EC303 Economic Analysis of the EU. EC303 Class Note 5. Daniel Vernazza * Office Hour: Monday 15:30-16:30 Room S109

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1 EC303 Class Note 5 * d.r.vernazza@lse.ac.uk Office Hour: Monday 15:30-16:30 Room S109 Exercise Question 7: (Using the BE-Comp diagram) i) Use a three panel diagram to show how the number of firms, mark-up and firm size would change in a closed economy if the demand for a particular good doubled. Closed economy no trade. Demand doubles Demand curve shifts to the right in a non-parallel fashion (D has 1/2 slope of D in figure 1). For a given mark-up (or price), double the number of firms will be able to break-even (since for a given price, break-even sales per firm are unchanged) the BE curve shifts to the right such that BE has ½ slope of BE. See Appendix A for proof. Short term The number of firms n is fixed in the short-run Hence, immediately after the doubling of demand the economy remains at E. Since E lies above the break-even curve BE, firms are making positive profits in the short-run. Long term Firms will enter the market until profits are restored to zero. This is achieved at the intersection of the BE and COMP curves, denoted E. During this restructuring process the economy slides down the COMP curve from E to E. The equilibrium number of firms rises from n to n. The increased competition lowers the equilibrium mark-up from µ to µ. Firm size increases; to be more precise sales per firm rise from x to x. * All errors are my own. 1

2 Conclusion The doubling of demand for a good in a closed economy results in the same long-run equilibrium (point E ) as the no-trade-to-free-trade integration with an identical Partner country. However, the transition is very different. You should find this very striking! Figure 1 FIRM MARKET Price µ BE-COMP D D BE BE p p AC p p µ µ E E A COMP x x MC Sales per firm Q 2Q Total sales n n 2n No. of firms ii) Using your answer to part (i) consider the no-trade-to-free-trade integration between a large and small nation, where size is defined by the position of the demand curve (the demand curve in the large nation is further out). Assume that the small country is half the size of the large country. (a) Show that the large nation has more firms pre-integration. This is clear from our answer to part i). Refer to figure 1. Let D and D be the demand curves faced by the small and large country respectively. Pre-integration the small country faces break-even curve BE, with equilibrium number of firms n. The large country faces break-even curve BE and has n firms in equilibrium. Since n >n the larger nation has more firms. 2

3 (b) Show what happens to the number of firms and mark-up when the two markets become integrated. Figure 2 FIRM HOME MARKET Price µ BE-COMP D S D L BE S BE L BE FT p S p L p* AC p S p L p* F H G I J K µ S µ L µ* µ A E S E L E* A 1 COMP x S x L x* MC Sales per firm C S C S C L C L Total sales n S n L n* 2n S 3n S n S + n L No. of firms Key point: The liberalization adds a market for each firm, so more firms will be able to survive. The BE curve in the integrated market is given by BE FT (the horizontal summation of BE S and BE L ). For example, at mark-up µ S, n S firms break-even in the small country and 2n S firms break-even in the large country. Therefore, in the integrated market n S +2n S =3n S firms break-even at mark-up µ S (Point 1 in figure 2). Short term: defragmentation and the pro-competitive effect (from E S, E L to A). In the short run there is no entry or exit of firms, the number of firms is fixed. Before liberalization, there are n S firms producing at mark-up µ S in the small country, and n L firms producing at mark-up µ L in the large country. Firms share the domestic market and have zero share in the foreign market. Immediately after liberalisation the total number of firms in the integrated market is n S +n L. The integrated economy is at point A in the right panel. The market share of each firm is the same in both domestic and foreign markets (each firm has a share 1/( n S +n L )). In other words, the number of competitors in each market has increased, hence the mark-up falls to µ A in both markets (after liberalisation there is only one price in home and foreign). The short-term impact on prices and sales can be seen in the middle panel. Price in the small country drops from p S to p A, and in the large country price falls from p L to p A. 3

