Non-negative Prices Research Articles

Room assignment-rent division: A market approach

A group of friends consider renting a house but they shall first agree on how to allocate its rooms and share the rent. We propose an auction mechanism for room assignment-rent division problems which mimics the market mechanism. Our auction mechanism is efficient, envy-free, individually-rational and it yields a non-negative price to each room whenever that is possible with envy-freeness.

Insisting on a Non-Negative Price: Oligopoly, Uncertainty, Welfare, and Multiple Equilibria

I study Cournot competition under incomplete information about demand while assuming that market price must be non-negative for all demand realizations. Although this assumption is very natural, it has only rarely been made in the earlier literature. Yet it has important economic consequences: (1) multiple (symmetric, pure strategy) equilibria can exist, despite the fact that demand and cost are linear; and (2) expected total surplus can be larger when the firms do not know demand than when they do, a result which has important implications for the social desirability of information sharing. The arguments of the paper are relevant also for price competition and for uncertainty about, e.g., cost or the number of firms, and these issues are discussed.

Insisting on a Non-Negative Price: Oligopoly, Uncertainty, Welfare, and Multiple Equilibria

I study Cournot competition under incomplete information about demand while assuming that market price must be non-negative for all demand realizations. Although this assumption is very natural, it has only rarely been made in the earlier literature. Yet it has important economic consequences: (1) multiple (symmetric, pure strategy) equilibria can exist, despite the fact that demand and cost are linear; and (2) expected total surplus can be larger when the firms do not know demand than when they do, a result which has important implications for the social desirability of information sharing. The arguments of the paper are relevant also for price competition and for uncertainty about, e.g., cost or the number of firms, and these issues are discussed.

Necessary and sufficient condition for the existence of a nonnegative equilibrium price vector in the capital market with short-selling

For the capital market satisfying standard assumptions that are widely adopted in the equilibrium analysis, a necessary and sufficient condition for the existence and uniqueness of a nonnegative equilibrium price vector that clears the mean-variance capital market with short sale allowed is derived. Moreover, the given explicit formula for the equilibrium price shows clearly the relationship between prices of assets and statistical properties of the rate of return on assets, the desired rates of return of individual investors as well as other economic quantities. The economic implication of the derived condition is briefly discussed. These results improve the available results about the equilibrium analysis of the mean-variance market.

Room Assignment-Rent Division: A Market Approach

A group of friends consider renting a house but they shall first agree on how to allocate its rooms and share the rent. We propose an auction mechanism for room assignment-rent division problems which mimics the market mechanism. Our auction mechanism is efficient, envy-free, individually-rational and it yields a non-negative price to each room whenever that is possible with envy-freeness.

Competitive Fair Division

Several indivisible goods are to be divided among two or more players, whose bids for the goods determine their prices. An equitable assignment of the goods at competitive prices is given by a fair‐division procedure, called the Gap Procedure, that ensures (1) nonnegative prices that never exceed the bid of the player receiving the good; (2) Pareto optimality, though coupled with possible envy; (3) monotonicity, such that higher bids never hurt in obtaining a good; (4) sincere bids that preclude negative utility; and (5) prices that are partially independent of the amounts bid (as in a Vickrey auction). A variety of applications are discussed.

What Is the Economic Meaning of FDH? A Reply to Thrall

In a recent issue of the Journal of Productivity Analysis, Thrall (1999) called for abandoning the Free Disposable Hull (FDH, Deprins et al. (1984)) approximation of production possibilities as economically meaningless in comparison to the Convex Monotone Hull (CMH; Banker et al. (1984)) approximation. This strong conclusion was solely based on Thrall's Principal Theorem, which essentially demonstrates that FDH can give a technically efficient classification to output-input vectors that are inefficient in terms of profit maximisation, i.e. at all non-negative price vectors there exists an alternative output-input vector that yields higher profit. In this short communication, we argue that the economic meaning of the competing empirical production sets cannot be inferred from this theorem. Specifically, we demonstrate that both empirical production sets are economically equally meaningful under the economic conditions that underlie Thrall's theorem. In addition, we demonstrate that FDH can be economically more meaningful than CMH under non-trivial alternative economic conditions.

Re-examining the Price Effects of Assumption Financing: The Case of Above-Market Interest Rates

Although previous research addresses the price effects of below-market loan assumptions in housing transactions, no evidence exists regarding the price effects of above-market loan assumptions. This study develops a hypothesis of strictly non-negative price effects in assumption financing and empirically documents a positive impact in housing transactions involving above-market loan assumptions. Based on a switching regimes regression analysis of 2594 single-family house transactions, we find evidence of a significant price premium in moderately priced homes involving above-market loan assumptions, but no evidence for a financing premium for more expensive homes. The results suggest that the source of the premium in the moderately priced home market is the assuming buyer's desire to avoid lenders' qualification criteria.

