Vertical Product Differentiation and Credence Goods: Mandatory Labeling and Gains from International Integration

Transcription

1 Vertical Product Differentiation and Credence Goods: Mandatory Labeling and Gains from International Integration Ian Sheldon and Brian Roe (The Ohio State University Quality Promotion through Eco-Labeling: Theoretical and Empirical Advances on the Feasibility of Developing Social and Environmental Claims nd International Workshop at Laboratoire d Economie Forestière Nancy, France, June 9-30, 009

2 Motivation Goods increasingly differentiated by process attributes Consumers unable to verify claims about attributes, i.e., a form of credence good (Darby and Karni, 973 Labeling possible, but there are implementation issues: discrete vs. continuous labels voluntary vs. mandatory exclusive vs. non-exclusive harmonized vs. mutual recognition Examine trade implications of choices in context of model of vertical product differentiation

3 Model Consumers, firms and quality Consumers have unit demand for quality-differentiated good, consumer utility is: ( U = u(y p, where u [u, ] and u > 0 is minimum quality-standard Income uniformly distributed on interval [a, b], and size of population is s Firms produce single differentiated good with zero production costs and a fixed, quality-dependent cost, F(u, sunk by firm after entry: F(u = ε + α(u u, ε and α >0

4 Game structure 3-stage game: ( entry/no-entry; ( choice of quality; (3 price Invoke sub-game perfection and Bertrand-Nash competition Labeling policy Public certifiers perfectly monitor and communicate quality of individual firms ex ante, total cost of certifying and labeling being: j I (u = I j for u > u, j {t, d}, and I t I d where t = continuous, and d = discrete labeling No economies of scale in public certification, and no variable costs of labeling

5 Entry and number of firms Assume: ( 4a > b > a or b/4 < a < b/. ensuring covered market of firms with quality levels 0 < u u < u Price equilibrium y is income at which consumer is indifferent to buying either high or low-quality good: (3 y = ( rp + rp, where r = u / (u u, and p q is price of good, q =,, and if p = y, consumer indifferent between good of quality u and no good

6 Firms profits are: (4 π = sp (y a F(u (5 π = sp (b y F(u Bertrand-Nash equilibrium prices being: (6 p = b - a 3 (r - (7 p = b - a 3r u( b - a (6 and (7 holding if p a, so that u ˆ u (u = b + a In covered market, equilibrium prices increase in b and (u u

7 Autarky Equilibrium with Perfect Information Suppose quality is observable, firms profit functions are: s( b - a ( u - u (9 π ˆ ( u ; u = - F ( u for u > u( u 9u s(b - a ( u - u (0 π ˆ ( u; u = - F ( u for u < u( u 9u where u ˆ is as defined, and uˆ ( u = u ( b + a/( b - a u Low-quality firm chooses u * = u in equilibrium Follows from differentiating (9: π s( b - a u ( ( u u F u u uˆ ; = - - ( < 0 for > ( u u 9 ( u

8 High-quality firm s optimal quality decision follows from (0: ( where π u s(b - a u ( u ˆ ; u = - F ( u for u < u ( u 9 ( u π - u s b a - F ( u = - <0 ( u 9 u u ( u Given u = u, firm s choice of quality induces a covered market: π ( u u u u ˆ ; = 0 for < ( u u Equilibrium quality in a covered market is implicitly defined by: (3 s(b - a u u u * = - F ( u = 0 9 ( u u *= u and (3 represent the Nash equilibrium in qualities

9 With perfect information on u *, profits of both firms increase with b and s This follows from inspection of (9 and (0 Aggregate consumer welfare in equilibrium is: y' b (4 W = u *( ψ - p * dψ + u *( ψ - p * dψ a y' As u increases, (i welfare of consumers purchasing lowquality good decreases, (ii proportion of consumers purchasing low-quality good declines, and (iii aggregate consumer welfare increases (i See utility function ( (ii Differentiate (3 w.r.t u, y uu(b - a = - < 0 3 u 3( u - u (iii In aggregate, consumers value quality over price increases

10 Figure : Autarky equilibrium with perfect information F(u, sr(u F(u sr (u, u π { sr (u, u π { ε { u u u

11 North-North Integrated Equilibrium Perfect information (PI - two economies, N=,, with same distribution of income integrate, a =a and b =b, although may be of differing sizes, i.e., s i = s + s - firms incur additional sunk costs ε i to enter integrated market, but u = u, - economy supports firms, i.e., firms have to exit, figure - increase in quality of good, quality of good remaining the same Trade with no labeling (XL - sunk cost of entry combined with 3-stage game supports entry of single firm into integrated market producing lowest quality - price is monopoly outcome given linear demand structure due to assumptions on income distribution

12 Figure : North-North trade equilibrium PI case F(u, sr(u s i R (u, u F(u { i π s i R (u, u i sr (u, u } i π sr (u, u ε i { u u u i u

13 Table : Labeling regimes North/North trade MEC MED Harmonized Replicates PI May be XL (Figure 3 Mutual recognition Replicates PI May replicate PI PI perfect information XL no labeling MEC mandatory, non-exclusive, continuous MED mandatory, exclusive, discrete

14 Figure 3: Harmonized MED case F(u, sr(u F(u s i R (u i, u s i R (u,u i s i R (u g, u s i R (u,u g ε i { u g u g u u i u

15 North-South Integrated Equilibrium Trade equilibrium with overlapping income distributions - if two economies, N and S initially support two goods using same technology, but a N >a S, and b N >b S, and u N > u S, there will be three goods in integrated equilibrium if, a N / < a S < a N < b N / < b S < b N - gains from trade occur due to lower prices in equilibrium - XL generates monopoly outcome - MEC replicates PI - harmonized MED, one or two firms may be forced from market in equilibrium, but not necessarily with mutual recognition