How would you find the golden rule quantity of capital per person? Select one – the most appropriate answer given provisions of Solow model of economic growth.

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Question: How would you find the golden rule quantity of capital per person? Select one – the most appropriate answer given provisions of Solow model of economic growth.
Option: Optimize the following objective function MPK = n + d and solve it for capital.

Analysis of the option:
- The golden rule condition in the Solow model is derived by maximizing steady-state consumption per worker, which leads to the rule that the marginal product of capital (MPK) should equal the sum of the depreciation rate and the population growth rate. In standard notation, this is MPK = δ + n, where δ (or d) is depreciation and n is the population growth rate. This captures the idea that the investment required to replace depreciating capital plus to equip new workers should be balanced by the return from capital.
- The given option states MPK = n + d, which matches the correct relationship MPK = δ + n, just with d used for depreciation. So structurally, it identifies the correct condition for the golden rule, namely equating MPK to the total effective depreciation that includes both physical depreciation and the dilution from population growth.
- However, there are some caveats about phrasing: calling this an objective function is a misnomer. The golden rule condition is not an objective function to optimize in itself; it is a first-order condition derived from maximizing consumption per worker, which yields MPK = δ + n as the optimality condition. The option’s wording could be interpreted as treating MPK = n + d as an optimization target rather than the condition that characterizes the golden rule.
- Putting it into context: if you set MPK equal to n + d and solve for capital, you are effectively finding the level of capital where the return on capital just covers the depreciation plus the dilution due to population growth, which aligns with the golden rule concept. This approach yields the golden rule steady-state capital stock per worker under standard Solow assumptions.
- Alternative interpretations that would render the option incorrect include misidentifying the condition (for example, thinking golden rule requires MPK = δ alone, or thinking the objective is to maximize MPK itself rather than to balance MPK with the required depreciation plus population growth). Those would deviate from the established golden rule derivation.
- In summary, this option captures the essential relationship MPK = δ + n (with d representing δ) that characterizes the golden rule, though the wording could be refined to emphasize that it’s a condition derived from maximizing consumption rather than an objective function to optimize directly.

econ_303_120251_245369 Lesson 9 Quiz

How would you find the golden rule quantity of capital per person? Select one – the most appropriate answer given provisions of Solow model of economic growth.

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