The home country has a pool of J firms. These have firms are heterogeneous in that they have different productivity levels (Helpman et al., 2004).7 All firms maximise shareholder value, i.e. expected profits discounted by the investor’s SDF (Heiland, 2018).
The derivation of the firm’s maximisation problem follows the framework of Help-man et al. 2004, but in a dynamic setting over an infinite time horizon with uncertainty as in Heiland 2018.8 I start by showing the profit function of firms. I assume that all operating firms produce for the domestic market in alltwith fixed costs, fjiD from labour costs. They also make two choices.
First, firms decide whether to enter a certain destination market, h by exports or FDI (the extensive margin).9 Secondly, exporting firms and MNCs decide on the optimal quantity, qjh,t∗ , to export to or produce in these markets (the intensive margin). Since demand in destination market h is determined in period t+ 1, following country-specific shocks, the firm makes it decision in period t based on
7All firms observe a productivity levelαj, drawn from a productivity distributionG(α)
8Although the problem is analysed as a two-period problem
9I assume that each firmjwill enter a destination market heither through exportsor FDI
The Model 15 expected profits (Heiland, 2018). Whether they decide to remain in the domestic market, export to, or directly invest in destination marketh depends on expected profits to be ≥ 0 in each option. Due to differences in the cost structure arising from the three options, the productivity level of the firm is the determining factor (Helpman et al., 2004, p. 301-302). When a firm decides to start exports to destination market h additional costs incur. These are additional fixed costs in terms of establishing production networks,fh,tX. When exporting products, variable melting-iceberg-costs,τjhare also involved.10 A firm deciding to enter a destination market with FDI encounters higher fixed costs, fjhI , from establishing affiliates and labour costs from production, but have lower variable costs from transporting products.1112 This yields one profit function for exporting firms, πjh,tX , and one profit function for MNCs, πjh,tI with the entry condition that they should be ≥0.
πjh,tX =pjh,t∗qjh,t−cjτjhqjh,t−fjhX (5)
πjh,tI =pjh,t∗qjh,t−cjqjh,t−fjhI (6)
The cost, cj reflects productivity differences between firms, and is simplified here to α1
j, the inverse of the productivity level. Based on the entry condition, the cutoff productivity level to enter as MNC, as compared to exports, is αIj = qjh,tfI(τjh−1)
jh−fjhX , implying that πjh,tI > πjh,tX . Firms with a lower productivity level export (or produce for the domestic market) while firms with a higher productivity do FDI in destination marketh. For a firm to enter destination markethwith FDI, profits πjh,tI > πXjh,t, implying thatcjτjhqjh,t−fjhX >.
The second choice the firm makes in periodt is what quantity,qjh,t∗ , it will produce for this market, and the price,pjh,t+1 it will charge. I assume, however, a time lag between production and sales as in Heiland (2018). Hence, the firm decides and
10These iceberg-costs imply that only a given fraction of the product arrives at the destination market, depending on factors such as distance, tariffs, and other barriers to trade
11Also known as the proximity-concentration trade-off
12I assume that the cost of labour is the same for all countries,wi=wh∀ h
the firm will sell the quantity it produces in the next period, t+ 1. Furthermore, I assume monopolistic competition, so the firm sets the price, pjh,t+1(qjh,t∗ ), based on demand and a price markup, θ, depending on its market share, ϕjh,t.
Since the state int+ 1 is uncertain, demand for qjh,t∗ from destination market his also uncertain. Hence, the firm operates with expected profits:
Et(πjh,t+1X ) =Et(pjh,t+1∗qjh,t∗ −cjτjhqjh,t∗ −fjhX) (7)
Et(πjh,t+1I ) = Et(pjh,t∗q∗jh,t−cjqjh,t∗ −fjhI ) (8)
The firm’s total profits is the sum of its profits in all destination markets:
E[πj,t+1] =
I
X
i=1
E[πjh,t+1] (9)
Since firms maximise shareholder’s value, the value of their production is discoun-ted by the investor’s SDF and reads:
max
In t+ 1, firm j’s actual sales, and hence profits, are realised, depending on the state of the world, s. Since the firm can make a decision in every period t about the quantity it will sell to market h in the next period, t+ 1, hence we get a two-period problem:
max
qjh,t∗ ≥0Vjh,t =Et[mi,t+1πjh,t+1] (11) Firm j’s realised profits are given by:
πjh,t+1 =Et(πjh,t+1)∗Yˆh,t+1 (12)
The Model 17 From (8) we also have that the firm’s expecteddiscountedprofits areEt(mi,t+1πjh,t+1).
