Accounting Problem Set 6 Spring 2017 Labor Economics 412

Subject: Economics / Accounting
Question

1. (20 points, A signaling model) Consider the model we learned in class where workers
can invest in education as a signal. There is a ? ? (0, 1) fraction of ’good guys’ with
high productivity xh, and (1??) of ’bad ones’ with low productivity xl
, where xh > xl
.
The total cost of acquiring an education level y is cly and chy (depending on the type
of worker). Education serves as an education device, but it costs utility. In particular,
it is more expensive for the ’bad ones’ (ch < cl). The utility for a worker is given by
Ui = w ? ciy ?i ? H, L, where w is the wage.
We assume that the firm’s production function is linear in workers’ productivity. The
profit function is given by ?(x, w) = x ? w, where x is the productivity of the worker,
and w the wage.
(a) Draw a typical indifference curve for the ’bad’ guys and for the ’good’ guys.
(b) What wage will the firm offer if signaling is NOT possible?
(c) Suppose now that the workers can signal, under what conditions a pooling equilibrium
exist? What are the offered wages in a pooling equilibrium?
(d) Suppose now that the workers can signal, under what conditions a separating
equilibrium exist? What are the offered wages in a separating?
2. (20 Points) Explain in a few sentences the logic behind each of these theories in accounting
the increase in inequality in the U.S. since the late 1970s. (i) Increasing trade
with least developed countries, (ii) Secular decline in the rate of union rate.
3. (30 points Skill-Biased Technical Change) Imagine an economy populated with unskilled
workers and skilled workers, denoted by U and S, respectively. They supply
labor inelastically at any time.
The technology available takes the form of CES.
Y (U, S) = [(AuU)
? + (AsS)
?
]
1/? (1)
where ? ? 1, and Au and As are factor-augmenting technology terms.

(a) Set up the firm’s problem.
(b) What is the wage of a skilled worker, ws and unskilled worker, wu, under perfect
competition? (Hint: the marginal product of an unskilled worker is given by
:[(AuU)
? + (AsS)
?
]
1/??1
(1/?)[A?
u
]?U??1
, and the marginal product of a skilled
worker is given by :[(AuU)
? + (AsS)
?
]
1/??1
(1/?)[A?
s
]?S??1
])
(c) What are the relative wages (the skill premium ws/wu) in this economy?
(d) Suppose that for the last five decades the economy has been characterized by an
increase in productivity of skilled workers, As, what can you say about the skill
premium in this economy providing that you have some information that ? is
between 0.5 and 0.9.
4. (30 points Capital-Skill Complementarity) Imagine an economy populated with unskilled
workers and skilled workers, denoted by U and S, respectively. They supply
labor inelastically at any time. The technology available takes the form of CES.
Y (Ke, U, S) = [(K?
e + S
?
)
?/? + U
?
]
(1/?)
,
with ? ? 1, ? ? 1
This production function takes equipment goods (computers) Ke into account; in particular,
the elasticity of substitution between computers and skilled workers is given
by 1/(1 ? ?), whereas the elasticity of substitution between computers and unskilled
workers are given by 1/(1 ? ?).
(a) Set up the firm’s problem.
(b) What are the wages of a skilled worker, ws and unskilled worker, wu, under
perfect competition? (Hint: the marginal product of an unskilled worker is given
by :[(K?
e +S
?
)
?/?+U
?
]
(1??)/?U
(??1), and the marginal product of an skilled worker
is given by :[(K?
e + S
?
)
?/? + U
?
]
(1??)/?(K?
e + S
?
)
(???)/?S
(??1)
(c) What are the relative wages (the skill premium ws/wu) in this economy?
(d) There was a substantial increase in the supply of college educated workers (skilled
workers) in the U.S. during the past five decades, what are the prediction for the
skill premium in this model? Show it.
(e) Suppose that for the last five decades the economy has also been characterized
by an increase in intensity of computers (Ke) used in production due to the lower
prices of computers, what can you say about the skill premium in this economy
providing that ? > ??
(f) What are the implications for the elasticities of substitution when ? > ?? Specifically,
which combination of inputs is more relatively complement?

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