Consider an economy where each worker is employed in either agriculture or services. Assume that log earnings of a worker are wo = µo + ɛo if she is employed in agriculture and w₁ = μ₁ + ₁ if she is employed in services, where μo and μ₁ are constants, o~ N(0,02), and 1 ~ N(0, 07). Assume also that the correlation between earnings in the two sectors is p = 01 0001' where 01 Cov(0, 1). Workers can be employed in agriculture at no cost, but they incur a cost C = exp(wo) if they choose to work in services. Finally, assume that workers maximize their net earnings. Each worker knows all the parameters relevant to her decision. (a) Derive a linear approximation of the equation that determines whether an individual chooses services or agriculture. Assume that C' is small compared to exp(wo), so you can ignore the error involved in this approximation. (b) Define v = 1 - 0 Calculate the probability that a randomly chosen worker is employed in services as a function of z, where z = (μo - μ₁ + π) /0₂. (c) How does this probability change when oo increases? Interpret your results. (d) Calculate the mean earnings of service workers had they worked in agriculture. Hint: use the fact that for two standardized joint normal random variables X and Y, E[Y|X] = Corr (X, Y). X. (e) Starting with an agricultural society, explain how you might test some of the predictions of this model, and what difficulties you might face.
Consider an economy where each worker is employed in either agriculture or services. Assume that log earnings of a worker are wo = µo + ɛo if she is employed in agriculture and w₁ = μ₁ + ₁ if she is employed in services, where μo and μ₁ are constants, o~ N(0,02), and 1 ~ N(0, 07). Assume also that the correlation between earnings in the two sectors is p = 01 0001' where 01 Cov(0, 1). Workers can be employed in agriculture at no cost, but they incur a cost C = exp(wo) if they choose to work in services. Finally, assume that workers maximize their net earnings. Each worker knows all the parameters relevant to her decision. (a) Derive a linear approximation of the equation that determines whether an individual chooses services or agriculture. Assume that C' is small compared to exp(wo), so you can ignore the error involved in this approximation. (b) Define v = 1 - 0 Calculate the probability that a randomly chosen worker is employed in services as a function of z, where z = (μo - μ₁ + π) /0₂. (c) How does this probability change when oo increases? Interpret your results. (d) Calculate the mean earnings of service workers had they worked in agriculture. Hint: use the fact that for two standardized joint normal random variables X and Y, E[Y|X] = Corr (X, Y). X. (e) Starting with an agricultural society, explain how you might test some of the predictions of this model, and what difficulties you might face.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![Consider an economy where each worker is employed in either agriculture
or services. Assume that log earnings of a worker are wo = 4o + €o if she
is employed in agriculture and wi = µ1+€1 if she is employed in services,
where µo and H1 are constants, ɛo ~ N(0, o3), and e1 - N(0, o?). Assume
also that the correlation between earnings in the two sectors is p = g01
where oo1 = Cov(Eo, E1). Workers can be employed in agriculture at no
cost, but they incur a cost C = T exp(wo) if they choose to work in services.
Finally, assume that workers maximize their net earnings. Each worker
knows all the parameters relevant to her decision.
(a) Derive a linear approximation of the equation that determines whether
an individual chooses services or agriculture. Assume that C is small
compared to exp(wo), so you can ignore the error involved in this
approximation.
(b) Define v = €1
chosen worker is employed in services as a function of z, where
z = (Ho – H1 +7)/0,.
(c) How does this probability change when oo increases? Interpret your
Calculate the probability that a randomly
results.
(d) Calculate the mean earnings of service workers had they worked in
agriculture. Hint: use the fact that for two standardized joint normal
random variables X and Y, E[Y|X] = Corr(X, Y) X.
(e) Starting with an agricultural society, explain how you might test some
of the predictions of this model, and what difficulties you might face.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F50e56197-12bc-4435-9d06-afde5115b3bd%2Fc0580b1a-084e-48d7-8ffd-806587bdadf5%2F5jyv9h9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider an economy where each worker is employed in either agriculture
or services. Assume that log earnings of a worker are wo = 4o + €o if she
is employed in agriculture and wi = µ1+€1 if she is employed in services,
where µo and H1 are constants, ɛo ~ N(0, o3), and e1 - N(0, o?). Assume
also that the correlation between earnings in the two sectors is p = g01
where oo1 = Cov(Eo, E1). Workers can be employed in agriculture at no
cost, but they incur a cost C = T exp(wo) if they choose to work in services.
Finally, assume that workers maximize their net earnings. Each worker
knows all the parameters relevant to her decision.
(a) Derive a linear approximation of the equation that determines whether
an individual chooses services or agriculture. Assume that C is small
compared to exp(wo), so you can ignore the error involved in this
approximation.
(b) Define v = €1
chosen worker is employed in services as a function of z, where
z = (Ho – H1 +7)/0,.
(c) How does this probability change when oo increases? Interpret your
Calculate the probability that a randomly
results.
(d) Calculate the mean earnings of service workers had they worked in
agriculture. Hint: use the fact that for two standardized joint normal
random variables X and Y, E[Y|X] = Corr(X, Y) X.
(e) Starting with an agricultural society, explain how you might test some
of the predictions of this model, and what difficulties you might face.
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