# Birgit Grodal's research while affiliated with University of Copenhagen and other places

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## Publications (26)

We consider economies with incomplete markets, one good per state, two periods, t=0, 1, private ownership of initial endowments, a single firm, and no assets other than shares in this firm. In Dierker, Dierker, Grodal (2002), we give an example of such an economy in which all market equilibria are constrained inefficient. In this paper, we weaken t...

Fifty years ago Arrow [1] introduced contingent commodities and Debreu [4] observed that this reinterpretation of a commodity was enough to apply the existing general equilibrium theory to uncertainty and time. This interpretation of general equilibrium theory is the Arrow-Debreu model. The complete market predicted by this theory is clearly unreal...

We consider economies with incomplete markets, one good per state, two periods, t=0,1, private ownership of initial endowments, a single firm, and no assets other than shares in this firm. In Dierker, Dierker, Grodal (2002), we give an example of such an economy in which all market equilibria are constrained inefficient. In this paper, we weaken th...

We use the two-factor, two-sector, two-country model of Melvin and Warne (1973) and Markusen (1981), in which the production of one good is monopolized in each country, in order to investigate the role of the price normalization. We illustrate several puzzling effects that occur if the price normalization is changed. However, we show that Markusen´...

Fifty years ago Arrow [1] introduced contingent commodities and Debreu [4] observed that this reinterpretation of a commodity was enough to apply the existing general equilibrium theory to uncertainty and time. This interpretation of general equilibrium theory is the Arrow-Debreu model. The complete market predicted by this theory is clearly unreal...

We consider economies with incomplete markets, production, and a given distribution of initial endowments. The main purpose of the paper is to present a robust example of an economy with only one firm and one good per state in which no production decision entails a constrained efficient outcome. In particular, the unique Dreze equilibrium is domina...

Given falling birth rates, ageing baby boomers approaching retirement age as well as a pension crisis in most advanced economies, understanding the characteristics of the labour supply function of the elderly have taken on a new significance. Even in developing countries, with labour surplus economies, this is a major issue as these poor countries...

This paper builds a general equilibrium model of finite economies with exchange and club formation. Agents trade multiple private goods widely in the market, can belong to several clubs, and care about the characteristics of other club members. Because club memberships are indivisible and choices of club memberships must be coordinated across the p...

We consider economies with incomplete markets, one good per state, private ownership of initial endowments, a single firm, and no assets other than shares in this firm. In this simple framework, arbitrarily small income effects can render every market equilibrium resulting from some production decision constrained inefficient. Thus, even if all uti...

We consider a firm acting strategically on behalf of its shareholder. The price normalization problem arising in general equilibrium models of imperfect competition can be overcome by using the concept of real wealth maximization. This concept is based on shareholders´ aggregate demand and does not involve nay utility comparisons. We explore the ef...

We present a theory of production that begins with an exogenously specified set of technologies, accessible to each potential firm. The technologies used in equilibrium are endogenous. Labor skills are differentiated, and the labor skills are acquired endogenously by workers, possibly by bearing private costs, and possibly by attending school. A te...

We consider a pure exchange economy with private ownership in which consumers have interdependent preferences. Hence, consumers’ preferences are defined on the states of the economy. In a Walras equilibrium for such an economy, it may, of course, be possible for two or more consumers to simultaneously change their net trades and thereby obtain a pr...

We consider a simple model of a firm acting strategically on behalf of its shareholders. The price normalization problem arising in general equilibrium models of imperfect competition is overcome by using the concept of real wealth maximization. This concept is based on shareholders' aggregate demand and does not involve any comparison of utility p...

General equilibrium models of oligopolistic competition give rise to relative prices only without determining the price level. It is well known that the choice of a numÊraire or, more generally, of a normalization rule converting relative prices into absolute prices entails drastic consequences for the resulting set of Nash equilibria when firms ar...

This paper defines a general equilibrium model with exchange and club formation. Agents trade multiple private goods widely in the market, can belong to several clubs, and care about the characteristics of the other members of their clubs. The space of agents is a continuum, but clubs are finite. It is shown that (i) competitive equilibria exist, a...

This paper provides an extension of general equilibrium theory that incorporates the actions of individuals both as demanders and suppliers of goods and as members of firms, schools, social groups, and contractual relationships. The central notion of the paper is a group: a collection of individuals associated with one another for some purpose. The...

This paper defines a general equilibrium model with exchange and club formation. Agents trade multiple private goods widely in the market, can belong to several clubs, and care about the characteristics of the other members of their clubs. The space of agents is a continuum, but clubs are finite. It is shown that (i) competitive equilibria exist, a...

