. 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 = AAkkax 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 (YGG) that maximises consumption per worker (yy is the fraction of income that is invested – saved). Prove that marginal product of capital (MPK) equals (88 + nn) at the golden rule level of saving - investment (88 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.) |

ENGR.ECONOMIC ANALYSIS
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ISBN:9780190931919
Author:NEWNAN
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Chapter1: Making Economics Decisions
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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 = AAkkax
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 (yyGG) that
maximises consumption per worker (yy is the
fraction of income that is invested – saved).
Prove that marginal product of capital (MPK)
equals (88 + nn) at the golden rule level of
saving – investment (88 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.)
Transcribed Image Text: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 = AAkkax 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 (yyGG) that maximises consumption per worker (yy is the fraction of income that is invested – saved). Prove that marginal product of capital (MPK) equals (88 + nn) at the golden rule level of saving – investment (88 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.)
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