Equilibria in the capital market with non-homogeneous investors

In this paper, we derive a necessary and sufficient condition for the existence of a nonnegative equilibrium price vector in a non-homogeneous capital market consisting of investors whose measure of risk may not be the same. The eigenvalue structure of a matrix which is constructed from the investor’s initial assets and the requested rate of return play an important role in this procedure. Also we present some economic implications of these conditions. In particular, we show that if investors pursue too much return then the market becomes unstable.

Incorporating monotonicity and concavity conditions in flexible functional forms

SUMMARY Empirical economists using flexible functional forms often face the disturbing choice of drawing inferences from an approximation violating properties dictated by theory or imposing global restrictions that greatly restrict the flexibility of the functional form. Focusing on the cost function, this paper presents an alternative approach which imposes monotonicity and concavity properties only over the set of prices where inferences will be drawn. An application investigating elasticities for Bemdt-Wood data set using the translog, generalized Leontief, and symmetric generalized McFadden flexible functional forms illustrates the technique. Violations of theoretical properties pose one of the most difficult challenges faced by empirical economists. The introduction of flexible functional forms provided specifications capable of approximating many technologies and of violating monotonicity and concavity conditions implied by theory. Imposing these restrictions at all non-negative prices eliminates this problem, but with a significant loss in flexibility. This paper assesses the benefits of imposing monotonicity and concavity on cost functions over a range of prices through appropriate choice of prior distribution. The evolution of flexible functional forms approximating cost functions over the last twenty years supplies a clear indication of the importance of incorporating properties from theory into empirical analysis. Diewert's (1971) introduction of the generalized Leontief and Christensen, Jorgenson, and Lau's (1973) translog supplied attractive alternatives to earlier Cobb-Douglass and CES forms. These fexible functional forms are capable of attaining arbitrary price elasticities at a point, unlike other forms which imposed strong restrictions on elasticities between inputs. Unfortunately, such advances leading to gains in flexibility also produced functional forms that often violate monotonicity and concavity properties implied by theory. Caves and Christensen (1980) and Barnett and Lee (1985) find small regular regions for the translog and generalized Leontief, and concavity violations often appear in empirical applications using these forms.1 For example, Diewert and Wales (1987) report violations of

EXISTENCE OF A NONNEGATIVE EQUILIBRIUM PRICE VECTOR IN THE MEAN‐VARIANCE CAPITAL MARKET

We derive a necessary and sufficient condition for the existence of a nonnegative equilibrium price vector under which the total demand and supply of each asset balances in the standard mean‐variance capital market. Also, we give an explicit formula for such a price vector. This formula shows that the price of assets is an increasing function of p̄, the weighted average of the requested rate of return of individual investors, which tends to infinity as p̄ approaches the expected rate of return on the market portfolio. Further, we construct a macroeconomic index which gives information about the soundness of the capital market.

Sectoral Rates of Profit and Productive Structure

This paper analyzes an economic system in which rates of profit are not uniform but differ from one sector to another, and discusses the acceptable intervals of variation of the rates of profit compatible with non-negative prices. The investigation is conducted in a Leontief price model with fixed capital. The limits of variation of the rates of profit are ascertained using a mathematical algorithm based on the properties of Z matrices and dominant-diagonal matrices.

Stability and instability in oligopoly

For regular oligopolies (both homogeneous and heterogeneous) the (local) Cournot-Nash equilibria are the (non-degenerate) critical points of a Morse-Smale vector field, defined on the feasible region of non-negative prices and outputs. When at the boundary of this feasible region this vector field points inwards, it follows from the Morse inequalities that there is at least one stable equilibrium. When there is a unique, non-stable, interior equilibrium, necessarily the vector field points outwards somewhere along the boundary of the feasible region. This raises to a stable boundary equilibrium.

A Note on Short-Run Employment and Real Wage Rate Under Competitive Commodity Markets

THIS PAPER EXPLORES the effects upon aggregate employment and the real wage rate of a decline of aggregate demand in two economies in which the commodity market is competitive. In the first economy, all goods just produced are supplied to the market perfectly inelastically, the costs of storage being too great to warrant the holding of stocks at any non-negative market price. In the second type of economy, holding costs are low enough that producers will carry over some stock into the next market period when the current market price is low enough on the speculation that future sales will be possible at a higher price. This latter model has been studied by Edwin Mills [7, (chapter 4)] and Edward Zabel [9], and it will be supposed here that firms follow the optimal production and sales policies derived by Zabel [9]. Consider a decrease of aggregate demand for commodities which does not prevent the continued existence of a full-employment equilibrium. Under what conditions concerning the dynamics of the system will the fall of aggregate demand cause involuntary unemployment, at least transitionally? In particular, is a failure of money wages immediately to fall in proportion to the price level (at any given level of employment) a necessary condition for involuntary unemployment? That is, will involuntary unemployment occur only if the fall of aggregate demand causes a rise of the real wage rate? This is the principal question to be studied in this paper.