We now turn to the case of Cournot competition in which firms choose quantities rather than prices at stage 2 after committing to quality levels at stage 1. The game played by firms is set out in 4.1 and the respective effects of LDC and developed country policies towards quality are explored in 4.2 and 4.3.

**4.1 The two-stage model of firm behavior: Cournot competition.**

Examining the second-stage first, we solve for p^{L} = P^{L}/q^{L} and p^{H} = P^{H}/q^{H} from the demand functions (5), so as to obtain the inverse demand functions:

This includes the possibility that both firms set the same qualities (i.e. q^{L} = q^{H}), since, setting r = 1 in (22), we obtain, P = (1- (x^{L} + x^{H} ))q‘ for i = L,H, as in (3). Recalling that productions are zero, for any given qualities, q^{L} and q^{H} , committed at stage 1, firm L sets x^{L} to maximize its revenue, R^{L} = P^{L}x^{L}, taking x^{H} as given and firm H sets x^{H} to maximize its revenue, R^{H} = P^{H}x^{H} , taking x^{L} as given. Thus from (22), x^{L} and x^{H} satisfy the first order conditions:

where the second order and stability conditions are also satisfied. Also, since 0R/0x is decreasing in x^{j} for i,j = L,H and i g j, the outputs are strategic substitutes as is typical for Cournot competition.

From the first order conditions, we obtain output levels and then quality-adjusted prices (from (22) and (4)) at the Cournot equilibrium as follows:

From (23), it is notable that the quality-adjusted price equals the quantity sold of each product. Also, since p^{L} and x^{L} both fall and p^{H} and x^{H} both rise, greater separation in quality, as shown by an increase in r now has mixed effects on prices and output and hence the degree of competition: i.e. from (23),

Using a superscript c to distinguish functions at the Cournot equilibrium, we express the revenues

Thus, holding own qualities fixed, the revenues of the two firms respond in opposite directions with respect to an increase in r = q^{H}/q^{L}, with firm L’s revenue falling and firm H’s revenue rising. This implies that revenues for firm L as well as for firm H are decreased by an increase in the rivals quality: i.e.

In contrast with the Bertrand case, firm L now gains as the products become more similar, but, as before, firm H gains from a greater separation of qualities. To understand these results, first note that, for both models, an increase in r, holding x^{L} and x^{H} fixed, shifts up the demand curve for good H, raising the willingness of consumers to pay for the high-quality good (i.e. 0p^{H}/0r = x^{L}/(r)^{2 }> 0 from (22)), but the willingness to pay for the low-quality good is unchanged (i.e. 0p^{L}/0r = 0 from (22)). Under Cournot competition, firm H responds to this higher demand due to greater separation of products by expanding output and firm L then reacts by cutting output (x^{L} and x^{H} are strategic substitutes). Since quality-adjusted price and output both fall for firm L and both rise for firm H (see (24)), firm L’s revenue falls (holding q^{L} fixed) and firm H’s revenue increases (holding q^{H} fixed). Instead, under Bertrand competition, firm H raises price in response to an increase in r and, since p^{L} and p^{H} are strategic complements, firm L also raises price (see (10)) causing the revenues of both firms to increase. The idea to travell all over the world is attractive but so much money is necessary to make your dreams come true. Not to waste time just speedy cash payday loans, they will solve all your problems not only with the travelling but other as well.

Incorporating the cost of investment for general cost parameters A^{L} and A^{H}, the respective profits of the low and high quality firms are given by:

where Thus, the Nash equilibrium qualities, denoted q^{cL} and q^{cH}, respectively satisfy the first order conditions:

In this Cournot case, marginal revenue with respect to own quality is always positive: i.e. from (25)

In considering the choice of qualities, there is again a tradeoff between competition affects arising from the extent of differentiation from the rival’s product and the profitability of a particular location in quality space based on revenues and investment costs for a given quality ratio, r. Since firm L gains from a narrowing of the quality gap, this gives firm L an incentive to increase q^{L}, which reduces r, holding q^{H} fixed (the term -r7 ‘(r) in (29) is positive). For firm H, analogously to Bertrand competition, a greater separation of products raises revenue leading it to also want to raise q^{H}. However, for both firm L and firm H, the profitability of an increase in quality is limited by the rising marginal cost of investment in quality. This web site www.speedy-payday-loans.com is a source of dreams realization. Everything you need is to make your mind what sum of money you desire to borrow.

