Question

2 Subsidies in Strategic Trade Policy This question asks you to show that the optimal unilateral subsidy in the strategic trade policy setting is always positive. We will take the example of Boeing and Airbus used in lecture, with all the same parameters. 1. The E.U. government's objective is to maximize domestic profits less the cost of the subsidy. Write down the E.U.'s maximization problem as a function of the chosen quantities of Airbus and Boeing, Q* and QR. Hint: see the lecture notes. 2. Substitute the price and the optimal quantities, given the E.U. subsidy, in the expression above to find the E.U. maximization problem as a function of sa, a, b and c. Assume the U.S. does not subsidize. Hint: see the lecture notes. 3. Differentiate the government objective with respect to sa. Hint: use the product rule of differentiation. 4. Show that the optimal subsidy is positive (Hint: assume a > c and explain why this makes sense). 5. Give the intuition for part 4.

Lecture notes for reference:

Answer 1

The optimal unilateral subsidy in, stiretegic trade policy setting is always positive. 1.) The E.U. gont.'y o balctive is to maximise domestic prabit lely cost of subsidy. The Fury maximization problem as a bumcation of the chosen quantities of Airbus and Boeing, at and an is given below:- Here we have identical constant cost of production en Boeing produces acantity in and aineus GA: We have a = QATQB Inverse demand bunction p= alog Each company maximizes its probit given. so, otherly weantily as takind Airbus solves... max. P (QA+Qo). QA - C. QA GA puttind this im inverse demand bunction we get, max (a-le (QATQB) QA - Q.QA GA Taking the derivative wind an eveal to zero we alto get, a-26QA6QB - C=0 - 7 P

BY symmetry, a an te - PAT lu solving two enuations, we get earuilli- unium quantities Quate Note that im perfect competition outcome would be p = c 7 QA = QB = a -e QA = 9 Now, govt. might want to maximise do- mestic welbare wling turade policy.ie imposing a per unit subsidy. The proubt em be comes 'max (a-le CQATQB).GA- (C-SA). QA, GA where s indicates subsidy, s7o. Let, only the EU subsidizes Airbus, same Jent locino gety no subsidy, usim techniques we get, I boeing gets mo subsidy brom us * a-(C-SA) QÅ quo qalant 24A a-c SA as = sto i 3 to The subsidy increases Airbusly decreases Boling's sales. sales and .

E.U sees a decline in their terms out trade, as well as the U.S. Ainously purabit goes up and Boeing of pro- bity ball ball. loftimal sulasidy the govt. wants to maxi- mise domestic pratit Lely cost of subst- dy on, max P Carta ah - (C-SA). QA - SAGA SA - max pat tad at - car SA where and art depend on subsidy themselves. selbstitutind the values of P and are we gets a- b -+248 + Le core + suv Sul max SA (a + 24 ) 1 max a-le (ala- + setting 3 Dibberentiating this worrit SA and carcial to zero we get - Zyl ca-C.2 (0-0) 2. 0 i 4(a-c) que t (a-c) + 4SA + 20: 0 que t qui t au :0 av de 50-e que > SA SA: 50,% 0 [:aze

4. Optimal amount of positive SA= 5a-c subsidy is sin 14 5 This makes sense because the govt. subsidy lowers Airbus cast, allous- ing them to compete more vigorously bour customers. Bocino, seeing ainuus' more competitive behaviour, backs down and produces less output. doum