International Trade Theorie (TU Wien, Austria)
75 flashcards · Economics · by Locke Lamora
Autarkic Economy (AE) Assumptions
two industries fixed technology 1 production factor mobile across industries immobile between countries
(AE) output xix_ixi
xi=φi⋅lix_i = \varphi_i \cdot l_ixi=φi⋅li
(AE) Labour demand
li=1φixi=alixil_i = \frac{1}{\varphi_i}x_i = a_{l_i}x_ili=φi1xi=alixi
(AE) Full employment condition
h=al1x1+al2x2=l1+l2h= a_{l_1}x_1+a_{l_2}x_2 = l_1 + l_2h=al1x1+al2x2=l1+l2
(AE) Production possibility frontier
x2=φ2h−φ2φ1x1x_2 = \varphi_2 h - \frac{\varphi_2}{\varphi_1}x_1x2=φ2h−φ1φ2x1
(AE) total factor income
y=w⋅h=w⋅al1+wal2y= w\cdot h = w\cdot a_{l_1}+wa_{l_2}y=w⋅h=w⋅al1+wal2
(AE) total production costs in industry iii
ci=walilic_i = w a_{l_i}l_ici=walili
(AE) zero-profit condition
pi=MCi ⟹ y=p1x1+p2x2p_i = MC_i \implies y = p_1x_1 + p_2 x_2pi=MCi⟹y=p1x1+p2x2
(AE) Budget constraint
Same as PPF x2=yp2−p1p2x1x_2 = \frac{y}{p_2}-\frac{p_1}{p_2}x_1x2=p2y−p2p1x1
(AE) Marginal Rate of Substitution
MRS=dx2dx1=−dudx1dudx2=−MU1MU2MRS = \frac{d x_2}{d x_1} = - \frac{\frac{d u}{d x_1}}{\frac{d u}{d x_2}}= - \frac{MU_1}{MU_2}MRS=dx1dx2=−dx2dudx1du=−MU2MU1
(AE) MRS in utility maximisation
MRS=−p1p2MRS = -\frac{p_1}{p_2}MRS=−p2p1
(AE) Conditions fullfilled in equilibrium
Full employment h=al1x1+al2x2=l1+l2h = a_{l_1}x_1 + a_{l_2}x_2 = l_1 + l_2h=al1x1+al2x2=l1+l2 Demand for goods = supply xid=φili∗=φiali∗xi∗=xi∗x_i^d = \varphi_i l_i^* = \varphi_i a_{l_i}^* x_i^* = x_i^*xid=φili∗=φiali∗xi∗=xi∗ zero-profit condition xipi=walixi ⟹ pi=ACix_i p_i = wa_{l_i}x_i \implies p_i = AC_ixipi=walixi⟹pi=ACi
Cobb-Douglas utility function
u(x1,x2)=x1α1x2α2 u(x_1, x_2) = x_1^{\alpha_1} x_2^{\alpha_2 } u(x1,x2)=x1α1x2α2 mit α1+α2=1\alpha_1 + \alpha_2 =1α1+α2=1
Cobb-Douglas demand
xi=αiypix_i = \alpha_i \frac{y}{p_i}xi=αipiy
Cobb-Douglas price index
p=p1α1p2α2p = p_1^{\alpha_1}p_2^{\alpha_2}p=p1α1p2α2
Constant elasticity of substitution (CES) utility function
u=(α11−ρx1ρ+α21−ρx2ρ)1ρu = \left(\alpha_1^{1-\rho}x_1^{\rho}+ \alpha_2^{1-\rho}x_2^{\rho}\right)^{\frac{1}{\rho}}u=(α11−ρx1ρ+α21−ρx2ρ)ρ1 with −∞<ρ≤1∧ρ≠0-\infty < \rho \leq 1 \wedge \rho \neq 0−∞<ρ≤1∧ρ=0
CES demand
xi=ypi⋅αipi1−σα1p11−σ+α2p21−σx_i = \frac{y}{p_i}\cdot \frac{\alpha_i p_i^{1-\sigma}}{\alpha_1 p_1^{1-\sigma}+ \alpha_2 p_2^{1-\sigma}}xi=piy⋅α1p11−σ+α2p21−σαipi1−σ with σ=11−ρ\sigma = \frac{1}{1-\rho}σ=1−ρ1
CES price index
p=(α1p11−σ+α2p21−σ)11−σp = \left(\alpha_1 p_1^{1-\sigma}+ \alpha_2 p_2^{1-\sigma}\right)^{\frac{1}{1-\sigma}}p=(α1p11−σ+α2p21−σ)1−σ1 with σ=11−ρ\sigma=\frac{1}{1-\rho}σ=1−ρ1
