Consider two countries, labeled 1 and 2. Each has the production function
𝑌
𝑖
=
𝐴
¯
𝑖
𝐾
𝑖
𝛼
𝐿
𝑖
1
−
𝛼
, for i = 1, 2. Assume that the countries currently have the same GDP per person,
𝐿
1
=
𝐿
2
, common saving, population growth, and depreciation rates, and
𝐾
1

Question

Consider two countries, labeled 1 and 2. Each has the production function 
𝑌
𝑖
=
𝐴
¯
𝑖
𝐾
𝑖
𝛼
𝐿
𝑖
1
−
𝛼
 , for i = 1, 2. Assume that the countries currently have the same GDP per person, 
𝐿
1
=
𝐿
2
 , common saving, population growth, and depreciation rates, and 
𝐾
1
<
𝐾
2
 . Based on this information you know that, in the long run, GDP per capita in country 1 (
𝑦
1
) is _______  
𝑦
2
.

Hint: Based on the information above, what do you know about 
𝐴
1
 relative to 
𝐴
2
?

BlackTom AI · Accepted Answer

To analyze which country will have higher GDP per capita in the long run, start by expressing GDP per capita in each country. - Each country has Yi = Âi Ki^α Li^(1−α). With Li equal across countries (L1 = L2) and per-capita GDP yi = Yi / Li, we get yi = Âi Ki^α Li^(−α) = Âi Ki^α / Li^α. Since Li is the same for both countries, the ratio of per-capita GDPs depends on Âi Ki^α. - We are given that K1 < K2 and that current GDP per person is the same (y1 = y2). Therefore, Â1 K1^α must equal Â2 K2^α to have the same y. Because K2 > K1, the term K2^α is larger, so to compensate and keep Â1 K1^α = Â2 K2^α, it must be that Â1 is greater than Â2. In other words, country 1 must have a larger technology or efficiency parameter than country 2. Now evaluate each option: - Option: greater than This is consistent with the relation Â1 > Â2 derived from the equality of y1 and y2 given K1 < K2. Since Â1 must be larger to offset the smaller K1^α and still yield the same per-capita output, this option aligns with the logic. - Option: less than If Â1 were less than Â2, then Â1 K1^α would be smaller than Â2 K2^α (given K2^α > K1^α), making y1 < y2, which contradicts the premise that they currently have the same GDP per person. Therefore this option is inconsistent with the given information. - Option: equal to If Â1 were equal to Â2, then y1 would be proportional to K1^α and y2 to K2^α. With K1 < K2, we would have y1 < y2, contradicting the stated equal GDP per person. Thus this option cannot hold. In summary, the combination of a smaller capital stock in country 1 (K1 < K2) and the requirement that y1 = y2 implies that country 1 must have a larger Â1 relative to Â2. This makes the per-capita GDP in country 1, in the long run, consistent with being driven by greater technology or efficiency. The only option that matches this reasoning is the one stating that y1 is greater than y2 when considering the underlying A terms, given the constraint on K.

FA25 ECON 302 002 Midterm 2

View Explanation

Log in for full answers

Similar Questions

In the Solow model with no population growth (i.e., L is fixed), a rise in the saving rate leads to a higher steady-state capital stock, and a rise in the depreciation rate leads to a lower steady-state capital stock.

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler