# Exercise No

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```					IØR, UMB                                                                  Ian Coxhead
ECN 454: Trade, resources and development                                   June 2009

Assignment 1: Exercises with basic trade models
Due date: 4 pm Monday June 8

Problem no.      Points
1             5
2            10
3            15
Total          30

Problem 1. Feenstra problem 1.4, p.29.

Problem 2. Specific factors model

Imagine an economy that engages in trade with the rest of the world, at world market
prices. It consists of two tradable sectors: manufacturing (an import-competing sector),
and plantation agriculture (an export-oriented sector). Production in manufacturing uses
capital and labor, and production in agriculture uses labor and land. Labor is mobile
between the two sectors, but capital and land are each used only in one sector.

Use diagrams or an algebraic model (you need not do both) to answer the following:

a. Identify the effects of growth in the labor force on the structure of production,
GDP, and the returns to different factors of production (capital, land, and
labor).
b. Now suppose instead that the country has a “frontier” of forest that can
potentially be converted to agricultural land. Imagine that investors convert
some forest land in order to expand plantations. What would the impacts of
increased investment in land be on the pattern of production, GDP, factor
returns, and the environment?
plantations is undertaken not by domestic investors, but by foreigners (FDI).
Does this change the calculation of growth in GDP, factor incomes, or the
welfare of a representative domestic consumer? Provide a brief explanation.
2

Problem 3. SFM with nontraded goods

This exercise is intended for you to satisfy yourself that you have grasped the essentials
of the analytical general equilibrium model used in class, and that you can use it
creatively to address development-related questions. For assistance with concepts and
algebra consult class notes, Bhagwati, Panagariya and Srinivasan (1998, Ch. 7, 9, 10),
and Feenstra (2004, Ch. 1, 3).

Consider a small open economy producing 3 types of goods, X, M, and N. Each sector
uses as inputs a specific factor (“capital”) and labor, which is mobile among all three
sectors. All factors are initially fixed in supply. Suppose that each sectoral production
function y j  f j (v j ) is strictly concave, HD1 in inputs, and satisfies f j  (0)   ,

f j  ()  0 . Prices of X and M are given in world markets; N is a pure non-traded good,
so its price is determined domestically. Define the real exchange rate by the ratio of pN to

an index of traded goods prices, pT  p X p1  . Using vector notation except where
M
specified, define the aggregate revenue function g(p,v) and the expenditure function of
the representative consumer e(p, u). Let L (labor) be one element of the endowment
vector v, the other elements being the specific capital vj. Recall from the revenue
maximization problem that by the envelope theorem, gp(p, v) = y(p, v) and that gv (p, v) =
w(p, v). On the consumer‟s side, the derivatives of e(p, u) with respect to prices are
compensated demands c(p, u). As seen in class, the equilibrium for this model consists of
the following:

e(p, u) = g(p,v)                             Aggregate budget constraint

eN(p, u) = gN (p,v)                          Non-traded goods market clearing,

along with the factor market clearing and equality of value marginal product conditions
[for mobile factors] that form the FONC of the revenue maximization problem. We can
manipulate these two equations to prove that when they are satisfied, excess demands for
all goods are zero and thus trade is in balance (i.e., we can prove a version of Walras‟
law). Finally, the „trick‟ used to obtain a money metric of welfare in aggregate income R
is to notice from the basic identities relating utility, income and expenditure (see Varian)
u
that 1  eu ( p,u) , thus dR  eu du .
R

a. Calculate the comparative static implications of a positive terms-of-trade shock (that
is, a rise in the relative price of the exportable good) for:

i.     The welfare of a representative consumer
ii.    The real exchange rate
iii.   Production in each sector
iv.    Factor prices.
3

b. In this experiment, what can we say about factor price changes relative to output price
changes in each sector? Which groups of factor owners are predicted to experience
real gains or losses?

c. Can you identify the key parameters governing this set of comparative static results?
(Hint: try converting the coefficients of total differential expressions to proportional
change form, and manipulate these to obtain solutions in terms of elasticities and
share parameters).

d. (Optional: for extra credit) The above simple model abstracts from many distinctive
and important features of developing economies, such as unresolved externalities;
poverty or income distribution constraints on policy; trade and transactions costs;
segmented or otherwise distorted labor markets, and many more. Propose one
extension that you consider important, and provide a brief justification in terms of the
development literature or a specific country case study. Try to construct the extended
model and to derive comparative static results for the key variables of interest
(aggregate welfare, product and factor prices, output by sector and so on). Use a
geometric model if you prefer, and if it accurately conveys the content of your model
extension.

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