1. II-C

2. II-C

3. II-C
Spot test!
Q. In the previous example, what is the optimal tariff, and how is it calculated?
Where absolute values of slopes of R and C are equal (marginal environmental benefit=marginal cost in terms of consumption)
Q. What is the optimal tariff on imports of a dirty good?
A. t = 0.

4. II. General equilibrium approaches—theory
II-C
II. General equilibrium approaches—theory

5. II-C

6. eudu = –(ep – rp)dp + rvdv
II-C
Comp. statics with TEF
Method: take total differential of TEF.
e(p, u) = r(p, v)
eudu + epdp = rpdp + rvdv
Rearrange, noting that ep – rp = net imports:
eudu = –(ep – rp)dp + rvdv
-- LHS is a money-metric of welfare
-- RHS captures effects of price and endowment changes

7. Details Welfare measure: Welfare effects of terms-of-trade shocks:
II-C
Details
Welfare measure:
eu = ∂e/∂u is the reciprocal of ∂u/∂y, the marginal utility of income. So eudu = dy, a money-metric of welfare change.
Welfare effects of terms-of-trade shocks:
Sign depends on whether goods are net imports or exports.
Welfare effects of endowment growth:
Recall that ∂r/∂v = w, the shadow factor price.

8. Extensions Policies, e.g. trade policy Externalities Non-traded goods
II-C
Extensions
Policies, e.g. trade policy
Externalities
Non-traded goods

9. Trade policy distortion (tariff)
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Trade policy distortion (tariff)
Suppose 2 goods, exports (x) and imports (m).
Let px = 1 and q = pm + t (= tariff)
Adding tariff revenues to income:
e(1, q, u) = r(1,q) + t(em – rm)
Then by differentiation (using dq = dt),
 dy = t(emm - rmm)dt < 0
where  = (1- tem) > 0.
A tariff increase reduces welfare.

10. II-C
Spot test!
In this model, a tariff clearly reduces welfare. What effect does it have on the sectoral structure of production?
How do we know?
The tariff raises output in the protected sector, and reduces it in the other sector.
Check 2nd derivatives of revenue function, using homogeneity property.

11. Externalities E.g. env. externality in production
II-C
Externalities
E.g. env. externality in production
TEF is now:
e(p, u) = r(p, v) - z'y
where z is qty of pollution per unit of y produced.
Env. externality in consumption:
u = u(c, z) ==> e(p, z, u)
NB assumption of separability.

12. II-C
Non-traded goods
Goods may be non-traded (or effectively so) for intrinsic and policy reasons.
If one good is non-traded, for this, mn = 0.
Equilibrium now requires additional equation:
e(p, u) = r(p, v)
en(p, u) = rn(p, v)
and solves for pn as well as agg. welfare.
With endogenous prices, preferences play a role in economic structure.

13. II-C
Salter-Swann diagram T
RER = pN/pT
(yT, yN) = (cT, cN) N

14. Effects of growth with non-traded good
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Effects of growth with non-traded good T
Income exp. path N

15. Two fundamental GE results
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Two fundamental GE results
Distributional effects of a price change: the Stolper-Samuelson theorem
Production effects of a factor endowment change: the Rybczinski theorem
Assume:
Two factors of production, two products, so yj = yj(x1, x2), for j = 1,2
Complete and competitive markets, CRTS.
Prices are ‘given’ in world markets.

16. A useful tool: ‘hat’ calculus
II-C
A useful tool: ‘hat’ calculus

17. Effects of a price change
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Effects of a price change

18. II-C

19. Stolper-Samuelson theorem
II-C
Stolper-Samuelson theorem
A rise in one commodity price raises the real return to the factor used intensively in producing that commodity, and reduces the real return to the other factor.

20. II-C
Applications of S-S
Effects of trade shocks or trade policy reforms on the returns to factors
For environmental analysis: changes in factor returns indicate incentives for exploitation or investment
Ex.1: If forests are open-access, a ‘shock’ that raises returns to timber may increase harvests
Ex. 2: raising returns to agriculture may promote soil-conserving investments

21. Effects of endowment growth
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Effects of endowment growth

22. II-C

23. II-C
Rybczinski Theorem
At constant prices, expansion of one factor endowment raises output of the good that uses that factor intensively, and reduces that of the other good. If 2 factors expand, one good's output grows more slowly than the rate of growth of either factor.

24. Implications of Ryb. result
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Implications of Ryb. result
Unequal rates of factor accumulation alter structure of production
Capital deepening causes labor-intensive or NR-intensive sectors to decline, other things equal
Thus investment in non-agricultural sectors may diminish pressures exerted on the natural resource base by primary industries.

25. Discussion of fundamental results
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Discussion of fundamental results
The S-S and R theorems provide ‘core’ insights for any GE analysis.
They hold for 2X2 models; similar, but weaker predictions apply for higher-dimension models.
Both theorems break down in presence of externalities.
In practice, however, can use these predictions to check the credibility of predictions obtained from larger models.