The name is absent

Moreover ,

To answer this question, we need to explore carefully the link between changes in
relative prices and output and productivity responses. In order to measure firm-level productivity,
we begin by defining a cost function as in Tybout, Gauthier, Barba Navaretti and de Melo (1997)
and Gauthier, Soloaga and Tybout (2002),
(1) C = f(Q,PL,P∣,Pκ,A)

where C represents the minimum attainable cost at output level Q, productivity level A
and a given set of input prices. We make use of a vector of effective (after tax, after tariff) prices
(i.e. perceived by firms) for intermediate goods, P∣ labour, PL, and capital, Pκ .

Assuming that firms behave optimally, by Shepard’s lemma we can obtain the cost
minimizing factor demands by taking the first derivatives of the cost function:

(2) d lnC = J — Id InQ + s∣(d lnP∣) + s_L(d InPL) + s_κ(d ∣nP_κ) + P^lnC ∣d InA
^ηj                              ^lv L'                       kð InA )

where η is the elasticity of output with respect to cost, i.e., the inverse of returns to scale, and s _j
denotes the share in totaI cost of the j^th factor.

Equation 2 expresses the rate of growth in totaI cost as the rate of growth in output,
weighted by the inverse of returns to scaIe, pIus the share-weighted average rate of growth in
input prices, pIus the eIasticity of cost with respect to time, hoIding output and prices constant.
This Iast term is a measure of the rate of productivity growth.

The standard decomposition of the sources of growth in cost per unit revenue is obtained
by normaIizing by the vaIue of output (e.g. Chambers, 1988):

d InC - dln ( QP_q ) = ∣^— -1 ∣ dlnQ + s∣ (d InP∣ - dlnPQ) + sL(dInPL - dlnPQ)
√η   )

+ s_κ(dInP_κ -d InP_o) + ∣-^n-C-1 d InA

^{K( κ Q)}    U InA )

11

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