Long-run growth in this model is driven by the ceaseless accumulation of knowledge capital resulting in an ever greater range of M-varieties. Given preferences, this ceaseless expansion of variety raises real consumption continually. While technology and output in the traditional sector is stagnant, the expansion of M-varieties forces up the price of T relative to that of the composite good CM. The value of the two sectoral outputs thus grows in tandem.
Stage-One’s Growth and Investment Rates
By definition, the initial interior solution entails symmetry, i.e.,0E=0K=l/2 and, as long as ф <фса1, this outcome is stable. The steady-state rate of К accumulation during this phase is found using the expression for L, from in, to get:
This common rate of К-accumulation is unaffected by the level of trade costs, ф.
Steady-state growth in real income is nominal Y divided by the perfect consumption price index. P. Given preferences, and pz=pz*=l, the perfect price index is PM“, where PM is the CES price index. Thus P and P* are:
In steady state, nominal Y and 0K are time-invariant, yet the P’s falls on the steady-state growth path since K” rises at the common rate of g. Thus PM falls at g/(o-l) and real income grows at ag/(a-l). Using :
where gintomi, is the real income growth rate. By inspection, the growth rate rises with X and a, but falls with p and a (all of which are standard results in the trade and endogenous growth literature). Again, trade costs do not play a role as long as the economy remains at the symmetric equilibrium.
Consider next, the rate of investment, which plays a central role in Rostow’s stages-of-growth approach. With labour as numeraire, the rate of investment in steady state is L,/Y. Using and the definition of Y, we have:
Again, the ratio is rising in к and a, falling in p and a, and unaffected by ф.
These results are simple to establish since stage-one is a steady state. The stage-three growth rate is similarly simple to establish, so we turn to it next.