6. A worker with a marginal value product of can earn w, = k√0 in self- employment. Marginal value products vary across the population according to the uniform distribution, i.e., 0~U[0, 2]. Firms cannot measure individual productivity, so all workers are paid a wage equal to the average of the marginal value products of those employed. b Find the condition for k under which every worker will choose self- employment. Also, find the condition for k under which all the workers will choose to be employed. Assume that k = 1. And, each worker can take a free test which can only te whether his marginal value product is in [0,1] or in [1,2]. Who will take the test and who will not? Also, who will be'self-employed and who will be employed? (c) Assume that k 1. And, each worker can take a test at the expense of c which can reveal his marginal value product exactly. Who will take the test and who will not? Also, find the condition for c under which there exist some workers who will choose to take the test. (d) Continuing from (c), the test is not perfect in the sense that if a worker with takes the test, the test reveals that the worker's marginal value product is + d with probability 1/2 and 0 d with probability 1/2. Will more or less workers take the test than in (c)? (Hint: After the test result is revealed, each worker can decide whether to be self-employed or employed.)
6. A worker with a marginal value product of can earn w, = k√0 in self- employment. Marginal value products vary across the population according to the uniform distribution, i.e., 0~U[0, 2]. Firms cannot measure individual productivity, so all workers are paid a wage equal to the average of the marginal value products of those employed. b Find the condition for k under which every worker will choose self- employment. Also, find the condition for k under which all the workers will choose to be employed. Assume that k = 1. And, each worker can take a free test which can only te whether his marginal value product is in [0,1] or in [1,2]. Who will take the test and who will not? Also, who will be'self-employed and who will be employed? (c) Assume that k 1. And, each worker can take a test at the expense of c which can reveal his marginal value product exactly. Who will take the test and who will not? Also, find the condition for c under which there exist some workers who will choose to take the test. (d) Continuing from (c), the test is not perfect in the sense that if a worker with takes the test, the test reveals that the worker's marginal value product is + d with probability 1/2 and 0 d with probability 1/2. Will more or less workers take the test than in (c)? (Hint: After the test result is revealed, each worker can decide whether to be self-employed or employed.)
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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![6. A worker with a marginal value product of can earn w, = k√e in self-
employment. Marginal value products vary across the population according
to the uniform distribution, i.e.,
0~U[0, 2].
Firms cannot measure individual productivity, so all workers are paid a wage
equal to the average of the marginal value products of those employed.
&
(a Find the condition for k under which every worker will choose self-
employment. Also, find the condition for k under which all the workers
will choose to be employed.
Assume that k = 1. And, each worker can take a free test which can only
te whether his marginal value product is in [0,1] or in [1,2]. Who will take
the test and who will not? Also, who will be'self-employed and who will be
employed?
(c) Assume that k = 1. And, each worker can take a test at the expense
of c which can reveal his marginal value product exactly. Who will take the
test and who will not? Also, find the condition for c under which there exist
some workers who will choose to take the test.
(d) Continuing from (c), the test is not perfect in the sense that if a worker
with takes the test, the test reveals that the worker's marginal value product
is 0+d with probability 1/2 and 0 - d with probability 1/2. Will more or
less workers take the test than in (c)? (Hint: After the test result is revealed,
each worker can decide whether to be self-employed or employed.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F01148604-49fa-4748-a56e-665f5e33aa44%2Fd039b2f6-d0af-4503-b840-c72bda25b3e5%2Fnfoy46_processed.jpeg&w=3840&q=75)
Transcribed Image Text:6. A worker with a marginal value product of can earn w, = k√e in self-
employment. Marginal value products vary across the population according
to the uniform distribution, i.e.,
0~U[0, 2].
Firms cannot measure individual productivity, so all workers are paid a wage
equal to the average of the marginal value products of those employed.
&
(a Find the condition for k under which every worker will choose self-
employment. Also, find the condition for k under which all the workers
will choose to be employed.
Assume that k = 1. And, each worker can take a free test which can only
te whether his marginal value product is in [0,1] or in [1,2]. Who will take
the test and who will not? Also, who will be'self-employed and who will be
employed?
(c) Assume that k = 1. And, each worker can take a test at the expense
of c which can reveal his marginal value product exactly. Who will take the
test and who will not? Also, find the condition for c under which there exist
some workers who will choose to take the test.
(d) Continuing from (c), the test is not perfect in the sense that if a worker
with takes the test, the test reveals that the worker's marginal value product
is 0+d with probability 1/2 and 0 - d with probability 1/2. Will more or
less workers take the test than in (c)? (Hint: After the test result is revealed,
each worker can decide whether to be self-employed or employed.)
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Step 1: (a) To find the condition for K under which workers will choose self-employment or employment:
VIEWStep 2: (b) To choose employment or self-employment based on marginal value product (MVP):
VIEWStep 3: (c) To find the condition for c under which there exist some workers who will choose to take test:
VIEWStep 4: (d) To analyze if more or less workers will take test than in c:
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