Economic growth and economic development 591

Introduction to Modern Economic Growth research may be very unprofitable and there may be zero R&D effort, in which case ηV (ν, t) could be strictly less than Nevertheless, for the relevant parameter values there will be positive entry and economic growth (and technological progress), so we often simplify the exposition by writing the free-and the condition as ηV (ν, t) = Note also that since each monopolist ν ∈ [0, N (t)] produces machines given by (13.10), and there are a total of N (t) monopolists, the total expenditure on machines is (13.15) X (t) = N (t) L Finally, the representative household’s problem is standard and implies the usual Euler equation: C˙ (t) = (r (t) − ρ) C (t) θ and the transversality condition Z t ả (13.17) lim exp r (s) ds N (t) V (t) = 0, (13.16) t→∞ which is written in the “market value” form and requires the value of the total wealth of the representative household, which is equal to the value of corporate assets, N (t) V (t), not to grow faster than the discount rate (see Exercise 13.3) In light of the previous equations, we can now define an equilibrium more for- mally as time paths of consumption, expenditures, R&D decisions and total number of varieties, [C (t) , X (t) , Z (t) , N (t)]∞ t=0 , such that (13.3), (13.15), (13.16), (13.17) and (13.14) are satisfied; time paths of prices and quantities of each machine and the net present discounted value of profits from that machine, [χ (ν, t) , x (ν, t)]∞ ν∈N(t),t=0 that satisfy (13.9) and (13.10), time paths of interest rate and wages such that [r (t) , w (t)]∞ t=0 (13.13) and (13.16), hold We define a balanced growth path equilibrium in this case to be one in which C (t) , X (t) , Z (t) and N (t) grow at a constant rate Such an equilibrium can alternatively be referred to as a “steady state”, since it is a steady state in transformed variables (even though the original variables grow at a constant rate) This is a feature of all the growth models and we will throughout use the terms steady state 577