Using the formula for expectations and covariances we get:
Et(mi,t+1πjh,t+1) = Et(mi,t+1)Et(πjh,t+1) +Covt(mi,t+1, πjh,t+1) (13)
Using that the expected value of the investor’s SDF equals the inverse of the risk-free interest rate, 1
Rfi,t+1, and Covt(mi,t+1, πjh,t+1) equals Covt(mi,t+1,Yˆi,t+1)∗ Et(πjh,t+1). Rewriting equation (13) we get that
Et(mi,t+1πjh,t+1) = 1
Rfi,t+1Et(πjh,t+1)(1 +Rfi,t+1∗Covt(mi,t+1,Yˆjh,t+1)) (14) From equation (11) we see that the expected discounted profits of the firm depend on expected profits as well as the covariance between the investor’s SDF and fluctuations over expected demand in market i where firmj operates.13
The exporting firm will then only decide to enter a destination market if its ex-pected value will be positive, i.e. if:
Vjh,tX = 1 +Rfi,t+1∗Covt(mi,t+1,Yˆjh,t+1)
Rfi,t+1 ∗Et(πjh,t+1X )≥0 (15)
Inserting for Et(πXjh,t+1) from (x) yields:
Vjh,tX = 1 +Ri,t+1f ∗Covt(mi,t+1,Yˆjh,t+1)
Ri,t+1f ∗Et(pjh,t+1∗qjh,t∗ −cjτjhqjh,t∗ −fjhX)≥0 (16) A multinational company will similarly only enter a destination market h if:
Vjh,tI = 1 +Rfi,t+1∗Covt(mi,t+1,Yˆjh,t+1)
Rfi,t+1 ∗Et(πjh,t+1I )≥0 (17)
Inserting for Et(πIjh,t+1) from (x) we get:
Vjh,tI = 1 +Rfi,t+1∗Covt(mi,t+1,Yˆjh,t+1)
Rfi,t+1 ∗Et(pjh,t∗qjh,t∗ −cjq∗jh,t−fjhI )≥0 (18)
13I use hat notation for realised value as a fraction of expected value, i.e. ˆX =E(X)X
I assume that the firm’s value function is ”market-separable”, i.e. we can express the total value of firm j as the sum of its values in all destination markets i:14
Vj,t =
I
X
i=1
Vjh,t (19)
The firm’s total value is given by the value for its shareholders Vj,t. The share price,vj,t of a share in firmj,sj,t+1, is determined by investori’s willingness to pay.
The investor’s willingness to pay depends on the return he requires in equilibrium:
Et[Rj,t+1] =Et[sj,t+1
vj,t ] =Rfi,t+1−Covt(mi,t+1, sj,t+1) (20)
Rearranging, I get the equilibrium price, vj,t, as a function of the covariance term, using the relationship between expectations and covariances:
vj,t =Et[mi,t+1sj,t+1] = Et[sj,t+1]
Ri,t+1f +Covt(mi,t+1, sj,t+1) (21)
The value its shareholders places on the firm, Vj,t, is then the number of shares times the price of these shares, vj,t∗sj,t+1.
In addition, since total demand in country h in t+ 1, Yh,t+1, determines sales of firm j, sjh,t+1 = pjh,t+1(qjh,t∗ )qjh,t∗ = ϕjh,t+1Yh,t+1, where 0 < ϕjh,t+1 < 1 is the share of demand for firm j products in country h. Since sales determine payoffs to the investors, the return from firm j to investori becomes:
E(Rj,t+1) = E(sj,t+1
vj,t ) = E(ϕjh,t+1Yh,t+1(s)
vj,t ) (22) Then, equation (15) can be rewritten to:
vj,t =Et[mi,t+1sj,t+1] =ϕjh,t+1Et[Yh,t+1(s)]
Ri,t+1f +ϕjh,t+1Covt(mi,t+1, Yh,t+1) (23) The investor’s willingness to pay for a share in firmj, in other words, also depends on the covariance between his SDF and demand in countryhwhere firmjoperates.
14This implies that the value of entering one marketj= 1 does not effect the value of entering marketj= 2.
The Model 19 This fact provides the basis for the link between the investor’s risk premium and the firm’s international organisation decision.
I have already defined the risk premium required by the investor asλij,t≡Et[Rj,t+1]−
Rt+1f . This can be rearranged to yield:15
λij,t =−Rft+1∗Covt(mi,t+1, Rj,t+1) (24)
In effect, when the Covt(mi,t+1, Rj,t+1) positive and higher in absolute value, the risk premium required by the investor is lower (discounted by the risk-free interest rate).
Here, I have shown that we can extend the framework of Helpman et al. with heterogeneous firms make different decisions on whether to export to or invest in a destination market, to shareholder-maximising firms who discount profits by the investor’s SDF within the framework of Heiland. Taking heterogeneous firms into account in equations (15) and (17), yields separate value functions for exporting firms and multinational companies. This provides a framework for analysing the effect of the investor’s risk premium on the firm’s decision, while taking into ac-count different profit maximisation problems, and separates this model from that of Helpman et al.. This also changes the cutoff levels for entering as an exporter or with FDI into a given destination market h, as a higher covariance term for the investor of entering the market will increase the value of the firm of entering.
Then, this reduces the cutoff productivity level to enter the market as an exporter or investor compared to Helpman et al.’s prediction Helpman et al., 2004, p. 302.
In order for the exporting firm or MNC to maximise shareholder value, it must make some assumptions about the investor’s stochastic discount factor as this is not directly observable. This is what I turn to next.
15See Appendix A for calculations.