Consider an economy in which the amount of investment is equal
to the amount of saving
(i.e., the economy is closed to international flows of
capital).
Any output that is not saved is consumed (all equivalently, C=Y-S;
C=Y-I; c=y-s; c=y-i).
The production function is ๐ฆ๐ฆ = ๐ด๐ด๐๐๐ผ๐ผ and labor force grows at
rate n while productivity (A) is
constant.
The โgolden rule level of saving โ investment โ is the โoptimalโ
saving โ investment rate
(๐พ๐พ๐บ๐บ) that maximises consumption per worker (๐พ๐พ is the fraction of
income that is invested โ
saved).
Prove that marginal product of capital (MPK) equals (๐ฟ๐ฟ + ๐๐) at
the golden rule level of saving
โ investment (๐ฟ๐ฟ is depreciation rate).
Show the golden rule level of saving โ investment on a graph.
On the same graph, show the case in which this economy is over
saving โ investing. (Hint: In
this case, higher saving - investment does increase GDP per worker,
but not consumption
per worker.)
Consider an economy in which the amount of investment is equal to the amount of saving (i.e., the economy is closed to i
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