chapter Features
Titans of International Economics: Francis Ysidro Edgeworth (1845-1926)
In the Real World: Consumer Expenditure Patterns in the United States
III. Purpose of Chapter
Since neoclassical trade theory at the undergraduate level relies heavily on a few basic graphical micro tools, we think it useful to gather these tools into one convenient place early in the book. The purpose of the chapter is to re-introduce the student to thinking in marginal terms and to re-emphasize principles of maximization. The student should become aware early in the course that the conceptual precision of economic analysis to which he or she was exposed in earlier work is going to be employed in the international trade course as well.
IV. Teaching Tips
A. In classes where the prerequisite for the international economics course(s) consists only of introductory economics, some of the tools will be new and this chapter should be required reading. If intermediate micro is a prerequisite, this chapter can be made optional, but it may still serve as a worthwhile reference point if difficulty is encountered in later chapters. Even then, however, the material on community indifference curves is likely to be new to the students.
B. Our less-than-complete discussion of relative factor intensity of production processes can be given more precision in class here rather than waiting until that material is more fully developed in Chapter 8.
C. In the discussion of consumer and producer maximization we think that the student’s grasp of the material is improved if the tangencies and equalities and the movements to them are not thought of as relationships to be memorized but rather as processes to be understood in economic terms. Thus, we stress that, with a disequilibrium such as (MUX/PX) > (MUY/PY), it is simple common sense to reallocate the consumption bundle toward more of good X and less of good Y because total utility is enhanced through spending the last dollar on a good that brings greater utility at the margin.
D. The material on the derivation of the PPF from the Edgeworth box at the end of the chapter seems particularly useful to us when we teach the course, and we recommend that special emphasis be put upon it. This material is helpful for the later discussion in Chapter 8 of the Heckscher-Ohlin trade pattern when using the physical definition of factor abundance.
E. If students have a ready grasp of the Edgeworth box and if time permits in a one-semester trade course, you might want to derive a community indifference curve from a consumption Edgeworth box by selecting a starting point on the contract curve and “sliding” one consumer’s individual curve along the other’s curve so that the origin that is changing traces out a community curve. Different starting points can then be shown to yield intersecting curves unless assumptions are made that both consumers have: (a) the same (or proportional) incomes and identical tastes; (b) identical and homothetic tastes; or (c) the same (or proportional) incomes and homothetic tastes.
V. Answers to End-of-Chapter Questions and Problems
1. In the graph below,
the initial equilibrium is at point E1 with relative prices (PX/PY)1. If the price of good X falls while the price of good Y remains constant, then a new flatter price line (PX/PY)2 line emerges from the original intercept at point A on the vertical axis. Because MUX/PX is now greater than MUY/PY at E1, the consumer will substitute toward greater consumption of the X good and less consumption of the Y good in order to increase total satisfaction. Equilibrium will move from E1 to E2, and the consumer will be on a higher indifference curve and will have increased the relative consumption of good X. Only if good X is a sufficiently “inferior” good will the relative increase in the quantity of X consumed not occur.
2. Consider an indifference curve diagram such as Figure 3 in the text. A shift in the income distribution toward consumers with a relatively stronger preference for good Y than in the original distribution (the distribution with the solid lines) will make each curve “flatter” and will shift each curve leftward toward the vertical axis. The curves become flatter because, for any total amount of Y taken away from consumers at the margin in proportion to their incomes, more X must be given to the community as a whole in order to restore each consumer to his or her original level of satisfaction. The leftward shift occurs because, at each given total amount of good Y consumed (which is now more preferred), less X is necessary in order for the community as a whole to attain a given utility level.
3. In Figure 8 in the text, consider the lower intersection point (not labeled) of isoquant Q0 with budget line B1. At that point, MPPL/MPPK is less than w/r because the isoquant is flatter than the isocost line. This indicates that MPPL/w < MPPK/r, or that, at the margin, the output obtained per dollar spent on labor by the firm is less than the output obtained per dollar spent on capital. The profit-maximizing entrepreneur will therefore, with the given budget, reallocate spending toward capital and away from labor. The reallocation will stop at point E, where, at the margin, the output per dollar spent on capital is equal to the output per dollar spent on labor. The higher isoquant Q1 will have been reached, and equality between MPPL/MPPK has been achieved by a rising MPPL as less labor is utilized and a falling MPPK as more capital is utilized.
4. No, it cannot be unambiguously determined. With capital on the vertical axis and labor on the horizontal axis, the new flatter isocost line will have a vertical-axis intercept lower than originally and a horizontal-axis intercept to the right of the original intercept. If this new isocost line passes above the original equilibrium point, the new level of output will be greater than it was before the factor price changes; if it passes below the original point, output will have fallen.
