Stock Market Valuation in a Dynamic
Monopolistically Competitive
Economy
Gabriel Talmain
University of Glasgow
Università degli Studi di Bari, 15 May 2008, 15 May 2008
Motivation
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Stock market rises with no corresponding change on
the productivity side,
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Nikkei early 90’s,
US stock market 1998-2000.
Talk about “new economy”:
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future gains in productivity justify immediate increase in the
valuation of firms.
It is clear that “good news” for a corporation makes its
shares go up well before its profits increase.
Is this possible also at the aggregate level?
Università degli Studi di Bari, 15 May 2008
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Two main approaches to valuation of the stock market:
the Lucas asset pricing model and the one based on
Tobin's q.
In Lucas asset pricing model, the fruit tree paradigm,
e.g. Aiyagari and Gertler (RED 1999) or Greenwood
and Jovanovic (AER 1999) or Hobjin and Jovanovic
(AER 2001), the stream of earnings on the asset is
exogenous.
In Tobin's q approach, e.g. Gilchrist and Leahy (JME
2002) or Danthine and Donaldson (RES 2002), the
value of a firm is the present value of its installed
capital.
Università degli Studi di Bari, 15 May 2008
Comparison
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Tobin's q approach allows for aggregate
economic conditions, such as the strength of the
aggregate demand and the cost of the factors of
production, to feed back in the earnings of the
individual firm.
The fruit tree model captures the flavour of
intangible assets which bear fruits beyond the
corporation' investment in machinery, bricks and
mortar.
Università degli Studi di Bari, 15 May 2008
Capturing both aspects
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One would really want a model which includes the general equilibrium
features of the Tobin's q approach, and which can spell out how each firm's
competitiveness (the fruit bearing quality of the tree) translates into valuation.
This paper will concentrate on a firm's monopoly position as the source of its
market value.
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If a firm's monopoly profits were independent of all other variables in the
economy, our model would reduce to the Lucas asset pricing model.
By letting general equilibrium determine these profits, our model also captures the
feed-back from the aggregate economy onto the individual firm, one of the nice
features of Tobin's q theory.
In addition, our model will feature heterogeneous and non-symmetric firms and
we can derive a closed form solution for its equilibrium.
The heterogeneity will enable us to contrast the effect on the stock market of an
anticipated increase of productivity at the aggregate level vs at the individual or
sectorial level.
Università degli Studi di Bari, 15 May 2008
differentiated input
firms
M.C.
Final good industry
P.C.
Firm 1
Ct
kn,t,ln, t
Kt
Firm n
qn,t
CES
aggregation
Yt
Kt+1
L
Firm N
regulated by wt, it
generates n, t
Università degli Studi di Bari, 15 May 2008
All income returns to HH
as wage, rental or profits;
asset markets open
Assumptions
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Intermediate input firms (IIF)
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heterogeneous,
monopolistic competitive on their supply market: the final good industry,
compete on the labour and physical capital markets,
distribute all profits as dividends (Modigliani-Miller environment),
shares traded on the stock market.
Households
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homogenous,
supply labour inelastically to IIF,
expected utility maximisers,
CRAA felicity function, one argument: consumption of final good,
own all physical capital, rent it out to IIF,
own and trade all the shares of stock.
Università degli Studi di Bari, 15 May 2008

Final good industry
perfectly competitive, representative firm,
 produce the final good which is used either for
immediate consumption (perishable and
homogenous commodity) or for capital in the next
period,
 100% rate of depreciation of capital.

Università degli Studi di Bari, 15 May 2008
Equilibrium being considered
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given the initial endowment of physical capital and
distribution of share across households,
a set of intertemporal prices must:
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temporary equilibrium: clear all markets in every period,
rational equilibrium: price realisations validate the households
believes,
fundamental equilibrium: the price of a stock of share
equates the value of the firm to the discounted value of the
stream of dividends (in the metric induced by the utility of
the households),
all agents are at an optimum:
Università degli Studi di Bari, 15 May 2008
households are maximising their intertemporal
utility,
 all firms, IIF and final good industry, are maximising
profits (face a static problem),
 households want to hold 100% of the stocks of
shares.
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Households’ equilibrium allocation is symmetric.
Università degli Studi di Bari, 15 May 2008
Increase in productivity and the
stock market
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instantaneous increases in productivity:
output increases,
 in this framework, factor shares remain constant,
 hence, stock market increase proportional to the
increase in productivity.
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anticipated future gains in productivity:

during 1998-2000 years, talk about a “new
economy”: stock market was supposed to be reacting
to future gains in productivity.
Università degli Studi di Bari, 15 May 2008
Anticipated future gains in
productivity
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Anticipated gains in sectorial or individual
productivity:
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the stocks of the firms expected to experience the
gains do increase in value.
Anticipated gains in aggregate productivity:
no immediate effect on the values of shares,
 at the time of the gain, shares’ value increase is
proportional to the productivity gains.

Università degli Studi di Bari, 15 May 2008
Intuition
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Aggregate profit share is a fixed proportion of the
aggregate output, same for the share of rent;
the rate of return on physical capital and on the stock
market portfolio are collinear: the interest rate is equal
to the rate of return on the stock market portfolio;
the anticipated future increase in aggregate productivity
will lift the forward interest rate for the period in
question, but by how much?
Università degli Studi di Bari, 15 May 2008
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Since the price of capital is fixed by the supply
side (equal to the price of the final good), the
forward rate of interest must leave today’s value
of physical capital unchanged;
since the aggregate stock market is an asset
collinear to physical capital, the increase in the
forward rate leaves the value of the stock market
unchanged.
Università degli Studi di Bari, 15 May 2008

Possible explanations for increase in stock
market in response to anticipated future factors:
break in our assumptions,
 this includes a bubble in stock market prices.
 The share of GDP going to monopoly profits is
anticipated to increase!

Università degli Studi di Bari, 15 May 2008