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The Economics of Geographical Indications

Daniela Benavente


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Appendix A: Club reputation dynamics

The firm’s maximization problem

1The firm faces the problem of maximizing the present value of profits subject to the state equation for reputation and under the constraint that profits de non-negative. Adopting the approach of Winfree and McCluskey (2005), firms follow a stationary Markovian strategy (wherein the firm conditions its actions at a certain period only on the state of affairs at that given perdio), so that qj = φ(R):

Image 100000000000042000000171168FEC18.jpg

2The current-value Hamiltonian (where λi is the current-value shadow price of reputation, a co-state variable) is:

Image 100000000000030700000070CC35C7D6.jpg

3Apply the Pontryagin recipe:

Image 10000000000003E6000001778AFC225D.jpg

4Solve for the isoclines:

Image 100000000000032A000000D15CFAD99D.jpg

5Equation (a) represent the first-order conditions with respect to the control variable quality.

6Equation (b) has a standard interpretation as the adjustment equation for the shadow value of reputation along an efficient path. Equation (c) is the reputation constraint.


7The steady-state equilibrium is found at the intersection of the isoclines  = 0 and q̇ = 0, with the symmetry assumption:

Image 100000000000036F00000196E9C860CF.jpg

p'(R*) is the marginal revenue of the representative firm (as output is set at unity); c'(q*) is the output marginal cost, and G'(R*)/N is the club-house marginal cost. The solution involves a price schedule where marginal revenue covers marginal cost at a premium Image 100000000000005D00000030C028D6F9.jpg. Under the assumption that p''(R) < 0 (downward-sloped marginal revenue curve), the model implies a lower equilibrium level of quality/reputation than that observed under collective reputation (in the latter case G = 0).

System stability: saddle-point path equilibrium

8The Jacobian matrix is:

Image 1000000000000387000001E37C5B6F41.jpg

Image 1000000000000333000000DC2C17C7AD.jpg

9The determinant of the Jacobian matrix at the steady-state provides information about behaviour near the steady-state. Under the assumptions of the model (c'' > 0, G'' ≥ 0 and c'' > p''), the determinant is unambiguously negative, indicating eigenvalues of opposite signs and a saddle-point path equilibrium. The stability condition < 0 is a curvature condition that asserts that the firm’s marginal revenue either declines (p'' < 0), or, if it rises, it rises no faster than the “relevant” marginal cost increases (the marginal cost includes the premium).

10Although a concave marginal revenue function is usually assumed, the model does not rule out a convex marginal revenue function (p'' > 0), which may occur, for example, in the case of extremely rare wine vintages – such as Champagne – wherein increases in quality are marketed at huge price premia:

Image 100000000000030C0000007904D5577F.jpg

11Additionally, the assumption that the function G is concave (G'' ≤ 0) does not rule out a saddle-point path equilibrium either, though it comes at the cost of an additional condition.

Image 10000000000002EE0000008CDD66B6EA.jpg

12Wherever the determinant is positive, the system is unstable – i.e. there is a direction in a 2-dimensional space in which the system will not tend to return back to the equilibrium point.

Quality is a function of membership

13The implicit derivative of quality with respect to number of firms at the equilibrium point is:

Image 1000000000000427000000CB041F918B.jpg

Image 100000000000042E00000214AC196BF9.jpg

Otherwise, quality will decrease, particularly at high levels of membership. Rearranging the terms, these conditions reduce to one simple condition: quality will increase with the number of firms as long as the premium over production cost Image 100000000000002D00000028311A53F6.jpg is lower than the per-firm GI-related marginal cost Image 100000000000002400000029C198BEE3.jpg; if not, quality will decrease. This indicates the potential existence of a scenario in which there is an inflexion point of some lever of N, up to which the equilibrium quality increases and after which it decreases.

Appendix B: The top-down approach to optimal membership

14In step 2, the social planner maximizes profits at the club lever assuming a steady-stage / symmetric equilibrium:

Image 10000000000004490000023876B2D0D2.jpg

15Profits are maximized at:

Image 100000000000045B00000215BE6738B2.jpg

Appendix C: Welfare perfect competition

Welfare functions

16The arguments of the integrands are omitted, but G = G[d], V = V[d] and U = U[d], and the other parameters are held constant. Asterisks denoting equilibrium values are also omitted (Y = Y*, Z = Z* and so on).

17Positive GI-variety sales:

Image 10000000000004B20000015975300CAA.jpg

18GI-variety sales deterred:

Image 100000000000037600000143D0D14C3F.jpg

19Under perfect competition, σ = 0 and Foreign firms have zero profits. Total welfaire is therefore given exclusively by Home consumer surplus.

∆W = ∆CS = CS1 – CS0

20The variables of integration (dd) are also omitted from now on (unless the notation is ambiguous).

GI-variety sales deterred (Y1 = 0), panel C of Figure 4.5.a

Image 100000000000026C000000A00E438792.jpg

21For Home consumer surplus, distribute the integrands into domains determined by consecutive quantities and simplify:

Image 10000000000003EE00000092E945B926.jpg

Image 100000000000026B000000BF51D98060.jpg

Positive GI-variety sales (Y1 > 0), panel D of Figure 4.5.a

Image 1000000000000543000002790C4BD3B1.jpg

Appendix D: Welfare oligopolistic competition


Image 10000000000003F4000000FBBF6AA2FD.jpg

Foreign sales increase

GI-variety sales deterred (Y1 = 0), panel C of Figure 4.6.a

Image 10000000000004F1000001F9F479537F.jpg

Image 10000000000003A2000001AF6A4FB354.jpg

22Global welfare is the sum of profits and consumer welfare. The difference in profits earned by Foreign firms is cancelled out by the equivalent loss in Home consumer surplus. The switch to GI-original goods (first term) may have a net positive or negative welfare impact, depending on the parameters of the model, because at X0, the first integral is positive, but it might be negative at X1 (in panel C of Figure 4.6.a, parameters were selected so that the welfare gain over compensates for the welfare loss for consumers of GI-original goods):

Image 10000000000003BC00000146DCF14892.jpg

Positive GI-variety sales (Y1 > 0), panel D of Figure 4.6.a

Image 10000000000004B9000002E27B743E96.jpg

23The net welfare impact of the switch to GI-original goods for those consumers is ambiguous:

Image 10000000000003890000013442FCFC40.jpg

Foreign sales decrease

GI-variety sales deterred (Y1 = 0), panel B of Figure 4.6.b

Image 10000000000003D7000000E6CC450D17.jpg

Image 10000000000003B1000001B1476B55E4.jpg

24Net welfare is unambiguously negative, as both terms are always negative. In particular, (G + V + a) is greater than c at both X1 and X0.

Positive GI-variety sales (Y1 > 0), not drawn

Image 1000000000000495000002E2CF6A9A8F.jpg

25Net welfare is unambiguously negative, as all terms are always negative (this is because σ0 > 0 and b' > b, so that σ0 + b' > b.

Image 10000000000003910000010FBEC4072D.jpg

Appendix E: Welfare enforcement

26An increase in b affects sales of GI-labelled goods Y[b], sales of GI-original goods X[b] and, under oligopolistic competition, the mark-up σ[X[b]]. In addition:

Image 100000000000017A0000009E6FB74C85.jpg


Image 10000000000001A4000000A5D3D76725.jpg

28Consumer surplus:

Image 10000000000004C80000014AEEB5DAB6.jpg

29Global welfare:

Image 10000000000002EE00000126AE52F1A9.jpg


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