Homework 5 Solution (pdf)

* −σyy(p / p)τAnd so, c h = and c f =* * 1 σL + L (( p / p)τ )−1−σ* * 1−σLτ+ L ( p / p)Substituting these into the market-clearing condition yields* 1−σy* y(p / p)τy = L+ L.* * 1−σ1−σ* * 1−σL + L (( p / p)τ ) Lτ+ L ( p / p)And simplifying1 x(1) 1 = +,1−σ 1−σ1+lrx 1/ l + x / r*where x = p / p , = 1−σ*r τ < 1, and l = L / L > 1 .Clearly, (D+D * )/y (the RHS of (1)) is increasing in*x = p / p . And evaluating the total*demand for each home variety at x = p / p = 1 shows that it falls short of supply.y 1 1 1/ l + 1/ r + 1+lr( + ) = yy1+ lr 1/ l + 1/ r 1/ l + 1/r + r + l< .*Therefore, in trade equilibrium we must have x = p / p > 1. Of course, the same is true*for w / w .c) Derive a version of the gravity equation in this monopolistic competition model withtransportation cost. Make sure that one of the terms in the equation is the product ofGDPs of each country. Discuss. How does τ affect trade?* *** −σ* L w f L GDP [ α(σ −1)/β ]( p / p)τ p LwVT = 2 D pNτ= 2 c p τ =( ) τ** 1−σ* * 1−σw ασ w Lτ+ L ( p / p)w ασ=p σ −11w σβ Lτ1(1/ p)τ*+ L ( p*−σ*2GDP×GDP*−σ* 1−σ/ p)p( )w1−σ2 * τ1= GDP×GDP( )1−σ* *L L ( p / p)1 −στ +wNormalize w ≡1 (we can do that but just for one country):*GDP × GDPVT = 2.* 1L + L ( x / τ )−σ*d) Determine d ( p / p)/ dτ when τ = 1. Discuss.1 x1 = +1−σ 1−σ1+lrx 1/ l + x / rImplicitly differentiating (1) yields2 2 2dxl /(1 + l)− l /(1 + l)= −dr12 1/ l + 1−(1 −σ)r=(1 −σ) l /(1 + l)−2(1/ l + 1)l(1− l)1−l= −= < 0 ,2(1 −σ) l − l − l σ σ (1 + l)and