Although positive profits can be made at the second-stage Cournot equilibrium when q^{L} = q^{H} , Lemma 3 shows (see Appendix B for the proof) that even if both firms face identical costs (i.e. if A^{L} = A^{H}), the first order conditions (28) imply that the quality game is asymmetric with q^{L} < q^{H}. and hence r > 1.

For firm H, we have R^{cH}HH < 0 for r > 1. However, satisfaction of n^{L}LL < 0 is made difficult by the fact that marginal revenue,

Lemma 4 (proved in Appendix B) concerns conditions under which (30) holds locally. For the case, F(q) = q^{2}/2, commonly used in the literature, we have F'”(q) = 0 and Lemma 4(i) applies for A^{L}/A^{H} > 1. Letting E = qF”(q)/F'(q) represent the responsiveness (or elasticity) of the marginal cost F ‘(q) of investment with respect to quality, since F ‘(0) = 0, the assumption F “(q) > 0 (see (1)) ensures F “(q) > F ‘(q)/q and hence E > 1. If E = 1 then F “(q) = 0 and Lemma 4(i) applies. However, to allow for more general investment cost functions and for any value of A^{L}/A^{H}, Lemma 4(ii) requires that firm L’s marginal cost of investment increases more steeply: i.e. for q^{L} satisfying n^{L}L = 0, that E^{L} = q^{L}F”(q^{L})/F'(q^{L}) > 2. For the example, F(q) = aq^{n}, E = n-1 is a constant and Lemma 4(ii) applies if n > 3.

Firm H continues to view q^{L} as a strategic complement to q^{H} , but since R^{cL}L is increased by a greater similarity of products, it follows that R^{cL}LH < 0 and hence that firm L views q^{H} as a strategic substitute to q^{L}: i.e. from (29) and (31),

Thus, as shown in Figure 4, firm L’s reaction function, q^{L} = p^{cL}(q^{H}), is negatively sloped in the neighborhood of equilibrium, whereas q^{H} = p^{cH}(q^{L}) has a positive slope; i.e. from (28), (32) and Lemma 4,

Analogously to Proposition 1 for Bertrand competition, for a sufficiently large cost disadvantage in the LDC, we are able to prove existence and uniqueness of the pure strategy equilibrium (see Appendix B for the proof) in which the LDC firm produces q^{L} and the developed country firm produces q^{H}. For the remainder of the paper we assume that Proposition 9 applies and hence A^{L} = y(1-s^{L}) and A^{H} = 1-s^{H} where s^{L} and s^{H} represent the investment subsidy policies by LDC and developed countries respectively.

**Proposition 9.** Assume Cournot competition in the output market. Under conditions (1), if y > 1 is sufficiently large, there exists a unique pure strategy equilibrium in which the low quality product is produced in the LDC and the high quality product in the developed country.

**4.2 LDC investment policy towards the low-quality product.**

For the Cournot setting, the effects of an investment subsidy, s^{L}, applied to firm L by the LDC on quality levels and profits are presented in Proposition 10.

Interestingly, comparing Proposition 10 with Proposition 2 for Bertrand competition, the direction of effects is the same. However, there are some critical differences behind the scenes, since, as shown in Proposition 11, the LDC has a unilateral incentive to tax the investment of its firm under Cournot competition, whereas a subsidy raises LDC welfare in the Bertrand case. For Proposition 11, we assume that LDC welfare, denoted W^{cL} = n^{L}(q^{L},q^{H},A^{L}) – s^{L}yF(q^{L}), is locally concave at the optimal policy, s^{cL}*. As shown in Lemma 6 of Appendix B, this holds for:

This tax policy may initially seem hard to understand, since, as can be seen from Proposition 10, the LDC tax lowers the profit of firm L and at the same time, since firm H benefits from a reduction in q^{L}, raises the profit of firm H and hence welfare in the developed country. However, LDC welfare rises because the tax revenue more than offsets the loss in firm L’s profit. Also, the fact that firm H’s profits are increased simply means that the rent-shifting aspect of the policy is entirely at the expense of consumers in the third country market. As illustrated in Figure 5, the LDC tax shifts the quality reaction function of firm L in towards the origin (shown by the dashed line) and both countries move to higher iso-welfare contours. Speedy loans! What may be easier for people to take a loan. A loan with low percantage, with no requires and no troubles. Just find the web site www.speedy-payday-loans.com it is an alternative way of having money if you feel some troubles you won’t get enough even for a month.

