Increasing returns versus national product differentiation as an explanation for the patter

CHAPTER 12GENERAL EQUILIBRIUM AND WELFAREThe problems in this chapter focus primarily on the simple two-good general equilibrium model in which “supply” is represented by the production possibility frontier and “demand” by a set of indifference curves. Because it is probably impossible to develop realistic general equilibrium problems that are tractable, students should be warned about the very simple nature of the approach used here. Specifically, none of the problems does a very good job of tying input and output markets, but it is in that connection that general equilibrium models may be most needed. The Extensions for the chapter provide a very brief introduction to computable general equilibrium models and how they are used.Problems 12.1–12.5 are primarily concerned with setting up general equilibrium conditions whereas 12.6–12.10 introduce some efficiency ideas. Many of these problems can be best explained with partial equilibrium diagrams of the two markets. It is important for students to see what is being missed when they use only a single-good model.Comments on Problems12.1 This problem repeats examples in both Chapter 1 and 12 in which the productionpossibility frontier is concave (a quarter ellipse). It is a good starting problem because it involves very simple computations.12.2 A generalization of Example 12.1 that involves computing the production possibilityfrontier implied by two Cobb-Douglas production functions. Probably no one should try to work out all these cases analytically. Use of computer simulation techniques may offera better route to a solution (it is easy to program this in Excel, for example). It isimportant here to see the connection between returns to scale and the shape of theproduction possibility frontier.12.3 This is a geometrical proof of the Rybczynski Theorem from international trade theory.Although it requires only facility with the production box diagram, it is a fairly difficult problem. Extra credit might be given for the correct spelling of the discoverer’s name. 12.4 This problem introduces a general equilibrium model with a linear production possibilityfrontier. The price ratio is therefore fixed, but relative demands determine actualproduction levels. Because the utility functions are Cobb-Douglas, the problem can bemost easily worked using a budget-share approach.12.5 This is an introduction to excess demand functions and Walras’ Law.5758 Solutions Manual12.6 This problem uses a quarter-circle production possibility frontier and a Cobb-Douglasutility function to derive an efficient allocation. The problem then proceeds to illustrate the gains from trade. It provides a good illustration of the sources of those gains.12.7 This is a fixed-proportions example that yields a concave production possibility frontier.This is a good initial problem although students should be warned that calculus-typeefficiency conditions do not hold precisely for this type of problem.12.8 This provides an example of efficiency in the regional allocation of resources. Theproblem could provide a good starting introduction to mathematical representations ofcomparative versus absolute advantage or for a discussion of migration. To make theproblem a bit easier, students might be explicitly shown that the production possibility frontier has a particularly simple form for both the regions here (e.g., for region A it is22100+=).x y12.9 This problem provides a numerical example of an Edgeworth Box in which efficientallocations are easy to compute because one individual wishes to consume the goods in fixed proportions.12.10 A continuation of Problem 12.9 that illustrates notions of the core and exchange offercurves.Solutions12.1 a.b. 9x2 = 900; x = 10, y = 20c. If x = 9 on the production possibility frontier,y =20.24y =If x = 11 on the frontier, 19.74.Chapter 12/General Equilibrium and Welfare 59Hence, RPT is approximately (0.50).252y.x ∆---==∆ 12.2 I have never succeeded in deriving an analytical expression for all these cases. I have,however, used computer simulations (for example with Excel) to derive approximations to these production possibility frontiers. These tend to show that increasing returns to scale is compatible with concavity providing factor intensities are suitably different (case [e]), but convexity arises when factor intensities are similar (case [d]). 12.3 a. Draw the production possibility frontier and the Edgeworth box diagram. Find whereP line is tangent to PPF ; then go back to the box diagram to find input ratio. See Corn Law Debate example in the text.b. P given, land/labor ratio is constant.Equilibrium moves from E to E '.Cloth (O C E' > O C E ) Wheat (O W 'E' < O W E )12.4 a. 32x y p p = b. If wage = 1, each person’s income is 10. Smith spends 3 on x , 7 on y . Jones spends 5 on x , 5 on y . Since20,23x y += and demands are 812,y xx y p p == we have81281220,or 2322xx y x p p p P +=+=12,1x y p p == So Smith demands 6x , 21y . Jones demands 10x , 15y .c. Production is x = 16, y = 36.20 hours of labor are allocated: 8 to x production, 12 to y production.12.5 a. Functions are obviously homogeneous of degree zero since doubling of p 1, p 2 and p 3does not change ED 2 or ED 3. b. Walras’s Law states 0iiip ED =∑Hence, if ED 2 = ED 3 = 0, p 1ED 1 = 0 or ED 1 = 0.60 Solutions ManualCan calculate ED 1 as p 1ED 1 = –p 2ED 2 – p 3ED 32221122331213[3622]/.ED p p p p p p p p p =-+++ Notice that ED 1 is homogeneous of degree zero also. c. ED 2 = 0 and ED 3 = 0 can be solved simultaneously for p 2 /p 1 and p 3 /p 1 .Simple algebra yields p 2 /p 1 = 3 p 3 /p 1 = 5. If set p 1 = 1 have p 2 = 3, p 3 = 5 at these absolute pricesED 1 = ED 2 = ED 3 = 0. 