Small open economy (SOE) assumptions
small country is price taker can sell and purchase any amount at world price producers first serve domestic market consumers first buy domestic products
(SOE) Budget constraint in foreign currency
y$=x1p1$+x2p2$ y^{\$} = x_1p_1^{\$} + x_2p_2^{\$} y$=x1p1$+x2p2$
(SOE) Exchange rate
E=y$yE = \frac{y^{\$}}{y}E=yy$
(SOE) Budget constraint on world market in national currency
y=p1wx1+p2wx2=1Ep1$x1+1Ep2$x2y = p_1^w x_1 + p_2^w x_2 = \frac{1}{E}p_1^{\$}x_1 + \frac{1}{E}p_2^{\$}x_2y=p1wx1+p2wx2=E1p1$x1+E1p2$x2
Two trading economies (TTE) assumptions
countries have labour endowment l1,l2l_1, l_2l1,l2 Labour is the only production factor Countries have different relative producitivity levels
(TTE) dynamics
Country 1 has comparative advantage in sector 2 Country 1 producers start selling good 2 in country 2 Country 1 consumers start buying good 1 in country 2 Country 1 specialises completely in industry 2
(TTE) free trade equilibrium (prices) with Country Two comparative advantage in sector one
\frac{p_1^w}{p_2^w}> \frac{p_1^2}{p_2^2}"> p11p21>p1wp2w>p12p22\frac{p_1^1}{p_2^1} > \frac{p_1^w}{p_2^w}> \frac{p_1^2}{p_2^2}p21p11>p2wp1w>p22p12
(TTE) exceptions to gain for both countries
Size difference (only the small country gains from trade) biased consumption (only country with biased preference gains)
Cobb-Douglas relative demand
x1x2=α1α2p2p1\frac{x_1}{x_2} = \frac{\alpha_1}{\alpha2}\frac{p_2}{p_1}x2x1=α2α1p1p2
Cobb-Douglas relative supply
φ12l2φ21l1=a21l2a12l1=α1w1a21α2w2a12\frac{\varphi_1^2l^2}{\varphi_2^1 l^1} = \frac{a_2^1l^2}{a_1^2l^1} = \frac{\alpha_1w^1a_2^1}{\alpha_2w_2a_1^2}φ21l1φ12l2=a12l1a21l2=α2w2a12α1w1a21
Cobb-Douglas relative wage
w1w2=α2l2α1l1\frac{w^1}{w^2} = \frac{\alpha_2l^2}{\alpha_1l^1}w2w1=α1l1α2l2 if w1w^1w1 fixed: w2=α1l1α2l2w^2 = \frac{\alpha_1l^1}{\alpha_2l^2}w2=α2l2α1l1
(TTE) equilibrium world prices
pi=wcalicp_i = w^c a_{l_i}^c pi=wcalic
(TTE) Balance of payments condition
α1w1l1=α2w2l2\alpha_1 w^1 l^1 = \alpha^2 w^2 l^2α1w1l1=α2w2l2 value of imports country 1 = value of exports country 2
(TTE) Demand-budget condition
(y1+y2)α1=y2(y_1 + y_2) \alpha_1 = y_2(y1+y2)α1=y2 demands for goods in country 2 (y1+y2)α2=y1(y_1 + y_2) \alpha_2 = y_1(y1+y2)α2=y1 demands for goods in country 1
CES relative demand
x1x2=α1σp2σα2σp1σ\frac{x_1}{x_2} = \frac{\alpha_1^\sigma p_2^\sigma}{\alpha_2^\sigma p_1^\sigma}x2x1=α2σp1σα1σp2σ
CES relative wage
