On the Incentive for a Self-Interested Policymaker to Mimic the Behavior of a Social-Welfare Maximizer

Abstract

We consider a government consisting of two policy implementation departments, each of which is self-interested. We examine whether each of these departments disguise itself as a social-welfare maximizer in the sense that it adopts welfare maximization as its “surface” objective to determine the policy variable, although its “true” objective is self-interest maximization under a tariff/subsidy scheme. We also examine whether an increase in the number of departments disguising themselves as welfare maximizers improves welfare. When the cost difference between home and foreign firms is at the intermediate level, the subsidy department does not disguise itself as a benevolent policymaker, whereas the tariff department may do so. In addition, the welfare level in the partial disguise case is lower than that in the no disguise case.

Appendices

Appendices

1.1 Appendix 10.1: Proof of Lemma 10.2

First, we compare the subsidy rate in the four cases . We compare s^WR with s^WW, i.e.,

$$ {s}^{WR}-{s}^{WW}=\left(1-\frac{2c}{3}\right)-\left(1-\frac{c}{2}\right)<0. $$

Next, the comparison between s^PW and s^WR yields

$$ {s}^{PW}-{s}^{WR}\propto 6\left(2-c\right)-13\left(3-2c\right)=20c-27<0. $$

Furthermore, by comparing s^PR with s^WR, we obtain

$$ {s}^{PR}-{s}^{WR}\propto 3\left(5-2c\right)-17\left(3-2c\right)=28c-36<0. $$

Subtracting s^PW from s^PR yields

$$ {s}^{PR}-{s}^{PW}\propto 13\left(5-2c\right)-34\left(2-c\right)=8c-3, $$

which means that if 0 < c < 3/8, then s^PR < s^PW; if 3/8 ≤ c < 1, then s^PR ≥ s^PW.

Secondly, we compare the tariff rate among the four cases. Comparing t^WR with t^RW yields

$$ {t}^{WR}-{t}^{PW}\propto 26c-3\left(3+5c\right)=11c-9, $$

which means that if c < 9/11, then t^WR < t^PW; if 9/11 ≤ c < 1, then t^WR ≥ t^PW.

Next, we compare t^WR with t^PR:

$$ {t}^{WR}-{t}^{PR}\propto 34c-9\left(1+3c\right)=7c-9<0. $$

Finally, by subtracting t^PR from t^PW, we obtain

$$ {t}^{PR}-{t}^{PW}\propto 39\left(1+3c\right)-17\left(3+5c\right)=8c-3, $$

which means that if 0 < c < 3/8, then t^PR < t^PW; if 3/8 ≤ c < 1, then t^PR ≥ t^PW. Note that t^WW < t^WR. Thus, the statements of Lemma 10.2 hold.

1.2 Appendix 10.2: Proof of Proposition 10.3

Suppose that the tariff department selects strategy R as its objective . Subtracting PS^WR from PS^PR yields

$$ {\displaystyle \begin{array}{c}{PS}^{PR}-{PS}^{WR}\propto 162{\left(5-2c\right)}^2-289c\left(9-5c\right)\\ {}=2093{c}^2-5841c+4050\\ {}=\left(7c-9\right)\left(299c-450\right)>0.\end{array}} $$

Suppose that the tariff department selects strategy W as its objective. Then, PS^PW > PS^WW = 0 clearly. Therefore, strategy P is a dominant strategy for the subsidy department.

Suppose that the subsidy department selects strategy P. Comparing TR^PR with TR^PW yields

$$ {\displaystyle \begin{array}{c}{TR}^{PR}-{TR}^{PW}\propto 1014{\left(1+3\mathrm{c}\right)}^2-289\left(3+5c\right)\left(1+6c\right)\\ {}=456{c}^2-563c+147\\ {}=\left(8c-3\right)\left(57c-49\right),\end{array}} $$

which means that if 0 < c < 3/8 or if 49/57 ≤ c < 1, then TR^PR ≥ TR^PW; if 3/8 ≤ c < 49/57, then TR^PR < TR^PW. Thus, we have proven Proposition 10.3.

1.3 Appendix 10.3: Proof of Lemma 10.3

First, we compare W^WR with W^WW:

$$ {W}^{WR}-{W}^{WW}\propto 4\left(13{c}^2+27\right)-54\left({c}^2+2\right)=-2{c}^2<0. $$

Secondly, by comparing W^PW with W^WR, we obtain

$$ {\displaystyle \begin{array}{c}{W}^{PW}-{W}^{WR}\propto 27\left(80{c}^2+18c+151\right)-169\left(13{c}^2+27\right)\\ {}=-37{c}^2+486\left(c-1\right)<0.\end{array}} $$

Thirdly, comparing W^PR with W^WR yields

$$ {\displaystyle \begin{array}{c}{W}^{PR}-{W}^{WR}\propto 216\left(16{c}^2+5c+32\right)-289\left(13{c}^2+27\right)\\ {}=-301{c}^2+1080c-891\equiv h(c).\end{array}} $$

Since h'(c) =  − 602c + 1080 &gt; 0 for c ∈ (0, 1) and h(1) =  − 112 < 0, h(c) < 0 for c ∈ (0, 1). This means that W^PR < W^WR. Finally, we compare W^PR with W^PW:

$$ {\displaystyle \begin{array}{c}{W}^{PR}-{W}^{PW}\propto 1352\left(16{c}^2+5c+32\right)-289\left(80{c}^2+18c+151\right)\\ {}=-1488{c}^2+1558c-375=-\left(8c-3\right)\left(186c-125\right)\end{array}} $$

which means that if 0 < c < 3/8 or if 125/186 < c < 1, then W^PR < W^PW; if 3/8 ≤ c ≤ 125/186, then W^PR ≥ W^PW. Thus, we have proven Lemma 10.3.