Econ 5021F - Fall 2020
Dana Galizia, Carleton University
Assignment 6
Due: by 11:59pm on Friday, December 11, 2020 (electronically; PLEASE SEE
SUBMISSION GUIDELINES IN THE COURSE OUTLINE).
Answer all of the following questions. The assignment is out of 50 marks total. Be sure to show
your work, but also please visually emphasize your final answer (e.g., by putting a box around
it, or writing it in a different colour).
1. (14 marks total) Consider the steady state equilibrium of the shirking model of LN4. For
each of the following parameter changes, determine what happens to the equilibrium wage w∗
and employment L∗ (i.e., does each one increase, decreases, stay the same, or is it not possible
to say?). Assume in all cases that φ < w¯ < φ/q both before and after the parameters change,
where w¯ ≡ F ′(1). While it’s not required, feel free to use a diagram as part of your answer.
(a) (5 marks) An increase in the exertion cost φ. Explain in detail the economic intuition
for your answer.
(b) (5 marks) Increases in both φ and q by the same proportion, so that φ/q is unchanged.
(NOTE: You don’t need to provide intuition for this case.)
(c) (4 marks) A decrease in the discount factor β. (NOTE: You don’t need to provide
intuition for this case.)
2. (21 marks total) Consider the search model of the labour market. Assume throughout that we
are in a steady-state equilibrium. In response to the following changes, determine whether
the steady-state levels of w, θ, U , and V increase, decrease, remain the same, or whether
the direction of change is ambiguous. Feel free to draw a diagram if that helps (though it’s
not necessary). In each case, explain the intuition for your result (for an example, see the
explanation in Section 3.4.1 of LN4 for the case of an increase in y).
(a) (6 marks) An increase in b.
(b) (8 marks) An increase in both y and c by the same amount. (HINT: You will likely need
to do some total differentiation to determine exactly what happens here. Also, note that
since m(θ) = θq(θ), we have m′(θ) = q(θ) + θq′(θ) = q(θ)[1 + θq′(θ)/q(θ)].)
(c) (7 marks) A decrease in λ. You don’t need to determine the effect on V for this change,
which is ambiguous. However, you should show why the effect on V is ambiguous.
3. (15 marks total) Consider the following modification to the Solow model. Rather than invest-
ing a constant fraction s of output, total investment is given by
I (t) = ρA (t)L (t) + φY (t)
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Econ 5021F - Fall 2020
Dana Galizia, Carleton University
where ρ and φ are exogenous parameters. Assume φ > 0 throughout, while ρ could in principle
be positive or negative (but not zero). As usual, Y = F (K,AL), and in per-effective-worker
terms, we have y = f (k).
(a) (5 marks) Find an expression for the law of motion of capital per effective worker (i.e.,
an expression for k˙) in terms of k only.
(b) (10 marks) A steady state level of capital is a value k∗ ≥ 0 such that k˙ = 0. Depending
on the values of the parameters, it is possible in this model to have (i) no steady states;
(ii) one steady state; or (iii) two steady states. For each of these cases, draw a Solow
diagram showing actual investment (AI) and break-even investment (BEI) as functions
of k. (HINT: Consider what happens to the AI curve as ρ changes.) Draw arrows
on the horizontal axis that indicate which direction k is moving depending on where
it is currently. For the cases where there are steady states, comment on whether each
steady state is stable; that is, whether if k is initially close to that steady state, it would
eventually converge to it.
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