Bargaining Power and Equilibrium Consumption



Proposition 1 Suppose that the household’s budget constraint is never binding. If
0 < α < α* < 1, then one of the following two assertions holds:

(i) Uι(xh(α)) = Uι(xh(α*)), U2(xh(αt)) = U2(xh(α*)).

(ii) Uι(xh('ɪ)) < U√x√α*)), U2(x√αt)) > U2(x√α*)).

The proof of Proposition 1 is given in the appendix. We next examine the case
when the budget constraint is binding.

3.3 Binding Budget Constraint

If the budget constraint is binding for household h, then (9) still holds true whereas

(6) becomes


∂F        ∂F

∂U1 ∙ DXiU1 + ∂U2 ∙ DXiU2 = ʌ (α )p (α ) ,

(11)


with positive Lagrange multiplier λ(α). Moreover, with binding budget constraints,

p(α) [x 1(α) + x2(α) - ωh,] = 0,

hence

p(α) [x01(α) + x02(α)] = -p0(α) [x1(α) + x2(α) - ωh] .               (12)

Substituting (11) and (12) into (9) yields

∂F

Φ 0 ( α ) = ⅛-


- λ(α)p0(α)[x1 (α) + x2(α) - ωh].


(13)


Without further qualification, it is impossible to sign Φ0(α). Under additional assump-
tions, however, one can gain some detailed insights. To this end, let us decompose the
effects of a change of consumer 1’s relative bargaining power from
α to α + e into two
parts:

1. a pure bargaining effect when α is changed to α + e whereas the price system
stays at
p(α);

2. a price effect when relative bargaining power remains constant at α + e while
the price system adjusts from
p(α) to p(α + e).3

3 Of course, the price effect could be further decomposed into a substitution and an income effect.
But that is immaterial to our analysis.

12



More intriguing information

1. Three Policies to Improve Productivity Growth in Canada
2. Assessing Economic Complexity with Input-Output Based Measures
3. The name is absent
4. The magnitude and Cyclical Behavior of Financial Market Frictions
5. Brauchen wir ein Konjunkturprogramm?: Kommentar
6. Improvement of Access to Data Sets from the Official Statistics
7. The name is absent
8. The name is absent
9. New Evidence on the Puzzles. Results from Agnostic Identification on Monetary Policy and Exchange Rates.
10. THE DIGITAL DIVIDE: COMPUTER USE, BASIC SKILLS AND EMPLOYMENT