Endogenous timing game with R&D decisions and output subsidies

This paper investigates strategic choices between duopolistic firms’ R&D investments and government’s output subsidies in an endogenous timing game with research spillovers. We show that a simultaneous-move game among three players appears at equilibrium if the spillovers are very low while government leadership with both firms’ simultaneous-move game appears otherwise. We also show that government followership appears unless the spillovers are low or high, while both the government leadership and followership outcomes are socially desirable at quilibrium. However, a single firm’s leadership equilibrium appears if the spillovers are high, but it causes a welfare loss

Endogenous timing game with R&D decisions and output subsidies

This paper investigates strategic choices between duopolistic firms’ R&D investments and government’s output subsidies in an endogenous timing game with research spillovers. We show that a simultaneous-move game among three players appears at equilibrium if the spillovers are very low while government leadership with both firms’ simultaneous-move game appears otherwise. We also show that government followership appears unless the spillovers are low or high, while both the government leadership and followership outcomes are socially desirable at quilibrium. However, a single firm’s leadership equilibrium appears if the spillovers are high, but it causes a welfare loss

Cournot-Bertrand comparison under R&D competition: Output versus R&D subsidies

This study compares Cournot and Bertrand firms with research and development (R&D) competition under government policies between output and R&D subsidies. We demonstrate that firms invest more (less) in R&D and the government grants more (less) subsidies under Cournot than Bertrand competition with output (R&D) subsidy policies. We also reveal that both competition modes yield the same welfare with output subsidy while Bertrand yields higher welfare than Cournot with R&D subsidy irrespective of product substitutability. Finally, we show that firms’ profits and social welfare are always higher under output subsidies in Cournot competition, while they can be higher under R&D subsidies in Bertrand competition if the product substitutability is high and the firm’s R&D investment is efficient

Timing of R&D Decisions and Output Subsidies in a Mixed Duopoly with Spillovers

This study considers a mixed duopoly with research spillovers and examines the interplay between firms’ R&D decisions and government’s output subsidies. We investigate and compare the timing of the game between ex-ante R&D and ex-post R&D decisions where the R&D decisions are chosen before the output subsidy is determined in the former case while the order is reversed in the latter case. We show that the equilibrium outcomes can be opposite between the two cases because both public and private firms have different objectives in choosing R&D investments, but the spillovers rate is a key factor that determines their incentives. In particular, we show that the output subsidy is smaller (larger) and the welfare is larger (smaller) under the ex-ante R&D decisions for a higher (lower) degree of spillovers rate. Finally, privatization increases the welfare in both cases only when spillovers rate is weak

Mixed ownership and R&D under discriminatory output subsidies

This study considers a (partially privatized) semi-public firm in a mixed duopoly and examines the welfare effects of discriminatory output subsidies under R&D competition. We find that the government grants higher subsidies to the private firm than to the semi-public firm, which induces the private firm to invest more in R&D and to produce a higher output than the semi-public firm. We also show that optimal subsidy rates are higher (lower) than uniform subsidy rates for a sufficiently high (low) degree of privatization, which could decrease (increase) social welfare. This finding sharply contrasts to the case that the committed discriminatory output subsidy always yields the highest welfare compared to non-committed cases

Mixed ownership and R&D under discriminatory output subsidies

This study considers a (partially privatized) semi-public firm in a mixed duopoly and examines the welfare effects of discriminatory output subsidies under R&D competition. We find that the government grants higher subsidies to the private firm than to the semi-public firm, which induces the private firm to invest more in R&D and to produce a higher output than the semi-public firm. We also show that optimal subsidy rates are higher (lower) than uniform subsidy rates for a sufficiently high (low) degree of privatization, which could decrease (increase) social welfare. This finding sharply contrasts to the case that the committed discriminatory output subsidy always yields the highest welfare compared to non-committed cases

Robust estimation of bacterial cell count from optical density

Optical density (OD) is widely used to estimate the density of cells in liquid culture, but cannot be compared between instruments without a standardized calibration protocol and is challenging to relate to actual cell count. We address this with an interlaboratory study comparing three simple, low-cost, and highly accessible OD calibration protocols across 244 laboratories, applied to eight strains of constitutive GFP-expressing E. coli. Based on our results, we recommend calibrating OD to estimated cell count using serial dilution of silica microspheres, which produces highly precise calibration (95.5% of residuals <1.2-fold), is easily assessed for quality control, also assesses instrument effective linear range, and can be combined with fluorescence calibration to obtain units of Molecules of Equivalent Fluorescein (MEFL) per cell, allowing direct comparison and data fusion with flow cytometry measurements: in our study, fluorescence per cell measurements showed only a 1.07-fold mean difference between plate reader and flow cytometry data

Time-inconsistent Output Subsidy/Tax Policies in Free-entry Mixed Markets

This study considers time-inconsistent output subsidy/tax policies in free-entry mixed markets under different competition modes. In a committed regime where the subsidy is determined before entry, the optimal rate is zero in either Cournot or Stackelberg game with private leadership, while it is negative in Stackelberg game with public leadership. In a non-committed regime where the subsidy is determined after entry, the optimal rate is always positive. We also show that private leadership is the best for social welfare regardless of the timing of subsidy policies, but public leadership might be equilibrium if the timing of entry decisions is endogenous