RDP 2015-11: Unprecedented Changes in the Terms of Trade: Online Appendix 3 Normalised Equilibrium Conditions

We normalise the variables as follows:

Households

1. 
2. 
3. 
4. 
5. 
6. λ_t = Λ_tZ_t
7. 
8. 
9. 
10. 
11. 
12. 
13. 
14. 
15. 
16. 
17. 
18. 
19. υ_t = V_t(1 + z_I)^t

Non-tradeable Firms

20. 
21. 
22. 
23. 
24. 
25. mc_N,t = MC_N,t
26. 
27. q_N,t = Q_N,t

Home-tradeable Firms

28. 
29. 
30. 
31. 
32. 
33. 
34. mc_H,t = MC_H,t
35. 
36. 
37. q_H,t = Q_H,t

Commodity Firms

38. 
39. 
40. 
41. 
42. 
43. q_X,t = Q_X,t

Relative Prices

44. τ_I,t = T_I,t(1 + z_I)^t
45. τ_N,t = T_N,t(1 + z_N)^t
46. τ_T,t = T_T,t(1 + z_T)^t
47. τ_H,t = T_H,t(1 + z_H)^t
48. τ_F,t = T_F,t(1 + z*)^t
49. τ_F*,t = T_F*,t(1 + z*)^t
50. 

Foreign Economy

51. 

Miscellaneous Variables

52. 

The Cobb-Douglas assumption for the tradeable consumption bundle implies that the growth rate of the tradeable consumption bundle is 1 + z_T = (1 + z_H)^γH(1 + z*)^γF. A similar relationship holds for the tradeable investment good. where it is implied by the bundles that:

and

and

UIP implies that that s staisfies

and if there is a steady state for τ_I,t then it follows that

Also, note that z_t = Z_t/Z_t−1. With these normalisations, the equilibrium conditions are as follows.

Household optimisation:

and

Capital accumulation:

Price and inflation indices:

Consumer demand:

Investment demand:

Production:

Tradeable firms:

Non-tradeable firms:

Commodity firms:

Importing firms

Law of one price:

Relative Prices:

Foreign sector:

Market clearing:

Interest rates and monetary policy: