Universidad Distrital Francisco José de Caldas

Firm decisions to enter the market are based on the expectation of future profits. Heterogeneous firms enter production as long as their future earnings expectations are positive. Hence, the mass of firms in the market is determined by expected profits being equal to 0. After computing the profit function of single firms i with their particular strategies, expected profits are determined by the profits of all firms in the specific market. 107 As in Knorrenschild (2008). y x x0 x1 x2 x3

For firms selecting a domestic strategy in Country A, we apply Gd[i_,nA_,nB_,τ_,t_]. We must consider that the tariff τ must be set to 0 because the trade barrier is not relevant in the domestic market. The same applies for transport costs t, which must be set to 1. To compute the profit of a firm from A with rank i, we must consider the mass of firms in A and B because of competitive conditions.

The profit of a firm in the export strategy is computed as Gex[i_,nA_,nB_,τB_,t_]. Profits of exporting firms i from Country A to Country B depend on the mass of firms in Countries A and B, nA and nB, the tariff being applied in Country B (i.e., Bτ ), and transport costs t.

The profit function of MNEs originally located in Country A with subsidiaries in B is coded as Gin[i_,nA_,nB_,τB_,t_]. Profits of a MNEs, i, from Country A (being MNEs) in Country B are also dependent on the mass of firms in A and B, nA and nB, the tariff rate τB, and the transport costs t.

Expected profits (EG) in an economy result from the integration of profits over all firms in the different strategies. For Country A, they are given by:

EG[nA_,nB_,τA_,τB_,t_]:=EGd[nA,nB,τA,t]+EGex[nA,nB,τB,t]+EGin[ nA,nB,τB,t].

The computation of expected profits includes conditions to ensure that profits are only integrated if the associated strategy exists.

Finally, coding the mass of firms in equilibrium results from firms entering the market competing the expected profits to zero. For firms in A, this is given by:

Firms[nB_,τA_,τB_,t_]. The process to find the null is coded with the instruction to test several values in defined steps. After determining the first negative value of expected profits, the program returns to approach the null exactly, while the width of the steps is permanently reduced. For example, the instruction to calculate the mass of firms in equilibrium in Country A given nB=20000, τA=3%, τB=3%, and transport costs t=1.03 is depicted by Firms[20000,0.03,0.03,1.03]. The example results in ≈25577 firms in Country A given 20000 firms in Country B, with associated expected profits of -4.06419×10-6. This is support for the previously described

method.

Considering the utility function in (45), households in the two symmetric countries benefit from consumption of homogeneous goods x0 and differentiated goods. To

implement the utility maximization process, we must first consider the stand-alone contribution of x0. Without the existence of a differentiated sector, the representative

household only generates utility by consuming x0. Hence, the benefit of one unit of

differentiated goods is constituted by its net contribution (i.e., additional utility versus additional costs). The computation of the equilibrium utilizes this notion to implement the utility-maximizing process. The equilibrium of this model is labelled Equilibrium[τA_,τB_,t_] and is dependent on the given value of the tariff τ in Countries A and B and the transport costs t. The equilibrium is computed so that the system delivers data that describe the equilibrium. Given the exogenous variables, the system endogenously determines the equilibrium mass of firms in A and B. The tariff rates being unequal (i.e., τA ≠τB) results in the mass of firms

differing in both countries nA≠nB. The programming of the mass of firms in equilibrium is visualized in figure 15.

Figure 15. The computation of the mass of firms,

τ

_τ

In the first step, the computation to find the correct value for the mass of firms begins with nB=1 and searches for the corresponding mass of firms in Country A conditioned on nB=1 [i.e., nA(nB)]. In the figure, this is denoted as a. Given nA(1) firms in Country A, the iteration proceeds by calculating the associated mass of firms

nA nB 1 a b C nA* nB* a* b* 1

in Country B, denoted as a*. Analogously, we assume nA=1 and search for the associated value for the mass of firms in B, denoted as b [i.e., nB(nA)]. Given nB(1) firms in B, the system calculates the corresponding mass of firms in A, denoted as b*. The intersection of the two resulting graphs gives the new starting value, denoted as C. This loop is repeated until the difference between the new starting value minus the old starting value ≤ 10 (i.e., nB3-nB0≤10) in the program or C in the figure. The computation proceeds by using calculations of expected profits for Country A and B. The system calculates expected profits and all further key figures for the different possible integration strategies and sums them up afterwards. Hence, EGewA denotes expected profits in A; EGewB denotes expected profits in B.

The next relevant variable is the consistent market size for Country A, which is calculated using Xm[nA_,nB_,τ_,t_] as defined in section 2.5.2, and analogously for B. The results show the contribution of the different strategies to total market size and separately for Countries A and B. For example, the share of output of all domestic firms in its market in A is computed as YDA=Yd[NA,XMA,τA,t], where capital letters denote equilibria values. The expression is dependent on the mass of firms in Country A, NA; on the overall market size in A, XMA; and on the transport costs t.108

The sum of expenses for differentiated goods in the representative household in A is represented by MA=MYDA+MYEXA+MYINA. MYDA=MYd[NA,XMA,τA,t] denotes expenses of the representative household in A for goods from domestic producers, MYEXA=MYex[NB,XMA, τA,t] are expenses for imports from Country B to country A consumed by households in Country A, and MYINA=MYin[NB,XMA,τA,t] is the calculation for expenses for MNE goods from B of the representative household in Country A. The analogous notion is used to compute expenses for households in Country B, (MB).

Equilibria and, therefore, welfare are constituted by the utility of consumption of differentiated goods. Again, to determine utility, we distinguish between Countries A and B and between the different strategies. For Country A, we compute the utility of consumption of differentiated goods from domestic firms, from imports from Country B, and from MNEs in A originally located in B. Then, the overall utility of the

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Analogously, we compute YEXA, YINA for the market size of the export and the MNE strategy in Country A. The analogue computation for Country B is given as YDB, YEXB, and YINB.

representative household from differentiated good consumption in A is given, dependent on the sum of the three subfunctions:

UA=1/µ (YCDA+YCINA+YCEXA)^µ,referring to (45) and respectively for Country B. Finally, welfare in A is given as WA=UA-MA for Country A and WB=UB-MB for Country B.