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Welfare assignment

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Tossa College of Economic Development
Assignment for welfare Economics
1. Assume that a very large number of firms in an industry all have access to the same
production technology. The total cost function associated with this technology is
TC(q) = 40q – 24q2 + 4q3. If the demand function for the industry’s product is Q = 19 – P, find
numbers of firms when the market is at its LR competitive equilibrium?
2. Assume that the taxi industry in the Dessie City is perfectly competitive. Also
assume that the constant marginal cost of a taxi ride is birr 5 per trip and that each taxi is
capable of making 20 trips a day. We will let the demand function for taxi rides each day
be D(p) = 1100 – 20p.
a) What is the perfectly competitive price of a taxi ride?
b) How many ride will the residents of Dessie city make every day?
c) How many taxis will operate in Dessie City?
d) Calculate the price that will equate demand with supply
e) Calculate the profit that each taxi will earn per day
3. Consider an economy with the supply of balls Qs = 4p and the demand for
balls given by Qs = 270 – 5p.
a) Calculate the equilibrium price and quantity.
b) Graph the supply and demand functions.
c) Calculate both the consumer and producer surplus.
d) calculate the new equilibrium price and quantity.
e) Draw a graph marking the after tax consumer surplus and producer surplus as
well as the tax revenue
f) Calculate the consumer surplus, the producer surplus, and the dead-weight loss.
g) Calculate the dead-weight loss imposed by the tax.
4. A monopoly sells its good in Dessie city , where the elasticity of demand is –2, and in Addis
Ababa, where the elasticity of demand is –5. Its marginal cost is $10
A. At what price does the monopoly sell its good in each country if resales are
impossible?
B. What happens to the prices that the monopoly charges in the two cities if retailers can
buy the good in Addis Ababa and ship it to Dessie at a cost of (a) $10 or (b) $0 per unit?
5. A monopoly sells in two countries, and resales between the countries are impossible. The
demand curves in the two countries are p1=100 – Q1, p2=120 – 2Q2. The monopoly’s marginal
cost is m = 30. Solve for the equilibrium price in each country.
6. Two players, Row and Column, are driving toward each other on a one-lane road. Each
player chooses simultaneously between going straight (S), swerving left (L), and swerving right
(R). If one player goes straight while the other swerves, either right or left, the one who goes
straight gets payoff 3 while the other gets –1. If each player swerves to his left, or each swerves
to his right, then each gets 0 (remember, they are going in opposite directions). If both go
straight, or if one swerves to his left while the other swerves to his right, then the cars crash and
each gets payoff –4.
A. Write the payoff matrix for this game.
B. Find all of the game's Nash equilibrium in pure strategies
C. Find a Nash equilibrium in which Row uses a pure strategy and Column mixes
between two of his strategies. Clearly identify which strategy or strategies have positive
probabilities for each player, and what Column's mixing probabilities are. (Hint: Which of Row's
pure strategies could make Column willing to put positive probability on two of Column's pure
strategies?)
D. Find a Nash equilibrium in which both Row and Column mix between two of their
strategies. Clearly identify which strategies have positive probabilities for each player, and their
mixing probabilities are. (Hint: Pick two pure strategies for each player— because the game is
symmetric, it's natural to try the same two strategies for each—and figure out what the mixing
probabilities would have to be on just those two strategies. Then compare each player's expected
payoff with what he could get by switching to his third strategy.)
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