Measuring the Effectiveness of Nonprice Promotion of U.S. Agricultural Exports Using a Supply-side Approach

November 1998                                          SCSB# 390

TRADE, POLICY AND COMPETITION:
FORCES SHAPING AMERICAN AGRICULTURE PROCEEDINGS

Chapter 9
Measuring the Effectiveness of Nonprice Promotion of U.S. Agricultural Exports
Using a Supply-side Approach

Juan J. Porras, H. Alan Love, and C. Richard Shumway

GNP Function Approach to Modeling Agricultural Trade

In this section, we lay out essential features of Kohli's GNP function approach to modeling international trade (Kohli 1991). Imports are regarded as a variable input into a production process that results in exports as a variable output distinct from output produced for domestic consumption. Variable inputs and outputs are treated as netputs, so variable inputs can be viewed as negative outputs. Capital and labor are treated as quasifixed inputs and are positively measured. Assuming that individual producers are competitive profit maximizers, and that the aggregate of all agricultural producers behaves as though it were a competitive profit-maximizing firm, profit is given by:

P(p,w,z,t) = p(p,z,t) - w´z, (9.1a)

where p denotes the vector of variable netput prices, z and w represent quantity and price vectors of the quasifixed inputs, t represents technology, p(p,z,t) represents variable profit that allows for Hicks nonneutral technological change and is defined as:

p = p(p,z,t) = max
x (p ´x:(x,z) T^t), (9.1b)

where x is the vector of variable netput quantities, and T^t is the production possibilities set at time t.

The variable profit function is a natural dual description of the technology if one views fixed input endowments and output and variable input prices as given, which is often assumed in international trade theory (Kohli 1993a). Under such conditions, p(·) is linearly homogeneous and convex in variable netput prices, nondecreasing in output prices, and nonincreasing in variable input prices. If the production function exhibits constant returns-to-scale, it is also linearly homogeneous and concave in fixed input quantities (Diewert 1974).

From Hotelling's lemma, differentiating P(·) with respect to variable netput prices, when quasifixed input quantities are constant, results in conditional netput supply equations:

x = x(p,z,t) = _pp (p,z,t), (9.2)

where _pp(·), is the vector of partial derivatives of variable profit, p(·), with respect to variable netput prices. Since p(·), is convex in p, it follows that conditional netput supply functions are necessarily nondecreasing in own prices (i.e., dx_i(·)/dp_i0, i = 1,2,...,I). Thus, if x_i is a variable input, an increase in its own price reduces the quantity demanded (or increases the negative value of its quantity). Differentiating P(·) with respect to quasifixed input quantities yields the quasifixed input inverse demand functions:

w = w(p,z,t) = _zp(p,z,t), (9.3)

where _zp(·) is the vector of partial derivatives of p(·) with respect to quasifixed input quantities. The concavity of p(·) with respect to z indicates that the inverse demand functions are nonincreasing in their own quantities (i.e., dw_j/dz_j0, j = 1,2,...,J).

The short-run price and quantity elasticities, E= [e_mn], associated with the variable profit function can be computed as follows:

e_xp e_xz p_p^-1 p_pp p_p^-1 S_x p_p^-1 p_pz p_z^-1 S_z

E = = p , (9.4)

e_wp e_wz p_z^-1 p_zp p_p^-1 S_x p_z^-1 p_zz p_z^-1 S_z

where p_p = diag[_pp(·)], p_z = diag[_zp(·)], S_x = diag(S_i), S_z = diag(S_j), S_i and S_j are the variable netput and quasifixed input shares of variable profit, respectively.

In the variable profit function, quasifixed input quantities and output and variable input prices are treated as exogenous, while quasifixed input prices and output and variable input quantities are endogenous. Hence, e_xp = [e_ih] are the elasticities of output supply and variable input demand with respect to changes in exogenous prices, e_xz = [e_ij] are the elasticities of output supply and variable input demand with respect to changes in factor endowments, e_wp = [e_ji] are the elasticities of the inverse quasifixed input demands with respect to changes in exogenous prices, and e_wz = [ e_jk] are the elasticities of the inverse quasifixed input demands with respect to changes in factor endowments. The submatrices, e_xz and e_wp, are also known as the Rybczynski and Stolper-Samuelson elasticities, respectively (Kohli 1991). All short-run elasticities are functions of (p,z,t). Through the homogeneity properties of the output supply and the variable input demand functions and the maintained hypothesis of constant returns to scale, the price and quantity elasticities are subject to the following restrictions:

S_he _ih = 0, S_j e_ij = 1, S_ie_ji = 1, S_k e_jk = 0,

i,h = 1,2,...,I, j,k = 1,2,...,J.

In our empirical application, the national sectoral endowment of capital and labor will be treated as being quasifixed in the short run (J=2).

If a longer-run perspective is taken in which the supply of either capital or labor is perfectly elastic while the supply of the other factor remains quasifixed, intermediate-run elasticities, (E^M), can be calculated from the short-run elasticities, (E). Let the quantity and price of the input that was previously quasifixed but is now variable be q and r, respectively, and the quantity and price of the input which remains quasifixed be y and v, respectively. Then the intermediate-run elasticities are:

e_xp^M e_xr^M e_xy^M

E^M = e_qp^M e_qr^M e_qy^M =

e_vp^M e_vr^M e_vy^M

e_ih-e_iqe_rh/e_rq e_iqe_rq e_iy-e_iqe_ry/e_rq

-e_rhe_rq 1/e_rq -eryr/e_rq , (9.5)

e_vh-e_vqe_rh/e_rq e_vq/e_rq e_vy-e_vqe_ry/e_rq

where i,h = 1,2,...,I.

References