12.6 PPF = f 2 + c 2 = 200dc f RPT = = df c -0.50.5U /f U /f cM R S = = = U /c U /c f∂∂∂∂ a. For efficiency, set MRS = RPT o r f c c f f c ==PPF: 2c 2 = 200, c = 10 = f = U , RPT = 1.b. Demand: P F /P C = 2/1 = MRS = c/f so c = 2f .Budget: 2f + 1c = 30 the value of production. Substituting from the demandequation: 4f = 30 f = 30/4, c = 15.U ; an improvement from (a) (the "demand effect"). c. Set RPT = 2/1 f = 2c .PPF : 5c 2 = 200, c fBudget now is: +Spend .f cc f ==A further improvement ("the production specialization effect")Chapter 12/General Equilibrium and Welfare 61d.12.7 f = Food c = Clotha. Labor constraint f + c = 100 (see graph below)b. Land constraint 2f + c = 150 (see graph below)c. Heavy line in graph below satisfies both constraints.d. Concave because it must satisfy both constraints. Since the RPT = 1 for the laborconstraint and 2 for the land constraint, the production possibility frontier of part (c) exhibits an increasing RPT ; hence it is concave. e. Constraints intersect at f = 50, c = 50. f < 50 1 so 1f c p dcdf p =-=f > 50 2so 2f cp dcdf p =-=f. If for consumers55so .44fc p dc df p =-= g. If p f /p c = 1.9 or p f /p c = 1.1, will still choose f = 50, c = 50 since both price lines “tangent” to production possibility frontier at its kink. h. .8f + .9c = 100Capital constraint: c = 0 f = 125 f = 0 c = 111.162 Solutions ManualSame PPF since capital constraint is nowhere binding.12.8 a. 2222,,100A A A A A A y y x x A Ay y x x L L L L ==+=+=Same for region 22so 44100B B By x += b. RPT ’s should be equal.c. B A A B A Bdy x dyx = = = = RPT RPT dx y dx y -- Therefore, A B A B x x = y y , hence 222BA A 2B y = .y x x ⎛⎫ ⎪⎝⎭But 22224()A B A B y y x x +=+ so substituting for 2A Y yields 222222141B B A B B B y y x x x x ⎛⎫⎛⎫+=+ ⎪ ⎪⎝⎭⎝⎭ x A = 2x B also y A = 2y B2239T A B B T B x x x x x x =+==2239T A B B T B y y y y y y =+== 22229()9100/4225T B T B y y x x +=+=⋅=If 2121449T T T y x x ===Note : Can also show that more of both goods can be produced if labor could move between regions.Chapter 12/General Equilibrium and Welfare 6312.9a. Contract curve is straight line with slope of 2. The only price ratio in equilibrium is 3to 4 (p c to p h).b. 40h, 80c is on C.C. Jones will have 60h and 120c.c. 60h, 80c is not on C.C. Equilibrium will be between 40h, 80c (for Smith) and 48h,96c (for Smith), as Jones will not accept any trades that make him worse off.U J = 4(40) + 3(120) = 520. This intersects the contract curve at 520 = 4(h) + 3(2h),h = 52, c = 104.d. Smith grabs everything; trading ends up at O J on C.C.12.10 (for diagram, see Problem 12.9)a. Core is O S, O J between points A and B.b. Offer curve for Smith is portion of O S O J above point A (since requires fixedproportions). For Jones, offer curve is to consume only C for p c/p h < 3/4 and consumeonly h for p c/p h> 3/4. For p c/p h= 3/4, offer curve is the indifference curve U J.c. Only equilibrium is at point B. p c/p h= 3/4 and Smith gets all the gains from trade--thebenefits of being inflexible.64。

Intangibles: Management, Measurement, and Reporting R&D and the Growth of Business EnterprisesThe contribution of R&D to the performance measure (profits ,sales) statistically to R&D expenditures –in the current and previous periods to allow for the delayed effect of R&D on business performance –and by controlling for the effect of other investments (physical assets ) on business performance. This statistical approach to empirically address issues concerning intangibles and their private and social impact was frequently used by economists and researchers in related areas. The empirical worked started with extensive historical case studies and proceeded to large sample (cross-sectional) analyses of R&D on firms’ productivity and growth .The research effort yielded several important findings:---R&D expenditures contribute significantly to the productivity(value added) and output of firms ,and the estimated rates of return on R&D investment are quite high —as much as—20-35 percent annually –with the estimates varying widely across industries and over time.--- The contribution of basic research (work aimed at developing new science and technology) to corporate productivity and growth is substantially larger than the contribution of other types of R&D ,such as product development and process R&D(where the latter is aimed at enhancing the efficiency of production processes).The estimated contribution differential of approximately three to one in favor of basic research is particularly intriguing ,given the widespread belief that public companies have been recently curtailing expenditures on basic research, in part as a response to the skepticism of many financial analysts and institutional investors about the commercialization prospects of basic research. Basic research is, of course, more risky than applied R&D (see chapter 2), but it is inconceivable that risk differentials by themselves account for a three-to-one productivity of basic research.