5. With labor on the horizontal axis and capital on the vertical axis, the original isocost line has a vertical-axis intercept of 300 hours of capital usage and a horizontal-axis intercept of 3,000 hours of labor usage. The slope of this isocost line is (-)1/10 or 0.10. With the specified changes in factor prices, the isocost line shifts inward on both axes because the prices of both inputs have increased. The new intercepts are at 250 hours of capital and 2,000 hours of labor, and the new isocost line is slightly steeper [having a slope of (-)12.5/100 or 0.125] than the old one. The equilibrium level of output has fallen because all inputs have risen in price; the firm has also shifted toward using more capital relative to labor because w/r has risen.
6. The PPF would exhibit constant opportunity costs. Suppose that the employment of all of the economy’s capital and labor in the X industry (an endpoint of the Edgeworth box diagonal) yields 100 units of X output (and 0 units of Y output). Alternatively, suppose that employment of all capital and labor in the Y industry yields 200 units of Y output (and 0 units of X output). With constant returns to scale in both industries, production at the midpoint of the diagonal (using one-half of the economy’s capital and labor in each industry) would therefore yield 50X and 100Y. Employment of one-fourth of the economy’s capital and labor in the X industry and three-fourths of the economy's capital and labor in the Y industry (i.e., at a point one-fourth of the distance along the diagonal from the X origin to the Y origin) would yield 25X and 150Y. Plotting these various output combinations (and the output combinations of all other production points on the diagonal) yields a straight-line PPF. This PPF would be analogous to the dashed line RTMWQ in Figure 13(b) in the text.
7. This statement is incorrect. The discussion in the text regarding the productionpossibilities frontier indicates that a PPF with increasing opportunity costs emerges when constant returns to scale exist in each industry, provided that the industries have different factor intensities. Thus, neither industry needs to be operating in a context of decreasing returns to scale in order to generate an increasing-opportunity-cost PPF.
8. The country is producing less of the capital-intensive good and more of the laborintensive good. The overall demand for labor would rise and the overall demand for capital would fall as the industry with the higher K/L ratio (lower L/K ratio), industry Y, contracts, while the industry with the lower K/L ratio (higher L/K ratio), industry X, expands. Hence, relative factor prices w/r will rise (or r/w will fall). No, the (absolute values of the) isoquant slopes at V’ will be higher than at S’ because, in equilibrium, these (absolute values of the) slopes are equal to the now-higher w/r. An alternative geometric explanation is that, with homothetic isoquants, a ray from 0X (0Y) through S’ would hit isoquant x2 (y4) at a point below and to the right (above and to the left) of V’, a point that would have the same slope as isoquant x1 (y6) at S’. Given the convex shapes of isoquants, V’ would then have a steeper slope than S’.
9. The Edgeworth box would become “taller” because the vertical capital axes become longer and the horizontal labor axes stay the same length. The PPF will also become “taller” because the good Y intercept shifts upward by a greater percentage than the good X intercept shifts rightward. Note, however, that the good X intercept does shift to the right because, with a larger capital stock, more X can be obtained when all resources are devoted to X production.
10. If the price of labor rises with no change in the price or rental rate of capital, w/r increases (r/w decreases). Producers in both industries would respond by using relatively less labor and relatively more capital, and the K/L ratio would rise in both industries. Note that, in this question, we do not specify the cause of the rise in the price of labor – the effects on output of each good and on total output would depend on this cause and would be different, for example, if the cause were technological change that increased the demand for labor rather than a desire on the part of labor to take more leisure time.
VI. Sample Exam Questions
A. Essay Questions
1. Suppose that, from an initial individual consumer equilibrium position in the indifference curve-budget line diagram, the prices of both goods rise by 10 percent. What happens to the position and slope of the budget line? Why does the consumer’s level of satisfaction from a given money income fall? Illustrate and explain. Would it be acceptable for an economist to say that the level of satisfaction of the consumer fell by exactly 10 percent? Why or why not?
2. Suppose that, from an initial individual consumer equilibrium position in the indifference curve-budget line diagram, the price of good X rises while the price of good Y falls. What will happen to the relative consumption of the two goods by the consumer and why? Can it be specified whether the consumer’s level of satisfaction has increased or decreased because of this change in absolute and relative prices? Why or why not? Could the satisfaction level of some consumers increase and the satisfaction level of other consumers decrease because of the price changes? Explain.
3. “If constant returns to scale exist for a firm, then a 10 percent rise in all factor prices will lead to a 10 percent decline in the equilibrium quantity of output for a given budget. However, if increasing returns to scale exist, a 10 percent rise in all factor prices will lead to a less than 10 percent decline in the equilibrium quantity of output for a given budget.”