w1=w2α2α1(al111−σσl21σal121−σσl11σ)w_1 = w_2 \frac{\alpha_2}{\alpha_1}\left(\frac{a_{l_1}^{1^{\frac{1-\sigma}{\sigma}}}l^{2^{\frac{1}{\sigma}}}}{a_{l_1}^{2^{\frac{1-\sigma}{\sigma}}}l^{1^{\frac{1}{\sigma}}}}\right)w1=w2α1α2(al12σ1−σl1σ1al11σ1−σl2σ1)
Import tariffs assumptions
setting: partial equilibrium single import good small country assumptions domestic supply curve has upward slope domestic firms still serve domestic markets
optimal tariff (large country influences world price)
t∗pw=121−αα1∣εd∣+∣εs∣\frac{t*}{p^w} = \frac{1}{2}\frac{1-\alpha}{\alpha}\frac{1}{|\varepsilon^d|+ |\varepsilon^s|}pwt∗=21α1−α∣εd∣+∣εs∣1 with εd=\varepsilon^d = εd= demand elasticity and εs\varepsilon^sεs === supply elasticity
Export subsidies (ES) assumption under perfect competition
small or large country partial equilibrium single export good
Export subsidies assumptions under non perfect competition (ESN)
2 firms (monopolies) compete in 3rd market choose production volume for good that is exported to 3rd marked export subsidies government choose level of export subsidies
Unilateral subsidies (US) demand
p(Q)=a−bQ=a−b(q+q∗)p(Q) = a-bQ = a-b(q+q^*) p(Q)=a−bQ=a−b(q+q∗) with Q=q+q∗Q = q+ q^*Q=q+q∗
US home firm profit
π=pq−C(q)+sq=(a−b(q+q∗))q−C(q)+sq\pi = pq-C(q)+sq = (a-b(q+q^*))q- C(q) + sqπ=pq−C(q)+sq=(a−b(q+q∗))q−C(q)+sq
US foreign firm profit
π∗=pq∗−C(q∗)=(a−b(q+q∗))q∗−C(q∗)\pi^* = pq^* - C(q^*) = (a-b(q+q^*))q^* - C(q^*)π∗=pq∗−C(q∗)=(a−b(q+q∗))q∗−C(q∗)
US Reaction functions
q=a−c−bq∗+s2bq = \frac{a-c-bq^*+s}{2b}q=2ba−c−bq∗+s q∗=a−c∗−bq2bq^* = \frac{a-c^*-bq}{2b}q∗=2ba−c∗−bq
US quantities in equilibrium
q=a+c∗−2c+2s3bq = \frac{a+c^*-2c+2s}{3b}q=3ba+c∗−2c+2s q∗=a+c−2c∗−s3bq^* = \frac{a+c-2c^*-s}{3b}q∗=3ba+c−2c∗−s
US after-subsidy profits in equilibrium
π=(a+c∗−2c+2s)29b\pi = \frac{(a+c^*-2c+2s)^2}{9b}π=9b(a+c∗−2c+2s)2 π∗=(a+c−2c∗−s)29b\pi^* = \frac{(a+c-2c^*-s)^2}{9b}π∗=9b(a+c−2c∗−s)2
US Welfare effects in equilibrium for home country
Two cases: 0:"> s>0:s>0:s>0: W=π−sq=(a+c∗−2c+2s)(a+c∗−2c−s)9bW = \pi - sq = \frac{(a+c^*-2c+2s)(a+c^*-2c-s)}{9b}W=π−sq=9b(a+c∗−2c+2s)(a+c∗−2c−s) s=0:s = 0:s=0: W=π=(a+c∗−2c+2s)29bW = \pi = \frac{(a+c^*-2c+2s)^2}{9b}W=π=9b(a+c∗−2c+2s)2
US optimal unilateral subsidy
0"> su=a+c∗−2c4>0s^u = \frac{a+c^*-2c}{4}>0su=4a+c∗−2c>0
Bilateral subsidies (BS) profits
π=(a−b(q+q∗))q−C(q)+sq\pi = (a-b(q+q^*))q-C(q)+sqπ=(a−b(q+q∗))q−C(q)+sq π=(a−b(q+q∗))q∗−C(q∗)+s∗q∗\pi = (a-b(q+q^*))q^*-C(q^*)+s^*q^*π=(a−b(q+q∗))q∗−C(q∗)+s∗q∗
BS reaction functions
q=a−bq∗−c+s2bq = \frac{a-bq^* -c+s}{2b}q=2ba−bq∗−c+s q∗=a−bq−c+s∗2bq^* = \frac{a-bq-c+s^*}{2b}q∗=2ba−bq−c+s∗
