Copying others: Lucas-Moll 14 (continuous time) and Perla-Tonetti 14 (discrete t
ID: 1150414 • Letter: C
Question
Copying others: Lucas-Moll 14 (continuous time) and Perla-Tonetti 14 (discrete time). These models are not constant-income-growth models. Incomes of the poor grow faster than the rich because the poor have more to gain from copying In their models you have to give up working time (and therefore current income) if you want to copy others - you "search" for someone to copy. That is the cost. The gain is the prospect of a higher income in the future. Therefore there is a tradeoff involving a present value calculation. We will skip that and simply assume that each everyone gets to copy someone for free. So, even the rich (who have less to gain from and more to lose from giving up current income if they "search" instead of produce) will do some copying, and their incomes will grow - faster than in the two models mentioned above a) You pick someone at random from F (y). Call the sampled income y' b) You inherit what they know and you will use it if it is better than what you know already, i.e, if y'>y. Therefore y+1 max (y,y') And if is drawn independently of y, its distribution is Ft (y) =Explanation / Answer
1) Cost of copying is zero
y1, y2, y3,...are independently distribution on F(y).
At time t,
If y' < y then no change and rich will stick to y in t+1
If y' > y then rich would move to y' in t+1
mathematically,
yt+1 = max(y',y)
we know that,
Ft(y) = Ft (yt)
similiarly,
Ft+1 (y) = Ft(y) Ft(y) = Ft(y)2 (Given)
Ft+1(y) = Ft+1(yt+1))
Ft(y)2 = Ft+1(max(y',y)) (From above)
proved