4 Long term: industrial restructuring and scale effects (A to E*) At point A firms are making negative profits (because point A lies below the BE FT curve). Firms exit the market until zero profits are restored. This is shown as a movement along the COMP curve from point A to point E* in the diagram. Postintegration equilibrium is given by the intersection of the BE FT and COMP curves, denoted by E*. In moving from point A to E* the overall number of firms falls from n S +n L to n*. During this process, firms enlarge their market shares and the mark-up rises from µ A to µ*. Conclusion The no-trade-to-free-trade liberalization results in fewer, larger firms, charging a lower mark-up. (c) What does your analysis tell you about the how integration affects firms in small nations versus large nations? Pre-integration, firms from a large country are exposed to more competition than firms from a small country (µ L < µ S ). Consequently, trade liberalisation forces firms from the small country to lower the mark-up they charge by more than firms from the large country. Our analysis in part (b) tells us that firms exit the market in the long-run. Importantly however, our diagram does not tell us which country the exiting firms come from. (d) Who gains more in proportion to size - the large or the small country? In our framework welfare is given by consumer surplus only, since producer surplus is zero when firms break-even. CS in small country = F + G + H + I CS in large country = H + I + J + K From the way I have drawn figure 2 it appears F + G > J + K, hence the small country gains more, especially in proportion to its size. 4

5 Appendix A (To see algebraically why double the number of firms can breakeven) Recall that the BE curve is given by the zero-profit condition: f P = AC = + c. q Hence, the mark-up µ is given by: f µ P c =. q In Cournot-Nash equilibrium (given identical cost functions) firms share the market: Q = nq. Hence, the mark-up is: n. f µ =. Q At a given mark-up µ (equivalently price), market quantity is Q, and the break-even number of firms n is given by: n ' f µ =. (1.1) Q ' If demand doubles to Q '' = 2 Q ', the break-even number of firms n at unchanged mark-up µ is given by: Equating equations (1.1) and (1.2) we have: n '' = 2 n '. µ = n '' f n '' f Q '' = 2 Q '. (1.2) In other words, for a given mark-up µ, double the number of firms break-even. Appendix B (Why the COMP curve doesn t shift) The demand curves as drawn are linear; however, if we did this properly they would come from an isoelastic demand function (as in question 5) and the constant elasticity (moving along the demand curve) part of that would mean that there would be no effect. To be more precise, with an isoelastic demand the position of the COMP curve depends only on the constant elasticity. Recall that for any demand function, a doubling of demand does not change the point elasticity (twice the original quantity offsets ½ the original 5

6 slope at a given price). Hence, for an isoelastic demand curve the constant elasticity (moving along the demand curve) is unchanged after a doubling of demand. dq P Recall, the price elasticity of demand is given by:. dp Q. When demand doubles we know that the demand curve has ½ slope of one in (P- Q) space. Hence, at any given price P we have: dp dq = 1. 2 Or equivalently: dq dp dp dq dq = 2. dp The other condition we need is that for a given price, the quantity demanded is double the quantity: Q = 2. Q Now we are done because at a given price P we have: dq P dq P dq P dq P. 2.. dp Q = dp Q dp 2. Q dp Q To summarise, with isoelastic demand, the constant elasticity of demand doesn t change when demand doubles, and hence the COMP curve doesn t shift. So we do get the neat result that the no-trade-to-free-trade liberalisation with an identical Partner results in the same long-run equilibrium in Home as a doubling of demand in Home. The same reasoning applies to part ii) of question 7. The COMP curves for the small and large countries are identical (given that the large country is defined to have double the demand of the small country). So what should you do in the exam, draw isoelastic demand curves? No, you will draw linear demand curves in the middle panel of the 3-panel diagram (because it makes life easier); however, you will not shift the COMP curve because you assume an isoelastic demand, even though you haven t drawn it like that! If any of you remain confused, I would simply say that all this is second order. 6