General equilibrium theory constitutes a sound basis for the discussion of policy issues if firms do not have market power. However, if firms influence prices strategically, the concept of profits loses its meaning due to the price normalization problem. Hence, it is unclear how to model the behavior of oligopolistic firms. In order to provide a co...

This paper defines a general equilibrium model with exchange and club formation. Agents trade multiple private goods widely in the market, can belong to several clubs, and care about the characteristics of the other members of thei r clubs. The space of agents and the number of possible club types are finite. It is shown that (i) approximate compet...

We consider oligopolistic markets in which the notion of shareholders' utility is well-defined and compare the Bertrand-Nash equilibria in case of utility maximization with those under the usual profit maximization hypothesis. Our main result states that profit maximization leads to less price competition than utility maximization. Since profit max...

In most economic literature, firms are assumed to maximize profits. If there is perfect competition and a complete market structure in the economy, this objective of firms has a sound economic interpretation. Profit maximization is well defined, it serves the needs of the shareholders, and shareholders unanimously instruct the managers of firms to...

General equilibrium models of oligopolistic competition give rise to relative prices only without determining the price level. It is well known that the choice of a numéraire or, more generally, of a normalization rule converting relative prices into absolute prices entails drastic consequences for the Nash equilibria. In this paper we show that, g...

## Citations

... Profit maximization as the objective for firms has at least two drawbacks as explained in Grodal (1996). It is typically not in the interest of shareholders, and it depends on price normalization. ...

... 8 The notion of minimal constrained efficiency was first introduced (to the best of my knowledge) by Dierker, Dierker and Grodal in [7] planner who can choose the production plan and redistribute consumption at date 0, but has to use the markets to purchase the date-1 consumption for every investor. The formal definition of this efficiency concept follows. ...

... Dierker and Grodal (1986) show that the latter nonexistence problem even occurs in the mixed extension of the Cournot game. ...

... Without the convexity assumption, Aumann (1966) shows the existence in a continuum economy, while Starr (1969) shows the existence of an approximate equilibrium in a large finite economy. 13 Especially close to our study are models with clubs, most notably Ellickson, Grodal, Scotchmer, andZame (1999, 2001). 14 Similar to our study, these papers consider both large finite and continuum economies and show the existence of (approximate) equilibria using Kakutani's fixed point theorem. ...

Reference: Stable Matching in Large Economies *

... It is easy to see that the social planner's optimal admission policy should take the following form: admit a candidate if and only if his quality is at least v . Since every member of the club is admitted by such a policy, the club's expected value per period per capita is (2n + 1)E[vjv v ]. 6 To calculate the expected search cost in each period, note that the probability that a candidate is admitted is x = 1 F (v ). Hence the expected delay in each period is ...

... In contrast to those that propose that profit maximization is a wrong concept (Drucker 1974;Li 1964), there are those who argue that executives and their corporations must seek profit maximization (Koplin 1963;Milton 1970). On the other hand, there are those who are either driven by secular (e.g., Sibley 2009;Dierker and Grodal 1996) or religious (e.g., Karns 2008) motives who postulate that excessive profit is not only undesirable, but also inconsistent with optimally serving a society. ...

Reference: Islamic Perspectives on Profit Maximization

... while Grossman and Hart's (1979) is GH y (y) = y 0 + i∈I δ i MRS i ( y) y 1 . 10 The notion of minimal constrained efficiency was first introduced (to the best of my knowledge) by Dierker et al. (2005). that the equilibrium allocations cannot be improved upon by a social planner who can choose the production plan and redistribute consumption at date 0, after using the markets to purchase date-1 consumption for every investor. ...

... In Grodal (1996) it is shown that for all efficient production plans there are price normalizations such that these production plans are Cournot-Walras equilibria where firms maximize profits. In Bejan (2008), Dierker and Dierker (2006) and Dierker and Grodal (1999) alternative objectives are suggested and studied. The common idea behind these suggestions is to compare aggregate demands of shareholders at different production plans and associated prices. ...

... But in an imperfect market, the choice of normalization rule a¤ects the relative prices when …rms can act strategically. (See, for instance, Gabszewicz and Vial, 1972;Roberts and Sonnenschein, 1977;Böhm, 1994;Kemp and Okawa, 1995;Dierker and Grodal, 1999;Dierker et al., 2003:) Böhm (1994 argues that whether partial or general equilibrium model should be scrutinized with respect to the normalization issue. Once a di¤erent normalization rule is considered, numerous traditional results in general equilibrium imperfect competition models are called into question. ...

... For a discussion of this assumption see [15], and within the context of social preferences [24]. 9 On the problem of the firm's objective within an oligopolistic framework, see [8] . one can also justify profit maximization by assuming that due to the complexity of the problem owners ignore the impact of the firms' profits on the wealth profile, and hence are only interested in profit maximization. ...