BS output levels in equilibrium
q=a−2c+c∗+2s−s∗3bq = \frac{a-2c+c^*+2s-s*}{3b}q=3ba−2c+c∗+2s−s∗ q∗=a−2c∗+c+2s∗−s3bq* = \frac{a-2c^*+c+2s^*-s}{3b}q∗=3ba−2c∗+c+2s∗−s
BS max profit levels
π=(a−2c+c∗+2s−s∗)29b\pi = \frac{(a-2c+c^*+2s-s^*)^2}{9b}π=9b(a−2c+c∗+2s−s∗)2 π∗=(a−2c∗+c+2s∗−s)29b\pi^* = \frac{(a-2c^*+c+2s^*-s)^2}{9b}π∗=9b(a−2c∗+c+2s∗−s)2
BS Welfare functions
W=π−sq=(a+c∗−2c+2s−s∗)(a+c∗−2c−(s+s∗))9bW = \pi - sq = \frac{(a+c^*-2c+2s-s^*)(a+c^*-2c-(s+s^*))}{9b}W=π−sq=9b(a+c∗−2c+2s−s∗)(a+c∗−2c−(s+s∗)) W∗=π∗−s∗q∗=(a+c−2c∗+2s∗−s)(a+c−2c∗−(s∗+s))9bW^* = \pi^* - s^* q^* = \frac{(a+c-2c^*+2s^*-s)(a+c-2c^*-(s^*+s))}{9b}W∗=π∗−s∗q∗=9b(a+c−2c∗+2s∗−s)(a+c−2c∗−(s∗+s))
BS Welfare maximising subsidies
sB=a−3c+2c∗5s^B = \frac{a-3c+2c^*}{5}sB=5a−3c+2c∗ s∗B=a−3c∗+2c5s^{*^B} = \frac{a-3c^*+2c}{5} s∗B=5a−3c∗+2c
BS equilibrium welfare levels
WB=2(a−3c+2c∗)225bW^B = \frac{2(a-3c+2c^*)^2}{25b}WB=25b2(a−3c+2c∗)2 W∗B=2(a−3c∗+2c)225bW^{*^B} = \frac{2(a-3c^*+2c)^2}{25b}W∗B=25b2(a−3c∗+2c)2
What are the assumptions for the Heckscher- ohlin model
2 factors: labour and capital, fully mobile across sectors but not countries 2 industries: one is capital intensive, one labour intensive standard production function(constant returns to scale, positive but decreasing marginal products) both countries have the same preferences both countries have the same production technologies countries differ in relative factor endowments
Explain the capital-labour ratio and the wage-rental ratio in the heckscher- ohlin model. What is the link between the two?
wage-rental ratio: wr\frac{w}{r}rw Capital-labour ratio: kili\frac{k_i}{l_i}liki an increase in the wage- rental ratio induces an increase in the capital - labour ratio.
What are the patterns/implications of free trade in the Heckscher- ohlin- model?
relative world price in between the relative prices of both countries holds if factor endowments do not differ too much (whatever "too much " is in this case) specialisation according to comparative advantages, however, no complete specialisation Both countries gain from trade
What are the effects of free trade on the income distribution in the heckscher-ohlin model? Who are the winners and loosers from trade?
In the country with advantage in the labour intensive industry, workers are the winners and capital owners the losers of trade. In the country with advantage in the labour intensive industy , the opposite is the case.
Which conditions for factor and goods prices are there in the heckscher-ohlin-model?
