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WIPO Journal - World Intellectual Property Organization

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164 The <strong>WIPO</strong> <strong>Journal</strong><br />

Q output<br />

P output price<br />

X 1 input factor 1 (land)<br />

X 2 input factor 2 (all other inputs including fertiliser, seeds, and labour)<br />

W 1 price of X 1 (land)<br />

W 2 price of X 2 (other inputs)<br />

Totally differentiating equations (1–6) and expressing the results as relative changes yields equations in<br />

terms of the relative changes and elasticities, the effect of a change in the price of one factor on the quantity<br />

demanded. The solution consists of linear equations expressing these relative changes in endogenous<br />

(internally determined) prices and quantities as functions of the parameters (such as demand and supply<br />

elasticities, elasticity of substitution, factor cost shares) and exogenous shifters. The shift variables, B1<br />

and B2, take particular forms to represent the price and quantity effects of a subsidy on an output or an<br />

input; they take different values, combined with extreme elasticity assumptions, to represent a quota on<br />

an output or an input. Alston and James derived price and quantity effects of subsidies or quotas in terms<br />

of cost shares and elasticities, as reported in Table 3.<br />

Table 3: Price and quantity effects of supply/demand shifters in a two-factor model 29<br />

k 1<br />

k 2<br />

η<br />

ε 1<br />

ε 2<br />

σ<br />

cost share X 1<br />

cost share X 2 such that k 1 + k 2 = 1<br />

elasticity demand for Q (absolute value)<br />

elasticity supply for X 1<br />

elasticity supply for X 2<br />

elasticity substitution between X 1 and X 2<br />

29 Source: Alston and James, “The incidence of agricultural policy” in Handbook of Agricultural Policy 2002.<br />

(2011) 2 W.I.P.O.J., Issue 2 © 2011 Thomson Reuters (Professional) UK Limited

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