Assess the validity of this statement.
4. Explain, using the isoquant-isocost diagram, why a rise in the rental rate of capital coupled with no change in the wage rate will lead to a rise in the price of the capital-intensive good relative to the price of the labor-intensive good.
5. Explain why any point on an economy’s PPF must be associated with a point on the production efficiency locus in the Edgeworth box diagram.
6. The textbook has developed the Edgeworth box diagram and the concept of the production efficiency locus or contract curve in the context of the production of two goods with two factors. Apply the Edgeworth box apparatus to the context of consumption of two goods by two consumers, and, in particular, explain how welfare for the two consumers as a whole when on the contract curve relates to welfare when the consumers are not on the contract curve.
B. Multiple-Choice Questions
7. In the following Edgeworth box diagram for a country’s production,
* a. point T has greater output of the A good than does point R.
b. output of the A good is greater at point S as at point R.
c. a plotting of the output combinations along the “diagonal” results in the productionpossibilities frontier for this country.
d. good A is the relatively labor-intensive good and good B is the relatively capitalintensive good.
8. In the diagram in Question #7 above,
a. a movement from point S to point T involves an increase in the capital/labor ratio used in the production of good A.
b. if the PPF is plotted from the “contract curve” (or “production efficiency locus”), the production combination of goods A and B associated with point R is on the PPF.
c. if the PPF is plotted from the “contract curve” (or “production efficiency locus”), with good A on the vertical axis and good B on the horizontal axis, the production combination of goods A and B associated with the 0B origin is at the origin of the PPF graph.
* d. if the PPF is plotted from the “contract curve” (or “production efficiency locus”), with good A on the vertical axis and good B on the horizontal axis, the production combination of goods A and B associated with point T is further up the vertical axis than the production combination associated with point S.
9. In the diagram in Question #7 above, a movement from point S to point T will lead to __________ in the capital/labor ratio used in the production of good A and __________ in the capital/labor ratio used in the production of good B.
a. an increase; will lead to a decrease
b. an increase; also will lead to an increase
*
c. a decrease; also will lead to a decrease
d. a decrease; will lead to an increase
10. If, for a consumer, (MUA/PA) is greater than (MUB/PB), then the consumer
a. has an incentive to consume relatively more of good A, which will increase his/her MUA.
* b. has an incentive to consume relatively more of good A, which will decrease his/her MUA.
c. has an incentive to consume relatively more of good B, which will increase his/her MUB.
d. has an incentive to consume relatively more of good B, which will decrease his/her MUB
11 In the following table of production possibilities for a country, Good X Good Y
0 units 13 units
1 unit 10 units
2 units 6 units
3 units 0 units
there are __________ opportuninferior inity costs in the production of good X, and there are __________ opportunity costs in the production of good Y.
* a. increasing; increasing
b. increasing; constant
c. constant; increasing
d. constant; decreasing
12. Two indifference curves for an individual consumer __________ intersect; two community indifference curves for a country __________.
a. cannot; also cannot intersect
*
b. cannot; can intersect under some circumstances
c. can; can also intersect under some circumstances
d. can; cannot intersect
13. Which one of the following sequences of specifications of relative preferences for bundles of goods A, B, and C by a consumer indicates the property of transitivity (where “>” indicates that the preferred bundle is on the left, “<” indicates that the preferred bundle is on the right, and “=” means indifference between the bundles)?
a. A > B; B > C; C > A
b. A > B; B = C; C = A
* c. A < B; C < A; B > C
d. A = C; B > C; A > B
14. In the following table of production possibilities for a country,
Good X Good Y
400 units 0 units
300 units 100 units
200 units 180 units
100 units 240 units
0 units 280 units
there are __________ opportunity costs when moving to greater production of good X and __________ when moving to greater production of good Y.
a. increasing; decreasing
b. decreasing; constant
c. constant; increasing
*
d. increasing; increasing
15. Suppose that, in the isoquant-isocost diagram, with given relative factor prices, an equilibrium input combination of 10 units of capital and 30 units of labor yields an output level for the firm of 120 units. Suppose that, for this firm, at the same relative factor prices but with a larger budget, an equilibrium input combination of 15 units of capital and 45 units of labor yields an output level of 160 units. Viewing these input-output relationships, an economist would say that, in its production process, this firm experiences
a. increasing returns to scale.
b. constant returns to scale.
*
c. decreasing returns to scale.
d. increasing returns to scale, constant returns to scale, or decreasing returns to scale –cannot be determined without more information.
