solow growth model 1 Flashcards
short-run and medium-run vs long-run
-sr + mr, only fop was labour, level of capital in economy assumed fixed
-concerned about how output fluctuates around natural rate of output
-definition of long-run: no fixed factors of production
-population can grow and be educated, can invest to increase amount of capital, can make technological discoveries, can change organisation of the economy
Solow growth model intro (characteristics, equation, returns)
-two key equations, three key curves:
-output, savings and required investment
-Y=f(K, AN)
-Y is output, K is capital, N is labour, A is technology
-assume constant returns to scale: if you double level of capital and technology in the economy, output will double
-can divide both sides by AN to write production function in effective labour terms- Y/AN= output per effective worker, K/AN= capital per effective worker
-assume decreasing returns to capital: increases n capital lead to smaller and smaller increases in output
savings and required investment
-savings=required investment
evolution of capital stock equation (explanation and two equations)
equation: Kt+1=(delat-1)Kt +It
-equation tells us that tomorrow’s capital stock depends on how quickly today’s depreciates and how much we invest today
-((Kt+1)/AN)-(Kt/AN)=sf(Kt/AN)-delta(Kt/AN)
-change in capital per effective worker=difference between savings and required investment
two additional features added to the Solow Growth Model (new equation from this and explanation)
-stock of tech in the economy grows at a fixed rate (gA=(At+1-At)/At))
-population in the economy grows at a fixed rate (gN=(Nt+1-Nt)/Nt)
-new equation: Kt+1/AN-Kt/AN= sf(Kt/AN)-(delta+gN+gA)Kt/AN
-explanation: if we save more and therefore invest more than what is required to maintain capital stock, our stock stock will grow
intuition of the investment curve (part of equation)
(delta+gN+gA)(Kt/AN)
-delta=percentage of investment that replaces depreciated capital
-gN=each period the pop grows, a percentage of investment is spent providing capital to new pop
-gA= when we make new tech discoveries, part of investment will be spent implementing (everyone wants access)
Solow growth model diagram and features
-axis: y- output per effective worker, x- capital per effective worker
-Y/AN at top, SY/AN proportion of output, (delta+gA+gN)(Kt/AN) straight line passing through (difference in top two is consumption, difference in second and axis is savings
-equilibrium: sf(Kt/AN)=(delta+gA+gN)(Kt/AN)
-steady state: Yt/AN=f(Kt/AN)
-if K/AN goes above/below steady state, K/AN will converge towards steady state
how capital per effective worker adjusts to changes in savings (and explanation through diagram)
1) if sf(Kt/AN)>(delta+gA+gN)(Kt/AN), level of investment exceeds required investment and level of capital per effective worker increases to steady state (set up graph as normal, increase to K1)
2) if sf(Kt/AN)<(delta+gA+gN)(Kt/AN), level of required investment exceeds investment, level of capital per effective worker falls until we reach steady state (same graph as before but falls)
growth assume that there is not technology (no case study, assumptions, graph and equation)
-initially assume gA=0 and gN=0
-equation: Yt/AtNt. fraction does not change, stock of tech fixed and pop fixed, therefore output stays fixed
-graph: output y, time x. stagnant output over time
growth assume there is no tech (with case study- brief history, explanation of theory, graph and how savings rate affects growth of output per effective worker)
-brief: several socialist economies (USSR, China, N.Korea) able to rapidly industrialise once state took control. economies grow at expense of pop, heavy industry prioritised and consumption sacrificed. very high savings rates leading to rapid short-run growth
-graphs. 1) Y/AN and K/AN, initial curves 2) output and time, stagnant growth
-explanation: 1) economy is initially at the steady state. 2) there is a rise in the savings rate 3) capital rises (large at first, then decreases until we reach steady state) 4) growth in capital and output per effective worker. on other graph: curved rise from savings rate until steady state where there is stagnant output
-final: no effect on long-run growth rate of output. rise in savings rate leads to rise in growth for some time
growth assuming tech (assumptions, no case study, equation and graph and then brief explanation through other graphs)
-assume gA and gN>0
-equation: fraction does not change, so all variables grow
-gY=gA+gN
-output and time: Y=A+N
-set up graphs as normal, steady growth in output-time graph
1) rise in savings, rise in capital per effective worker, 2) K/AN grows so we grow above steady state. 3) output-time graph curved until new steady state and reach growth above original
growth assuming tech (how it affects output per effective worker, graphs and explanations)
-no effect on long-run growth, affects level of output in long-run
-set up graphs as normal
-industrial revolution (gA, gN>0)
1)savings rate does not change but required investment changes
2)now we have to pay for tech discoveries out of savings, if savings rate does not change, then we do not have enough savings to maintain capital stock
1) when gA increases, we must implement tech discoveries
2) level of K/AN per effective worker falls
3) however once we reach steady state, output will grow at a faster rate even though K/AN is lower
graph: required investment rises. grow below new steady state until we reach
growth miracles post ww2
-UK+US high real income per person, had lowest avg growth 50-11
-france: large loss, over 1% of pop died. capital stock 30% lower than pre-war
-grew relatively quickly post 1945
