Notes for Chapter 14: Entry Costs, Market Structure, and Welfare The basic question : What determines the market structure or more simply, the number of firms in a given industry? Common sense : There will be more firms if the market is large, and if entry costs are small. The two main factors we focus on are (i) the size of the market, and (ii) the (fixed) entry costs. Entry costs and market structure Empirical evidence suggests that market size and industry‐specific factors influence the number of firms. A very simple model : All firms are identical with cost function: TC(q) = F + cq. The market demand is given by function: Q(p) = S(A−p), where S measures the market size. The equilibrium number of firms (see the ‘free entry with Cournot equilibrium’ handout for detailed derivation.) Assume Cournot competition. Inverse demand function: p = A − Q/S. The profit for firm i is Πi = (p − c)qi – F = [ A − (q1+q2+q3+…+qi+…+qn)/S – c ]qi. We differentiate with respect to qi and set equal to zero: A − (q1+q2+q3+…+qi+…+qn)/S – c − qi/S = 0. Since all firms have the same cost function, we will have q1* = q2* = … = q’* =…= qn* in the ⎛ A−c⎞
Cournot‐Nash equilibrium. We rearrange the above equality to get q* = S ⎜
⎟ . With n ⎝ n +1 ⎠
A
n
. +c
firms Q* = nq*. We insert this into the demand function to obtain p* = n +1
n +1
The profit function for firm i is (p* − c)q*. With the substitutions and some simplification we 2
⎛ A−c⎞
can write the per firm profit in the Cournot equilibrium as: Πi*(n , S) = S ⎜
⎟ . ⎝ n +1 ⎠
In a free‐entry equilibrium, no active firm wishes to leave the market ‐ i.e., Πi*(n , S) ≥ F, and no inactive firm whishes to enter the market ‐ i.e., Πi*(n+1 , S) ≤ F. The equilibrium number of firms given by setting Πi*(n , S) = F and taking the largest integer that is less than or equal to n. 2
S
⎛ A−c⎞
S⎜
− 1 . This n* is the equilibrium number of firms. ⎟ = F Î n* = ( A − c )
F
⎝ n +1 ⎠
Please keep in mind that the analysis depends on an assumption of Cournot competition. A few observations The equilibrium number of firms n* increases with market size, measured by S (directly) and a (indirectly) The equilibrium number of firms decreases when fixed costs (F) and variable costs (c) increase The relation between S and the equilibrium number of firms n* is nonlinear ‐ to double n*, S must quadruple. Put differently, if S is doubled, n increases approximately 40 %. This is because in a larger market, competition is stronger (the price‐cost margin is smaller). Note that with a fixed price, n would double when S doubles. An important concept MES The Minimum efficient scale (MES), is defined as the lowest output level where Average Cost is minimized. Operationally: the minimum scale where average cost is within 10 % of minimum AC. Let TC(q) = F =cq. Then we have AC = F/q + c. MES is minimum scale where AC = c’. Then we have c’ = F/q + c, so q = F/(c’ − c) = MES. Hence, MES is proportional to F. If MES increases by a factor 2, the number of firms decreases with a factor of 2 . Why not proportionally? As MES increases, there will be fewer firms, which makes competition less intense and gives the firms higher price cost margins. A measure of MES/market size is used in empirical studies. Complications and extensions We have assumed that – all firms have the same technology – firms have perfect information Entry is well coordinated (sequential) In practice, – Learning curve (aircrafts, titanium dioxide) First‐mover advantage (network effects, consumer awareness) – Sustainable competitive advantage (see the above examples, patents) VERY IMPORTANT IDEA : Some entry costs may be endogenous (endogenous versus exogenous entry costs) • Some costs are dependent on the size of the market: • Advertising – Concentration in consumer products equivalent in small and large countries • R&D – ”Homogenous” products (research by John Sutton) Empirical evidence • Endogenous entry costs suggest no (or weak) relation between market size and industry concentration – This is so especially in Advertising‐intensive, differentiated products industries • Exogenous entry costs suggests stronger relation between market size and concentration – Homogenous products with low advertising ratios • The exact relation between market size and concentration