Technology: 2-Country Model


R&D spending in a country will have two effects 1. change the country's relative position in the world technology hierarchy, with transitory growth in both technology and income 2. increased R&D will lead to faster growth in technology for the world as a whole.


  • Technology is nonrival and frequently nonexcludable
  • One-country model key equations:
    1. γ_A=L_A/L (fraction of labour force in R&D)
    2. y=A(1-γ_A) from L_Y=(1-γ_A)L & Y=AL_Y
    3. A-hat=L_A/μ - where μ is price of the new invention.
    4. If γ_A is constant then γ-hat = A-hat i.e. technology
  • Two-country model key equations
    • wo-ways to develop technology 1. innovation 2. imitation, cost of latter (μ) is lower.
    • Assume technology leader has higher A, fraction of labour force in R&D (γ_A,1>γ_A,2) than technology follower but same size labour forces - collectively guaranteeing one is technology leader.
    • μ_i>μ_c - where cost of copying decreases with a larger gap in technology.


One-country model

  • Increase in γ_A leads to long-run (permanent) increase in A-hat and y-hat but a temporary decrease in y

Two-country model

  • In the steady-state the countries grow at the same rate
  • μ_c=γ_A,2/γ_A,1*μ_i


  • One-country model predicts that a country with a larger γ_A will have a larger growth rate. Also larger countries will have more R&D workers therefore larger A-hat.
  • Two-country model predicts that increase in γ_A,1 shift imitator curve up and shift steady-state to the left (smoother curve than one-country model) but crucially there is never convergence in the long-run.
  • Tacit knowledge means 1. much more difficult to transfer between countries than within a country because tacit knowledge is a general rather than specific 2. successful transfer of one technology can lead to large positive externality effects (e.g. taiwan/south korea)


  • There is no evidence that larger countries (with larger numbers of researchers) growth faster.
  • Historically there has been a massive increase in the number of researchers but with tech progress being relatively stable.


  • Unlike Solow model increases in capital or savings, increases in γ_A lead to long-term (not temporary) increases in growth rate.
  • Technology leader is not necessarily better off (with a higher quality of living) because it also has to forgo a larger proportion of its workforce to research.
  • Now technological superiority is much more diffuse (unlike perhaps USA post-WW2 and UK in the early 19th century)
  • However technological transfer often doesn't happen for two reasons developing countries 1. choose not to use inappropriate technology (page 246 graph for capital-biased tech change) 2. are unable to use advanced tech (lack tacit knowledge)
  • Embodied technological progress is where new tech is fundamentally tied to capital investment (e.g. new machine). Can lead to leap-frogging where only those countries with the worst tech upgrade, but when they do they go to the best e.g. mobiles>land-lines
  • Assume that cost of technology is independent of level of technology however 1. -ve fishing out-effect of easy ideas 2. -ve time it takes to get to frontiers of knowledge 3. -v marginal value of additional researcher falls with larger numbers of researchers 4. +ve benefits of more areas to work on
  • In the long-run technological growth will probably decline because 1. limited number of new researchers from developing countries 2. fraction of labour force in research cannot grow 3. labour force will not grow. 
  • Tech growth could be zero in long-run if demand is for complements and therefore doesn't increase and f.o.p are shifted to other activities (manufacturing --> services), or if they substitutes it can lead to continued growth (improvements in services)