... likely-looking equation involving prices and in-
come on the right-hand side and commodity quantities on the left-hand side and
expect it to b e a valid demand function. To see why, note two things:
12
Draw ... AND THE MARKET
2. In a market of a thousand consumers the demand curve for the commodity
is given by
p = A bq
where q is total quantity demanded and A and b are positive...
... results on the …rm’s demand and supply functions and
the consumer’s demand functions.
18
Prove this law, using the facts that (a) for each household income equals expenditure,
and that (b) each household’s ... R
5
sketch the attainable set for commodities 1 and 2.
5 .8. READING NOTES 117
the household – to the analysis of labour supply and of the demand for loans
and the suppl...
... y
blue
) = (y + r
0
; y + r
) (8. 13)
186 CHAPTER 8. UNCERTAINTY AND RISK
Figure 8. 8: Indepe nd enc e axiom: illustration
Axiom 8. 3 (Revealed Likelihood) Let x
and x be two payo¤s such that
under ... small risks and risk-averse for large risks.
8. 5. LOTTERIES AND PREFERENCES 199
Figure 8. 18: The probability diagram: # = 3
7 .8 and B.21) The $ = 3 case can be seen...
... Boadway
and Bruce (1 984 ). On the “constitution” approach see Arrow (1951), Black
(19 58) and the excellent paper by Vickrey (1960) ; for the basis of Theorem 9.2
see Black (19 48) .
The standard ... Table 10.4, if Alf takes
b
as given and
chooses probability
a
his expected utility is
8
3
b
1
a
+ 1
b
; (10 .8)
8
Use Table 10.4 to derive (10 .8) and (10.9) .
......
... classic contributions whose logic underlies so much
modern work are to be found in Bertrand ( 188 3), Cournot ( 183 8) and von
Stackelberg (1934).
10.10 Exercises
10.1 Table 10.10 is the strategic form ... page 84 ]
18
Take the labour-monopsony example of notes 7 .and 8
(a) Show how the optimal labour contract is deter mined by using an analogy to Figure
11.7.
(b) What is the analogy...
... (12. 28) is as follows. Each agent h is
required to pay:
23
P
h
p
1
; p
2
; :::
=
8
>
>
<
>
>
:
z
h
if = 1 and h is not pivotal
z
h
h
if = 1 and h is pivotal
0 if = 0 and ... complements the market analysis of previous chapters.
12.6. DESIGN: APPLICATIONS 413
Figure 12 .8: Two types of Agent: Full-information solution
able workers with talent
a
and t...