---The contribution of corporate-financed R&D to productivity growth is larger than corporate-based –but government-financed —R&D (granted primarily to government contractors).The fact that most contracts with the government are basedon cost-plus terms may partially explain this findings. This result should not detract from the significant contribution to the industrial and technological infrastructure of publicly funded research conducted by government agencies and in federal laboratories (such as the contribution by the National Institutes of Health to pharmaceutical and biotech companies) as well as the substantial contribution of university research to technology.It should be noted that much of the research summarized above was based on survey data and industry aggregates, due to severe limitations in corporate published data. In fact, most of the examined variables and attributes—such as basic versus applied research and company versus government-sponsored R&D—cannot be directly estimated from information publicly disclosed to investors. Thus an important implication of these and similar findings is to suggest which kinds of currently unavailable information and data would be useful to managers, investors, and policymakers.Alternative Output Measures: Market Value and PatentThe research presented above relates R&D inputs (intensity, capital) to firms’ productivity, sales, or profit growth, in an attempt to estimate the return on corporate investment in innovation as well as to examine macro-economic issues, such as the productivity decline in the United States in the 1970s and early 1980s. This methodological approach encounters various problems; in particular the time lag between the investment in R&D and the realization of benefits (such as sales) is often long (particularly for basic research) and generally unknown, increasing the uncertainty about the estimated R&D contribution. Furthermore, biases and distortions in reported profits—arising from firms’ attempts to ―manage‖ investors’ perceptions (see chapter 4)—might cloud the intrinsic relationship between R&D and its subsequent benefits.These measurement difficulties have prompted a search for alternative and more reliable indicators of R&D output than reported sales and profitability measures. Two output indicators have received considerable in attention: capital market values of corporations and patents. Believers in efficient capital markets argue that stock priceand returns provide reliable signals of enterprise value and performance; hence R&D contribution can be evaluated using market values. Patents, and particularly citations in patent applications, provide an additional of the value of R&D and firms’ technology.Concerning capital market studies, the research persuasively indicates that investors regard R&D as a significant value-increasing activity. For example, a number of event studies register a significantly positive investor reaction (stock price increases) to corporate announcements of new R&D initiatives, particularly of firms operating in high-technology sectors and using cutting edge technology. When information is available, investors distinguish among different stages of the R&D process—such as program initiation and ultimate commercialization —most significantly rewarding mature R&D projects that are close to commercialization. Furthermore, econometric studies that relate corporate market values or market-to-book ratios to R&D intensities consistently yield positive and statistically significant association estimates. Further probing of the data suggests that investors value an R&D dollar spent by large firms more highly than that spent by small firms, probably a reflection of economies of scale in R&D. For example, large companies may benefit from lessons of failed R&D projects as they pursue the development of other project.The evidence thus indicates unequivocally that investors view R&D expenditures as on average enhancing the value of firms and that that also demonstrate some ability to differentiate the contribution of R&D across industries, firm sizes, and stages of R&D maturity. Investors’ ability to fine-tune R&D valuations is obviously hampered by the absence of detailed information on these attributes in corporate financial reports.Data on R&D expenditures available in financial statements are crude indicators of R&D contribution and value creation: there is productive R&D and wasteful R&D (Motorola and partners’$5 billion investment in the Iridium satellite communications project, currently in bankruptcy, is an example of the latter). The R&D productivity estimates discussed above obviously averaged the good and the bad, missingconsiderable information in the process. In an attempt to improve the estimation of R&D contribution, researchers experimented with patents, which can be considered an intermediate output measure of R&D (the final output measure is, of course, the benefit—sales, cost savings—generated by the R&D expenditure). Patents are only partial indicators of R&D output, since not every R&D project id patented. Yet patent research provides interesting insights.The Findings of Patent ResearchVarious attributes of patents, such as the number of patents registered by a company (patent counts), patent renewal and fee data, and citations of and to patents were examined by researchers. Both patent counts and the number of innovations emerging from a company’s R&D program were found to be associated with the level of corporate investment in R&D (the higher the R&D expenditures, the larger, on average, the number of consequent patents and innovations) as well as with firms’market values (the larger the number of patents and innovations, the higher the market value, on average). Patents are thus related to both inputs (R&D) and outputs (market values) of the innovation process and, therefore, are meaningful intermediate value measures.It is clear, however, that patent and innovations are noisy measures of R&D contribution, due to the skewness of their value distributions—that is, the tendency of a few patents or innovations to generate substantial returns (blockbusters), while the majority turn out to be virtually