University of Rochester International Trade Worksheet
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Figure 1: Relative earnings from employment by level of educational attainment for 25-64 yearolds (2009 or latest available year). Upper secondary and post-secondary non-tertiary education are
normalized to 100.
All agents in the economy have preferences described by the following CES utility function:
U (c1 , c2 , …cN ) ?
N
!
c?i = c?1 + c?2 + … + c?N
i=1
where ci denotes consumption of good i, for i = 1, …N . N is the total number of goods available
in the economy (and the total number of firms present in the economy), and ? ? (0, 1) is
a parameter expressing substitutability across goods: high ? denotes high substitutability,
while low ? denotes low substitutability, or high differentiation.
Consumers in the economy maximize utility subject to the budget constraint:
N
!
i=1
2
pi ci = I
where pi denotes the price of good i, and I denotes income.
The country is populated by L agents, and in equilibrium total consumption of a good must be
equal to total production of that good: xi = Lci .
(a) By solving the consumers utility maximization problem, show that the (inverse) residual
demand that the firm producing good i faces is described by the following equation:
pi =
? ” xi #??1
? L
(1)
where ? is the Lagrange multiplier associated to the budget constraint. Plot the residual
demand function (1) on the (xi , pi ) plane.
(b) Does the residual demand function depend on the number of firms? And on the prices
charged by other firms? To answer this question, you can solve for ? by plugging (1) into
the budget constraint.
(c) Labor is the only factor of production, hence production costs are expressed in units of
labor. Each firm i produces with the same technology, described by the following cost
function:
l(xi ) = ? + ?xi
where l(xi ) are the units of labor firm i needs to produce xi units of good i, ? > 0 denotes
the marginal cost, and ? > 0 denotes the fixed cost of production. Both ? and ? are
common across firms.
Write down the firms profit maximization problem.
(d) Solve the firms profit maximization problem, i.e., compute the optimal quantity produced
x?i and the optimal selling price p?i .
(e) Does the optimal price depend on the number of firms N ? Does the optimal price differ
across firms? Why?
(f) In equilibrium full employment must hold, i.e. all the labor force of the country must be
employed by the firms. Compute the long-run equilibrium number of firms N ? . Describe
how N ? depends on the parameters of the model. Provide economic intuition for your
answer.
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(g) Suppose the country opens to trade with another country, identical to it in all its characteristics. How do optimal prices pi and optimal quantities xi change? How does the
equilibrium number of firms change?
(h) By comparing agents utility at the equilibrium under autarky and at the equilibrium under
free trade, show that consumers gain from trade.
(i) Suppose firms are heterogeneous: the marginal cost ai is now different across firms. Will
firms charge the same prices? Describe the relationship between marginal costs, optimal
prices and optimal quantities. Which firms will exit following trade liberalization? (Your
answer to this question should be qualitative).
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Explanation & Answer:
Worksheet
Tags:
business
international
Trade
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