Monopolistic Pricing in the Banking Industry: a Dynamic Model



βt {Ptq +(1 - q)(ωt - z) - u - α [(1 - q)2Dt - (1 - q)Ft + (1 - q)NW] +

1  ^ɪ  q) { - ωt + α [(1 - q)Dt - Ft + NW]

+ υt + z} +


+ γYK~Ett'{ - ωt+1 + α [(1 - q)Dt+1 - Ft+ NW] + υt+` + z}} = 0.

(63)


Rearranging and dividing everything by βt we obtain a difference equation for Ft and Dt. Since
Xt = Et [Xt] we can include everything under the expectation, from which we will from now on
omit the time index, since all expectations are at time
t.

E^γβαFt= αFt + ^γβ(1 - q)αDt+` - α(1 - q)Dt + [β^γα - α] NW +

+κ [ρtq + (1 - q)(ωt - z) - u] + [1 - к(1 - q)][ωt - υ - z] - γγβ[ωt+` - Ut+` - z] [.    (64)

The next step is to simplify the resulting expression and to substitute for the value of Dt in
Equation (64), the expression of the dynamic constraint that is obtained from Equation (58).

EyγβαFt+ι = αFt + γγβ(1 - q)α [ɪ - (^γ- q)^ Dt - ɪ - ʃ- q)^ Ft + ` +

+ 1 - (Г- q)кNW + gTX(1 g-"q+1 ] - α(1 - q)Dt + (βγγα - α)NW +

+κ [ρtq + (1 - q)(ωt - z) - u] + [1 - κ(1 - q)][ωt - Ut - z] - γγβ[ωt+` - Ut+` - z] ∣,    (65)

and

E{^γβ I - (α- ,)κFt + ' = αF + ^γβ: 1 - q)α{ I - (β q)κ D +

+1 - β- q)кNW + gβ--1 g-"O' } - α( 1 - q)Dt + <β^γα - α>NW +

+κ [Ptq + (1 - q)Ut - u] + (^γβ - L)[Ut + ` - ωt+`] + (β^^γ - 1)z.          (66)

Dividing both sides of the former equation for α, and introducing the lag operator L, we obtain:

+E { 1 - (1 - q )κ

I   ^γ βα


As before we end up
constraint:


Dt =


^γ


E [ Ft+'] = 1   (1   q )K Ft +

^γ β

+ β^γ + (1 - q ) к
^γ β


{κ [ Ptq + (1 - q ) Ut


with a


1 - к (1 - q )


Dt-1


(1 - q) [^γβ - [1 - (1 - q)κ]]


^γ β


Dt +


1NW + (1 - q )[ g 3 rD - g 4 rB ] +


u] + (^γβ - L) [Ut+' - ωt+'] + (β^γ - 1)zj.


(67)


system of two equations, the other is obtained from the dynamic


--κ----Ft +--K----NW +

1 - к (1 - q )      1 - к (1 - q )


g3 rD


g4rtB


1 - к (1 - q )


= 0.


(68)


We can simplify the value of the second intercept term as:

Zt+1 = к [ptq + (1 - q)Ut - u] + (^γβ - L) υt + ` - ωt +`] + (β^γ - 1)z =

(^γβ - l) [rB+' - rD+' - a - brB+' +  . - cf] + к [(rR - rD)q + (1 - q)(rB - rD) - u] +

+ ( β^γ - 1)z = { ^γβ (1 - b ) + [(1 - q )к - (1 - b )] L} rB+' +

-(γγβ - l)et+' + к [t - rD - u] + (β^γ - 1) (z - b) (69)

23



More intriguing information

1. The Variable-Rate Decision for Multiple Inputs with Multiple Management Zones
2. Stable Distributions
3. Business Cycle Dynamics of a New Keynesian Overlapping Generations Model with Progressive Income Taxation
4. Output Effects of Agri-environmental Programs of the EU
5. The bank lending channel of monetary policy: identification and estimation using Portuguese micro bank data
6. Migration and Technological Change in Rural Households: Complements or Substitutes?
7. THE CO-EVOLUTION OF MATTER AND CONSCIOUSNESS1
8. A Classical Probabilistic Computer Model of Consciousness
9. Reconsidering the value of pupil attitudes to studying post-16: a caution for Paul Croll
10. Chebyshev polynomial approximation to approximate partial differential equations
11. Midwest prospects and the new economy
12. The name is absent
13. Searching Threshold Inflation for India
14. The Veblen-Gerschenkron Effect of FDI in Mezzogiorno and East Germany
15. Incorporating global skills within UK higher education of engineers
16. The Modified- Classroom ObservationScheduletoMeasureIntenticnaCommunication( M-COSMIC): EvaluationofReliabilityandValidity
17. ESTIMATION OF EFFICIENT REGRESSION MODELS FOR APPLIED AGRICULTURAL ECONOMICS RESEARCH
18. Tourism in Rural Areas and Regional Development Planning
19. INTERPERSONAL RELATIONS AND GROUP PROCESSES
20. The name is absent