Exercises

Exercise 4.1. Derive eq.’s (4.3) and (4.4).

Exercise 4.2. Derive eq. (4.7). Explain how and why the behavior implied for technology by this equation differs from (4.4). Do you find the assumptions leading to (4.4) or to (4.7) more plausible?

Exercise 4.3.

stant income per capita throughout.

(2) Modify eq. (4.2) to

for some β ∈ (0,1). Justify this equation and derive the law of motion technology and income per capita under the two scenarios considered in the text. Are the implications of this model more reasonable than those considered in the text?

Exercise 4.4. In his paper “Tropical Underdevelopment”, Jeff Sachs notes that differences in income per capita between tropical and temperate zones have widened over the past 150 years. He interprets this pattern as evidence indicating that the “geographical burden” of the tropical areas has been getting worse over the process of recent development. Discuss this 162

thesis. If you wish, offer alternative explanations. How would you go about testing different approaches? (If possible, suggest original ways, rather than approaches that were already tried).