Consider the Following Distribution of Income in a 12-Person Economy

question 6

Essay

Consider the following distribution of income in a 12-person economy, with the modern urban wage  10, the traditional rural income  2, and the informal urban wage  4: (2,2,2,2,4,4,4,4,10,10,10,10).
(a) Suppose rural incomes are raised to 3, other things equal.Show the change using the Lorenz curve.How would this type of growth be characterized? (It is suggested that you use the Fields growth decomposition in answering.This shows traditional sector enrichment growth.)
(b) Calculate the Ahluwalia-Chenery welfare index for terciles (3 fractiles) under GNP weights and equal weights.Which index is higher and why?

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Definitions:

F-ratio

The F-ratio is a statistic used to compare the variance among group means in an ANOVA test, helping determine if there are any statistically significant differences between the means of three or more unrelated groups.

P-value

A statistical metric indicating the probability of observing the results of a test, or more extreme, under the assumption that the null hypothesis is true.

SSE

Sum of Squared Errors, a measure used in statistics to describe the total deviation of predicted values from the actual values in a dataset.

Class Size SS

An educational metric that refers to the number of students enrolled in a particular class or course.