Consider the standard Romer model from the textbook with the following properties. Country
𝐵
has a larger population than country
𝐶
(i.e.
𝐿
¯
𝐵

𝐿
¯
𝐶
), but the two countries have the same initial knowledge stock
𝐴
𝑡
¯
, research share
ℓ
¯
, productivity in producing knowledge
𝑧
¯
, and population growth rate
𝑛
. Initially, the growth rate of GDP per capita in country
𝐵
is [ Select ] in country
𝐶
. In the long run, GDP per capita in country
𝐵
will grow [ Select ] in country
𝐶
.

Question

Consider the standard Romer model from the textbook with the following properties. Country 
𝐵
 has a larger population than country 
𝐶
 (i.e.  
𝐿
¯
𝐵
>
𝐿
¯
𝐶
), but the two countries have the same initial knowledge stock 
𝐴
𝑡
¯
, research share  
ℓ
¯
, productivity in producing knowledge 
𝑧
¯
, and population growth rate 
𝑛
. Initially, the growth rate of GDP per capita in country 
𝐵
 is [ Select ] in country 
𝐶
. In the long run, GDP per capita in country 
𝐵
 will grow [ Select ] in country 
𝐶
.

BlackTom AI · Accepted Answer

We start by restating what the question provides and what is being asked, then we evaluate each possible option in light of the Romer model’s mechanisms.

Restatement of the setup:
- Country B has a larger population than country C (LB > LC).
- They share the same initial knowledge stock A_bar, same research share l_bar, same knowledge production productivity z_bar, and same population growth n.
- The question asks about two things: (i) the initial growth rate of GDP per capita in B relative to C, and (ii) the long-run growth rate of GDP per capita in B relative to C, given these common parameters.

Option 1: Initial growth rate in B is higher than in C
- In Romer-type endogenous growth models with knowledge spillovers, a larger population can yield more researchers and stronger cumulative knowledge creation, all else equal. Since both countries start with the same knowledge stock, identical productivity of researchers (z_bar) and the same fraction of labor devoted to research (l_bar), the country with a larger population effectively benefits from a larger pool of potential researchers. This tends to raise the immediate (initial) rate at which knowledge stock grows, which in turn can translate into a higher initial growth rate of GDP per capita (through faster technology progress and productivity improvements).
- However, a caveat: GDP per capita growth in the Romer framework depends on how rapidly knowledge accumulates relative to population and how that knowledge translates into per-capita output. If the model’s mechanism specifies that the per-capita growth rate is driven by the growth rate of knowledge scaled by population (or by the externality from researchers) and if the externality is directly tied to the number of researchers rather than population per se, then a larger population typically raises the initial per-capita growth rate as long as the share of labor allocated to R&D and productivity parameters are the same.

Option 2: Long-run growth rate in B will grow higher than in C
- In the long run, several Romer-type models predict that the growth rate of the economy is driven by the rate of technological progress, which arises from research activity and knowledge spillovers. With LB > LC and identical research intensity (l_bar) and productivity (z_bar), the country with the larger population can sustain a higher absolute rate of knowledge creation, assuming its researchers are effectively translating that knowledge into new ideas. This would suggest a higher long-run growth rate for GDP (per capita or total GDP depending on model specification) in B relative to C.
- Yet, it is also possible in some formulations that long-run growth converges to a common rate if the model’s balanced-growth path features the same Pandora of externalities, or if the per-capita growth rate is governed by a form of knowledge accumulation that scales in such a way that the population difference does not alter the steady-state growth rate. In that case, long-run growth would be the same across both countries.

Putting the pieces together:
- Given LB > LC with all else equal (A_bar, l_bar, z_bar, n identical), the intuitive channel is that a larger population increases the potential number of researchers, which raises knowledge accumulation more quickly. This supports the view that the initial growth rate of GDP per capita in B could be higher than in C.
- For the long-run growth rate, the outcome depends on the specific details of how the Romer model translates knowledge growth into per-capita growth and whether the steady-state growth rate is exogenous or endogenous to population size. In many standard Romer setups, a larger population tends to raise the long-run growth rate as well, but there are formulations where the long-run rate is the same across countries if the key determinants of sustainable growth are identical aside from population.

Because the problem statement does not provide the explicit model equations or a definitive rule about how long-run growth scales with population in this particular textbook’s Romer setup, we cannot conclusively declare which option is correct for the long-run comparison without making an assumption about the exact mechanism. The absence of explicit answer options in the provided data further limits our ability to select.

In summary:
- For the initial growth rate: the case for 'higher than' is plausible given a larger pool of researchers driving faster knowledge accumulation, though it hinges on how per-capita growth is tied to knowledge creation.
- For the long-run growth rate: there is equal plausibility for 'higher than' or 'the same as' depending on the specific endogenous growth mechanism assumed in the textbook’s Romer model; without the exact formulation, we cannot deterministically pick one.

Note on missing information:
- The provided input lacks explicit answer options for the two dropdowns, so we cannot map these analyses to a definite selection. If the textbook states a particular relationship (e.g., long-run growth scales with population in a fixed way), that would fix the correct choice.

If you can share the exact model equations or the textbook’s stated mechanism for how population size enters the growth rate in the Romer framework, I can give a precise yes/no for each dropdown and tailor the justification accordingly.

SP25 ECON 312 001 Midterm Exam #2 (Chapters 6-9): Sample Questions

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