16. In the Edgeworth box diagram for production,
a. a point off the “contract curve” (or “production efficiency locus”) cannot have more production of one of the goods than can some point on the curve.
b. a point off the “contract curve” (or “production efficiency locus”) can involve more production of both goods than can any point on the curve.
* c. a movement from autarky to trade can be associated with a movement along the “contract curve” (or “production efficiency locus’).
d. the “contract curve” (or “production efficiency locus”) will always be the “diagonal” of the box.
17 In the following graph showing an isoquant and an isocost line, at point X,
*
MPPL/MPPK is w/r and the producer has an incentive to use relatively more in producing the given output.
a. greater than; capital
b. greater than; labor
c. less than; capital
d. less than; labor
18. In the Edgeworth box diagram in production with two goods and two factors of production,
a. a movement from any point off the “production efficiency locus” (“contract curve”) to any point on the locus must involve greater production of one good and less production of the other good.
b. a movement from any point on the “production efficiency locus” (“contract curve”) to any point off the locus must involve less production of both goods.
c. a point that is off the “production efficiency locus” (“contract curve”) must be associated with unemployment of at least one of the factors of production.
* d. a movement from any point on the “production efficiency locus” (“contract curve”) to another point on the locus must involve greater production of one good and less production of the other good.
19. The equilibrium condition for consumer behavior pertaining to goods A and B is
a. (MUB/PA) = (MUA/PB)
b. MUB = MUA
c. (MPPB/MPPA) = (PB/PA)
* d. (MUB/MUA) = (PB/PA)
20. You are given the following two possible community indifference curve maps for a country, where curves S1 and S’1 pertain to income distribution #1 and curves S2 and S’2 pertain to income distribution #2:
The differing shapes of the curves in these two maps could reflect the fact that in income distribution #2, in comparison with income distribution #1, a greater share of total income is held by individuals who value __________. In addition, in this diagram, point B is preferred to point A __________.
a. good X relatively more highly than good Y; on the basis of income distribution #2 but not on the basis of income distribution #1
b. good X relatively more highly than good Y; on the basis of income distribution #1 but not on the basis of income distribution #2
c. good Y relatively more highly than good X; on the basis of income distribution #2 but not on the basis of income distribution #1
* d. good Y relatively more highly than good X; on the basis of income distribution #1 but not on the basis of income distribution #2
21. A production isoquant shows the various combinations
* a. of two factors of production that can produce the same amount of output of a good.
b. of two factors of production that can be hired by a firm for the same cost.
c. of two goods that can be produced by the firm with the same quantity of the factors of production.
d. of two goods that bring an equivalent satisfaction level to an individual consumer
22. The slope of a consumer indifference curve at any given point on the curve reflects (ignoring the negative sign)
a. the marginal rate of transformation (MRT) in production of one commodity into the other commodity.
b. the marginal rate of technical substitution (MRTS) between the factors of production.
c. the relative prices of the commodities in the consumption bundle of goods.
* d. the marginal rate of substitution (MRS) of the consumer between the two goods.
23. The equilibrium condition for producers (i.e., the condition that exists when the isocost line is tangent to an isoquant) is __________.
a. (MPPL/r) = (MPPK/w)
* b. (MPPL/MPPK) = (w/r)
c. (MUB/MUA) = (PB/PA)
d. (MUB/PA) = (MUA/PB)
24. Given the following table showing various combinations of goods X and Y that bring equal satisfaction to an individual consumer:
In this table, as the individual consumes a greater amount of X, a __________ amount of good Y is given up for each additional unit of good X. This pattern suggests that, as more of good X is consumed and less of good Y is consumed, the ratio MUX/MUY is __________.
* a. larger; increasing, which contradicts economists’ usual expectations
b. larger; decreasing, which conforms to economists’ usual expectations
c. smaller; increasing, which contradicts economists’ usual expectations
d smaller; decreasing, which conforms to economists’ usual expectations
25. The curve in the following diagram is called an , and its slope (ignoring the negative sign) indicates the ratio
*
a.. isoquant; w/r
b. isoquant; MPPL/MPPK
c. isocost line; w/r
d. isocost line; MPPL/MPPK
26. Suppose that, in the context of the Edgeworth box diagram in production, there are constant returns to scale in each of the two industries and that one good is relatively labor-intensive in its production process and the other good is relatively capital-intensive in its production process. In considering this Edgeworth box diagram and the PPF that can be derived from it,
a. all points on the “diagonal” of the Edgeworth box diagram will have corresponding points on the PPF.
b. no point on the “diagonal” of the Edgeworth box diagram will correspond to a point on the PPF.
* c. the PPF will show increasing opportunity costs.
d. the PPF will show constant opportunity costs.