New PDF release: A Theory of International Trade under Uncertainty (Economic

By Elhanan Helpman

ISBN-10: 0123396506

ISBN-13: 9780123396501

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Additional resources for A Theory of International Trade under Uncertainty (Economic theory, econometrics, and mathematical economics)

Example text

I. 5yt−2 + ????t ii. yt = yt−2 + ????t iii. yt = 2yt−1 − yt−2 + ????t iv. 25yt−3 + ????t b. Show that each of the backward-looking solutions is not convergent. c. 5Δyt−1 + ????t . Find the particular solution for Δyt . tex V3 - 09/02/2014 12:52pm Page 45 QUESTIONS AND EXERCISES 45 d. Similarly transform the other equations into their first-difference form. Find the particular solution, if it exists, for the transformed equations. e. Write equations i through iv using lag operators. f. Given an initial condition y0 , find the solution for yt = a0 − yt−1 + ????t .

67) Again, the solution can depend only on a constant, the elements of the {????t } sequence, and t raised to the first power. As in the previous example, t does not need to be included in the challenge solution if the characteristic root differs from unity. 64). tex V3 - 09/02/2014 12:52pm Page 37 THE METHOD OF UNDETERMINED COEFFICIENTS 37 Matching coefficients of intercept terms and coefficients of terms containing t, we get b0 = a0 + a1 b0 − a1 b1 b1 = a1 b1 Again, there are two cases. If a1 ≠ 1, then b1 = 0 and b0 = a0 ∕(1 − a1 ).

A quick check shows that the discriminant d is negative so that the characteristic roots are imaginary. 949. 843. 567). 2 sets ????1 = 1 and ????2 = 0 and plots the homogeneous solution for t = 1, … , 30. 6. 89. Comparing the two graphs, you can see that increasing the value of ???? acts to increase the frequency of the oscillations. 5. Arc A0B is the boundary between Cases 1 and 3; it is the locus of points where d = a1 2 + 4a2 = 0. The region above A0B corresponds to Case 1 (since d > 0), and the region below A0B corresponds to Case 3 (since d < 0).

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A Theory of International Trade under Uncertainty (Economic theory, econometrics, and mathematical economics) by Elhanan Helpman


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