depends on other factors, e.g., type of competition Number of entrants and mode of competition • Cournot competition ‐ number of firms increases with sqrt of market size • Bertrand competition ‐ number of firms do not increase with market size (=1) Exogenous costs: Cost functions and parameters that cannot be influenced by firms’ choices and behaviors – Ex: TC(q) = F + cq Fixed and marginal cost parameters not chosen Endogenous costs: Costs determined by firms’ choices and behaviors – Strategic choices about costs to influence industry structure to its profit advantage For some industries economists observe similar concentrations across countries Industries dominated by few firms in one country tend to also be dominated by few firms in other countries – Despite differences in market size – Might expect bigger markets will have more competitors (be less concentrated) The U.S. Beer Industry is dominated by three firms: Anheuser‐Busch, Miller, and Coors The Portuguese Beer Industry is dominated by two firms: Centralcer, and Unicer BUT, the U.S. economy is 30 – 50 times bigger than the Portuguese economy so we may expect the number of firms to be 5 – 7 times greater, roughly 30 = 5.5, 50 = 7.1 Advertising Costs Advertising is a significant sunk entry cost for the beer industry Advertising to sales ratio similar in U.S. and Portugal But, total sales much higher in U.S, so the total advertising is much higher in U.S.; which implies Larger sunk entry costs for U.S. market New firm must keep up with huge advertising budgets of Anheuser Busch, Miller, and Coors Exogenous v. Endogenous entry costs • Scale economies are assumed to be: – Achieved by incurring sunk costs • Level of sunk costs are exogenous: determined by the underlying technology • Advertising and R & D are both: – Sunk costs – Incurred to increase consumers’ willingness to pay for the good: shift demand up – Endogenous variables Intuition: “Escalation Wars” • When firms compete by “one‐upping” each other (advertising, R & D, product quality) this creates endogenous sunk entry costs – Increases in the value of the market (market size) tend to be competed away – Number of firms may not change with increases in market size • Increased market size causes increased endogenous sunk costs, which deters entry Empirics & Testable Predictions • John Sutton (1991) collects industry data for cross‐section of countries – Non‐advertising, non‐R&D intensive industries: Expect inverse relationship between lower bound concentration and market size – Advertising and R&D intensive industries: Expect no relationship between lower bound concentration and market size Sutton’s Data • Six countries: – U.S., Japan, Germany, France, U.K., and Italy • Twenty industries in year 1986: – Salt, sugar, flour, bread, processed meat, canned vegetables, frozen food, soup, soft drinks, margarine, RTE cereals, mineral water, roast and ground coffee, instant coffee, sugar confectionery, chocolate confectionary, biscuits, pet foods, baby foods, beer Observed Variables • For each industry and country measures: – Relative market size (S) • Total output volumes or value of total sales – Concentration • Four firm concentration ratio: CR4 – Exogenous sunk entry costs • Proxy for minimum efficient scale (MES): ratio of output level of industry’s median plant to total industry output: µ Industries are divided into 2 Groups based on advertising to sales ratio – Cut‐off is advertising to sales ratio of 1% – Low advertising (commodities): salt, sugar, bread, flour, canned vegetables, and processed meat. These have Exogenous sunk costs only – Advertising intensive: remaining 14 industries • Exogenous and endogenous sunk costs Empirical specification S is the market size measure, σ is the MES variable. Remember that MES and the fixed entry cost F are linked by MES = F/(c –c’) equation) Entry and (social) welfare With Cournot (imperfect competition) competition in the post entry stage, free entry may result in excessive entry. The last entrant compares its profit with the entry cost. Part of that profit is taken from its competitors, the ” business stealing effect”. In differentiated‐
products markets, there is a value in variety. Excessive entry most likely under soft competition and homogenous products