Answer Happy

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 𝑦𝑦 = 𝐴𝐴𝑘𝑘𝛼𝛼 and labor force grows at
rate n while productivity (A) is
constant.
The “golden rule level of saving – investment ” is the “optimal”
saving – investment rate
(𝛾𝛾𝐺𝐺) that maximises consumption per worker (𝛾𝛾 is the fraction of
income that is invested –
saved).
Prove that marginal product of capital (MPK) equals (𝛿𝛿 + 𝑛𝑛) at
the golden rule level of saving
– investment (𝛿𝛿 is depreciation rate).
Show the golden rule level of saving – investment on a graph.
On the same graph, show the case in which this economy is over
saving – investing. (Hint: In
this case, higher saving - investment does increase GDP per worker,
but not consumption
per worker.)