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Assignment 1 Answer all three questions

Economics

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Assignment 1
Answer all three questions.
1. Burnt out and sick of being criticised by the press as racist, hypocritical dinosaurs,
two former stars retire from the entertainment industry to live a simple reclusive life
in Toyland. Noddy sets up an apple farm, while next door his former best friend Big
Ears starts a flower business. Producing both apples and flowers requires only one
input – bees, which pollinate the blossoms. Given b bees, Noddy can produce ) ln(b ?
apples, which sell for £1/apple, and Big Ears can produce ? ln(b) flowers, which sell
for £1/flower. You know that ? ? ? . Every bee costs £c. Both Noddy and Big Ears
pay for their own hives, but their bees fly over the fence and pollinate each other’s
blossoms as well as their own. Denote Noddy’s number of bees as bN and Big Ears’
number of bees as bBE.
a) If both Noddy and Big Ears each aim to maximise profits, how many bees will each
keep? (Hint: find a first order condition for each person, taking the other’s choice as
given. When thinking about the best response functions, remember that bN and bBE
cannot fall below zero.)
Illustrate this equilibrium using a diagram with bBE on the vertical axis and bN on the
horizontal axis. (Note that isoprofit curves are the production equivalent of
indifference curves and trace out all the combinations of bBE and bN that give the same
level of profit.)
What additional restrictions must we make on α and β to ensure that Noddy and Big
Ears both make positive profits?
(6 marks)
b) Find the locus of Pareto efficient allocations by calculating the slopes of the
isoprofit curves and setting them equal. What is the Pareto efficient total number of
bees, N BE B = b + b , that is, the number of bees that maximises total profits in
Toyland?
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(4 marks)
c) Tired of the pair’s antics, the social planner of Toyland, Enid, decides to impose an
equal-sized lump-sum tax on both Noddy and Big Ears and spends the money on a
communal bee hive. How much would she have to tax each to achieve efficiency?
Discuss the intuition behind your answer.
(10 marks)
d) Discuss the empirical evidence on the effectiveness of policies designed to raise the
amount of public goods. Does it support the assumptions made at the beginning of
this question. Why or why not?
(20 marks)
2. The inhabitants of the planet Lepidoptera are a race of advanced and highly rational
butterflies. Each Lepidopteran lives a maximum of two years, but might die after the
first year. In the first year Lepidopterans exist as caterpillars and work hard eating
leaves and in the second they retire to live work free as butterflies. The living
expenses associated with retirement are £100. Each Lepidopteran knows his/her own
probability of surviving between years 1 and 2, but no one else does. The probability
of survival, p, is uniformly distributed on the interval [0,1]. Lepidopterans are willing
to pay up to £150p for a pension.
a) Pensions are available and offer insurance against the risk of surviving beyond the
first year. The pension market is competitive and pensions always cover the full cost
of retirement if a person survives to the second year. If an insurer charges a premium
π, what will its expected payout be? Given that insurers must break even, which
individuals will take out a pension in equilibrium? Show all your working and
illustrate your answer with a diagram.
(3 marks)
b) What premium would insurers offer if the government required that all individuals
must take out a pension. Explain why this does not represent a Pareto improvement
over the situation in part (a).
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(2 marks)
c) What is the nature of the market failure in parts (a)-(b)? Discuss how empirical evidence has examined this problem and what it has found.
(15 marks)
3. In no more than 1000 words, discuss whether the problem of global warming can be viewed as one of the tragedy of the commons, what policy solutions economic theory implies and what practical problems might be encountered if such solutions were pursued.
(40 marks)