To understand why a switch from Bertrand to Cournot competition causes LDC policy to switch from an investment subsidy to an investment tax, we again appeal to the correspondence of the model with a Stackelberg leader-follower model in which firm L is the leader and there is no government intervention. Since firm H raises q^{H} in response to an increase in q^{L} under both Bertrand and Cournot competition, the fact that the revenues of firm L are increased by an increase in q^{H} under Bertrand competition (i.e. R^{L}H > 0) and are reduced by an increase in q^{H} under Cournot competition (i.e. R^{cL}H < 0), means that a Stackelberg leader would increase q^{L} above its Nash equilibrium value in the Bertrand case and reduce q^{L} in the Cournot case. If both firms play Nash in quality, the same outcome is achieved by an investment subsidy in the LDC under Bertrand competition and an investment tax under Cournot competition.

Fundamentally, by taking q^{H} as given at the Nash quality equilibrium, firm L overestimates the effect of an increase in q^{L} in making the products more similar under both forms of competition. However, since firm L gains from a greater separation of products in the Bertrand case and from a greater similarity of products in the Cournot case, it sets q^{L} too low in the Bertrand case and too high in the Cournot case for maximum profit. To correct for this, the LDC policy moves firm L (and hence firm H) up the quality ladder under Bertrand competition and down the quality ladder under Cournot competition.

**4.3 Developed country policy towards the high-quality product**

For the Cournot setting, Proposition 12 concerns the effects of an investment subsidy, s^{H}, applied to firm H by the developed country. An increase in s^{H} increases quality q^{H}, but in contrast to the Bertrand setting, firm L’s reaction function has a negative slope and q^{L} falls. As might be expected, Firm H enjoys higher profits, but firm L’s profits are reduced.

Next, Proposition 13 shows that a shift form Bertrand to Cournot competition gives country H an incentive to subsidize rather than tax the investment of its firm. As illustrated in Figure 6, under Cournot competition, the subsidy shifts up the quality reaction function of firm H (shown as the dashed line), moving the equilibrium from point N^{c} to point S^{c}, which, as before, corresponds to the Stackelberg leader-follower point with firm H as the leader and s^{cH} = 0. Since firm H gains from a reduction in q^{L} under both forms of competition (i.e. R^{cH}L < 0 and R^{cH}L < 0), in each case the policy is aimed at reducing q^{L}. For Cournot competition, it follows from the negative slope of firm L’s reaction function that a subsidy will raise q^{H} and hence lower q^{L}. By contrast, in the Bertrand case, since firm L raises q^{L} in response to an increase in q^{H}, the relevant policy is an investment tax. For Proposition 13, we assume that the welfare function, W^{cH} , for country H is locally concave at the optimum subsidy, s^{cH}*. From Lemma 7 (see Appendix B for the proof), this holds under the same conditions, E^{L} > 2 and a(q) > 0, used to ensure local concavity of LDC welfare.

Finally, as in the Bertrand case, the jointly optimal investment policy corrects for the cross effects of the quality chosen by each firm on its rival’s profit. Since Firm H gains from the widening of the quality gap due to a reduction in q^{L} and firm L gains from the narrowing of the quality gap due to a reduction in q^{H}, joint profit maximization involves a move by both firms down the quality ladder. Consequently, as shown in Proposition 14, the policy requires that each country tax investment, with the tax given by country H. Relative to the Nash policy equilibrium, the joint choice of policies increases the investment tax in the LDC and results in a switch from a subsidy to a tax in the developed country. Since an increase in product differentiation has mixed effects on price competition (p^{H} rises and p^{L} falls), in contrast to the Bertrand case, there is no clear relationship between the size of the quality gap and the ability to raise prices at the expense of third country consumers. Rather the jointly optimal policy is directed at finding the optimal location in quality space taking into account revenues and the increasingly high investment costs as quality is increased.

**Proposition 14.** Under Cournot competition, the joint welfare of the two producing countries is maximized by an investment tax in both countries with s^{cL J} < s^{cL}* < 0 and s^{cHJ} < 0 < s^{cH}*.

*Figure 4 Quality reaction functions: Cournot competition*

*Figure 5 The LDC’s optimal tax: Cournot competition*

*Figure 6. The developed country’s optimal subsidy: Cournot competition*

**Appendix B: Cournot Competition**

**Appendix B: Cournot Competition (continue)**

**Appendix B: Cournot Competition (continue 2)**

**Appendix B: Cournot Competition (continue 3)**

**Appendix B: Cournot Competition (continue 4)**

**Appendix B: Cournot Competition (continue 5)**