worthless. Citations (references) to a firm’s patents included in subsequent patent applications (forward citations) offer a more reliable measure of R&D value, since such citations are an objective indicator of the firm’s research capabilities and the impact of its innovation activities on the subsequent development of science and technology.Various studies show that patent citations capture important aspects of R&D value. For example, Manuel Trajtenberg reports a positive association between citation counts and consumer welfare measures for CAT scanners; Hilary Shane finds that patent counts weighted by citations (the firm’s number of registered patents divided by the number of citations by others to these patents) contribute to theexplanation of differences in Tobin’s q measures (market value over replacement cost of assets) across semiconductor companies; and Bronwyn Hall and colleagues report that citation-weighted patent counts are positively associated with firms’market values (after controlling for R&D capital). Patents and their attributes thus reflect technological elements used by investors to value companies.In a direct test of the usefulness of patent citation measures as indicators of value, studies have been conducted to examine the ability of various citation-based measures to predict subsequent stock returns and market-to-book values possess such predictive ability: the number of patents granted to the firm in a given year, the intensity of citations to a firm’s patent portfolio by subsequent patents, and a measure based on the number of citation in a firm’s patents (backward citations) to scientific papers (in contrast with citations to previous patents).The third measure reflects the scientific intensity of a patent and may provide a proxy for the extent of basic research conducted by the company. The fact that patent indicators are associated with subsequent stock prices and returns suggests that investors are not fully aware of the ability of these measures to convey useful information about firms’ innovation processes and capabilities. This is of course not surprising, given the novelty of patent-related measures as indicators of enterprise value.Patents are the intangible assets actively traded in markets (see chapter 2), in the form of licensing and sale of patents. An examination of firms’royalties from the licensing of patents indicates that the volume of royalty income is swiftly increasing and that investors value a dollar of patent royalties (the implicit, market multiplier of royalty income) two to three times higher than a dollar of regular income. The reason for the high valuation of patent royalties probably lies in the stability of this income source (patents are usually licensed for several years) relative to other more transitory components of income. Patent royalties also impact investors’valuation of R&D, namely the market value they assign to a dollar of R&D expenditures. The valuation of the R&D of firms with royalty income is higher than the valuation of the R&D of firms that do not license patents, probably due to investors’ belief that the quality andprospects of the R&D of firms able to license patents is relatively high.SummerR&D, a major form of corporate intangible investment, is found to be an important contributor to firms’productivity, growth, and capital market value. The magnitude of this contribution—return on R&D investment —varies across industries and over time but is, by and large, considerably higher than firms’cost of capital; hence the value creation capability of R&D. The research record, therefore, strongly supports the assertions made in chapter 2 concerning the scalability of intangibles due to their nonrivalry and increasing returns properties as well as the existence of positive network effects (externalities) of many intangibles.In addition to the general findings about the positive contribution of R&D to corporate value and growth, the empirical record indicates the following: ---The return on basic (fundamental) research is substantially higher than that of applied or process R&D.---Despite the expensing of R&D outlays in financial reports, investors consider R&D an important asset.---Even for internet companies, where the uncertainty regarding future benefits is currently considerable, investors value much of the R&D(product development) as an investment (asset) rather than an expense .---Patents and their attributes (for example, citations) constitute useful intermediate output measures of R&D value.---In recent years, Internal R&D has been complemented by acquired R&D and technology under development, where the latter often surpasses the former in volume of expenditure.---Royalties from patent licensing are a potent (in terms of creating market value) source of corporate income.Organizational CapitalThe extensive research focusing on R&D provides important insights about the organization of R&D activities (such as economies of scale), the private and social returns on R&D, the appropriation of R&D benefits (such as the effectiveness ofpatent protection), and investor’s valuation of innovation activities. R&D, however, is but one component of firms’ intangible capital (knowledge assets), which is of course particularly pronounced in the technology-and science-based sectors. Other components of intangibles—human and organizational capital—have received substantially less research attention than R&D. Consequently, our knowledge concerning important intangibles is rudimentary at best.Resource：Baruch Lev. Intangibles: Management, Measurement and Reporting [M]. The Brookings Institution,2001.55-62.。