In a Solow economy, the current steady state has a marginal product of capital f'(k*) = 0.06 and a depreciation rate δ = 0.10. What does this imply about current policy?
AThe economy is at the golden rule — no change is needed
BThe economy is dynamically inefficient — reducing the savings rate would raise steady-state consumption
CThe economy is below the golden rule — increasing the savings rate would raise steady-state consumption
DThe economy is growing too fast — consumption must be permanently reduced to stabilize capital
The golden rule requires f'(k*) = δ. Here f'(k*) = 0.06 < δ = 0.10, meaning the economy has accumulated too little capital relative to the optimum — it is below the golden rule. Increasing savings would raise capital and increase steady-state consumption. Dynamic inefficiency (too much capital) occurs when f'(k*) < δ in the other direction — when the economy is so over-capitalized that the extra output barely covers the maintenance cost.
Question 2 Multiple Choice
An economy is found to have f'(k*) < δ. This is called dynamic inefficiency. Why is it considered a 'free lunch'?
AThe government can tax capital and transfer to workers without any efficiency loss
BReducing the savings rate raises consumption in both the current period and all future steady-state periods simultaneously — no generation need sacrifice for another
CThe economy can grow faster by investing less, so future generations benefit at no cost to anyone
DDynamic inefficiency means capital is depreciated instantly, so investment is costless
In a dynamically inefficient economy (f'(k*) < δ), the economy maintains more capital than is optimal — the maintenance cost (depreciation on the extra capital) exceeds the output it produces. Reducing investment immediately frees up resources for consumption. And because the new steady state also has higher consumption (less wasted on unproductive capital maintenance), every generation benefits. This 'free lunch' is rare in economics precisely because it requires no tradeoff between current and future welfare.
Question 3 True / False
A dynamically inefficient economy can increase steady-state consumption by reducing its savings rate, without any permanent sacrifice by current generations.
TTrue
FFalse
Answer: True
This is the striking implication of dynamic inefficiency. When f'(k*) < δ, the economy over-invests — maintaining excessive capital costs more in forgone consumption than the capital produces. Reducing the savings rate raises consumption immediately and raises steady-state consumption permanently. Unlike a dynamically efficient economy (where reaching the golden rule requires transitional sacrifice), a dynamically inefficient economy can improve welfare in all periods by simply saving less.
Question 4 True / False
The golden rule of capital accumulation identifies the steady state that maximizes output per capita.
TTrue
FFalse
Answer: False
The golden rule maximizes consumption per capita, not output per capita. These are different objectives because consumption = output − investment, and investment (the cost of maintaining the capital stock) must be subtracted. The golden rule condition — marginal product of capital equals the depreciation rate — is found by maximizing c* = f(k*) − δk*, not f(k*). An economy with more capital than the golden-rule level has higher output per capita but lower consumption per capita.
Question 5 Short Answer
Why is dynamic inefficiency described as a 'free lunch,' and what is the golden-rule condition that identifies whether an economy is dynamically efficient or not?
Think about your answer, then reveal below.
Model answer: Dynamic inefficiency (f'(k*) < δ) means the economy maintains more capital than is optimal — the depreciation cost of the extra capital exceeds its marginal product. Reducing savings raises consumption now and permanently raises steady-state consumption, so no generation sacrifices for another. The golden-rule condition is f'(k*) = δ: the marginal product of capital exactly equals the depreciation rate, balancing productivity gain against maintenance cost.
Most economic improvements involve tradeoffs — you sacrifice current consumption for future growth, or redistribution creates disincentives. Dynamic inefficiency is exceptional because the tradeoff disappears entirely: the economy is literally wasting resources on capital that costs more to maintain than it produces. The golden rule condition f'(k*) = δ identifies the boundary between efficient (below) and inefficient (above) over-accumulation.