1. Answer all parts (a)-(e) of this question.
A risk-averse expected-utility maximizer has initial wealth w and utility function u. She faces
a risk of a financial loss of L dollars, which occurs with probability π. An insurance company
offers to sell a policy that costs p dollars per dollar of coverage (per dollar paid back in the
event of a loss). Denote by x the number of dollars of coverage.
(a) [5 marks] Give the formula for her expected utility V (x) as a function of x.
(b) [10 marks] Suppose that u(z) = e
−zλ
, π = 1/4, L = 100 and p = 1/3. Write V (x)
using these values. There should be three variables, x, λ and w. Find the optimal value of x,
as a function of λ and w, by solving the first-order condition (set the derivative of the expected
utility with respect to x equal to zero). (The second-order condition for this problem holds but
you do not need to check it.) Does the optimal amount of coverage increase or decrease in λ?
(c) [10 marks] Repeat exercise (b), but with p = 1/6.
(d) [7 marks] You should find that for either (b) or (c), the optimal coverage is increasing in λ,
and that in the other case it is decreasing in λ. Reconcile these two results.
2. Answer all parts (a) – (e) of this question.
Demand for potatoes is given by p(q) = 11 − q and supply by p(q) = 1 + q.
(a) [6 marks] What are equilibrium prices and quantities in this case? Calculate consumer
surplus and producer surplus.
(b) [6 marks] Assume that there is a unit tax of t = 2. What price do producers get? What is
the price that consumers pay? How high is tax revenue?
(c) [6 marks] Calculate consumer surplus, producer surplus and deadweight loss for the case
in (b).
Now set the tax to zero again t = 0. Assume that because of war supply shifts to p(q) = 1+4q.
The government puts in place a price cap such that price is regulated to be the same as in (a).
(d) [7 marks] What are the effects on producer surplus and consumer surplus of the price cap?
(e) [7 marks] In situations as in (d) price caps are often combined with rationing–a certain
allotment per person. What might be an economic argument for rationing? Against?
EC402
3. Answer all parts (a) – (c) of this question.
(a) [7 marks] Consider an agent whose preferences over any couple (x1, x2), where x1 ∈ R+
and x2 ∈ R+, e.g., apples and oranges, is such that she prefers the bundle that is closest to
having the same number of apples and oranges. Write a utility function u : R
2
+ → R+ which
represent these preferences.
A politician remarks ”Our recent increases in the wage rates of teachers has been a total success! The shortage of teachers has been reduced drastically. Another, similar wage increase
should eliminate this shortage entirely”
(b) [11 marks] Explain and illustrate in a diagram what is meant by “income effects” and
“substitution effects” of a wage rate change.
(c) [15 marks] Explain and illustrate how you would model the labour supply decision of a
potential teacher. Do you agree that the wage increase will increase the labour supply in this
case? Carefully outline the assumptions underlying your argument.
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The post Demand for potatoes is given by p(q) = 11 − q and supply by p(q) = 1 + q. (a) [6 marks] What are equilibrium prices and quantities in this case? Calculate consumer surplus and producer surplus. (b) [6 marks] Assume that there is a unit tax of t = 2. What price do producers get? What is the price that consumers pay? How high is tax revenue? (c) [6 marks] Calculate consumer surplus, producer surplus and deadweight loss for the case in (b). Now set the tax to zero again t = 0. Assume that because of war supply shifts to p(q) = 1+4q. The government puts in place a price cap such that price is regulated to be the same as in (a). (d) [7 marks] What are the effects on producer surplus and consumer surplus of the price cap? (e) [7 marks] In situations as in (d) price caps are often combined with rationing–a certain allotment per person. What might be an economic argument for rationing? Against? EC402 appeared first on Apax Researchers.