Total labour mobility across sectors: r1=r2=rr_1 = r_2 =rr1=r2=r and w2=w1=ww_2 = w_1 =ww2=w1=w Relationship between goods and factor prices: p1=a1,l(w,r)w+a1,kk(w,r)rp_1 = a_{1,l} (w,r)w + a_{1,k} k(w,r)rp1=a1,l(w,r)w+a1,kk(w,r)r p2=a2,l(w,r)w+a2,kk(w,r)rp_2 = a_{2,l} (w,r)w + a_{2,k} k(w,r)rp2=a2,l(w,r)w+a2,kk(w,r)r There is a bijective relationship between relative goods prices and relative factor prices. Changes in factor prices have a stronger effect in the industry which uses mo…
Rybcynski Theorem
Assuming fixed factor and goods prices the following holds: An increase in the endowment of one factor will increase the output of the industry which uses this factor intensively and lower the output of the other industry.
Specific factor endowments and trade (SFET) model
1 mobile factor (labour) 1 specifi (immobile) factor (capital)
SFET Cobb-Douglas production function
xi=φikiγili1−γix_i = \varphi_i k_i^{\gamma_i} l_i^{1-\gamma_i}xi=φikiγili1−γi with γi∈(0,1)\gamma_i \in (0,1)γi∈(0,1)
SFET CES production function
xi=φi(γkikiΦ+γliliΦ)1Φx_i = \varphi_i\left(\gamma_{k_i}k_i^{\Phi}+\gamma_{l_i}l_i^{\Phi}\right)^{\frac{1}{\Phi}}xi=φi(γkikiΦ+γliliΦ)Φ1 with γki+γli=1\gamma_{k_i}+ \gamma_{l_i}=1γki+γli=1
Monopolistic competition (MC) assumptions
CES preferences on a continuum of product varieties number of workers and production technology fixed wage rate is given one industry
MC without competition demand and inverse demand
q=α−βbq = \alpha - \beta bq=α−βb p=αβ−1βq=a−bqp = \frac{\alpha}{\beta}- \frac{1}{\beta}q = a-bqp=βα−β1q=a−bq
MC without competition revenue
r=pq=(a−bq)q=aq−bq2r = pq = (a-bq)q = aq-bq^2r=pq=(a−bq)q=aq−bq2
MC without competition demand and price (profit maximising)
qm=a−c2bq^m = \frac{a-c}{2b}qm=2ba−c pm=a−bqm=a+c2p^m = a-bq^m = \frac{a+c}{2}pm=a−bqm=2a+c
MC with iso-elastic demand and inverse demand
q=A−εq = A^{-\varepsilon}q=A−ε p=A1εq1−1εp = A^{\frac{1}{\varepsilon}}q^{1-\frac{1}{\varepsilon}}p=Aε1q1−ε1
MC with iso-elastic demand and price (profit maximising)
qm=(1−1ε)εAc−εq^m = \left(1-\frac{1}{\varepsilon}\right)^{\varepsilon}A c^{-\varepsilon}qm=(1−ε1)εAc−ε pm=c(εε−1)p^m = c\left(\frac{\varepsilon}{\varepsilon-1}\right)pm=c(ε−1ε)
MC labour demand
l(i)=σfl(i) = \sigma fl(i)=σf
MC FE condition
h=n⋅l(i)=nfσh = n \cdot l(i) = nf\sigmah=n⋅l(i)=nfσ
MC price and price index
p=(σσ−1)1φwp = \left(\frac{\sigma}{\sigma-1}\right)\frac{1}{\varphi}wp=(σ−1σ)φ1w P=pn11−σP = pn^{\frac{1}{1-\sigma}}P=pn1−σ1
MC real product wage
wp=(σ−1σ)φ\frac{w}{p} = \left(\frac{\sigma-1}{\sigma}\right)\varphipw=(σσ−1)φ
MC firm size
q=f(σ−1)φq = f(\sigma-1)\varphiq=f(σ−1)φ
MC number of firms
n=hfσn = \frac{h}{f\sigma}n=fσh
MC real wage
wP=(σ−1σ)φ(hfσ)1σ−1\frac{w}{P} = \left(\frac{\sigma-1}{\sigma}\right)\varphi \left(\frac{h}{f\sigma}\right)^{\frac{1}{\sigma-1}}Pw=(σσ−1)φ(fσh)σ−11