Lecture 1

• the production equation is Y=A*K^aL^(1-a)
• a (alpha) is the share of output that eventually goes to capital
• 1-a is the share of output that eventually goes to labour
• The resource equation is that Ct+It=Yt
• Ct is consumption
• It is investment
• capital accumulation is Kt+1 = Kt + It -dKt
• labour supply is assumed to be exogenous, so Lt= L bar
• Investment is Y* Sbar, the fraction of total output invested
• Sbar is exogenous
• Ct= (1-s)* Yt
• the solow model has 5 equations: Production function, capital accumulation, labour force, Resource constraint, and allocation of resources
• the production function is that Yt=AKt^a * Lt^(1-a)
• capital accumulation is that the change in K = It-dKt
• capital accumulation shows a change over time, so it turns the model into a dynamic model, with intertemporal relationships
• The resource constraint is that Ct+It= Yt
• allocation of resources is that It= sYt
• Saving = investment. Yt-Ct=It
• net investment = sYt - dKt = change in capital
• In the production function, Kt having an exponential means that Y is a concave, increasing function. It also means there is diminishing returns, so if you start with a low K, Y increases lots, and if K starts high, Y growth is small
• at the steady state, sYt=dKt
• at the rest point of the economy (where investment= depreciation), all endogenous variables are steady
• transition dynamics take the economy from an intial level of capital to the steady state
• steady state Y (y*) is caused through higher A, L, alpha and s. it is also caused through a lower d
• growth of the economy through increasing s is limited because s is limited at 1 (100%) and as it increases, consumption decreases
• short term growth can come from changes in K
• long term growth only occurs through technological changes and changing A
• Per-Capita output (y) only grows with changes in alpha
• most of the difference in countries' y* is due to differences in A; different levels of productivity. A1/A2 is known as the solow residual
• a change in investment (s) will cause y to move up to a new steady state. it takes time on the time-series graph
• a change in investment slowly increases Y because K grows only slowly
• an increase in A causes both an immediate and gradual increase in y
• an increase in A causes a jump in y through y=aKL
• an increase in A causes an increase in sY, which causes a gradual increase in y towards a new steady state
• when A grows continuously through exogenous factors, yt grows at the same rate over time. a change in A and s causes shifts in the yt/t line (but the long-term rate of growth will not change
• changes in A and s cause only short term changes to growth rate
• as the steady state is approached, growth shrinks to 0; explaining why rich countries grow slower than poorer ones
• the convergence principle is that poorer countries grow quicker than richer countries
• the convergence criteria only held for OECD countries (not the whole world) suggesting conditional convergence; that the criteria only holds for similarly developed countries
• more recently, the conditional convergence criteria has been holding uncondionionally