Profit maximizationIn economics, profit maximization is the short run or long run process by which a firm may determine the price, input and output levels that will lead to the highest possible total profit (or just profit in short). In neoclassical economics, which is currently the mainstream approach to microeconomics, the firm is assumed to be a "rational agent" (whether operating in a perfectly competitive market or otherwise) which wants to maximize its total profit, which is the difference between its total revenue and its total cost.
Cournot competitionCournot competition is an economic model used to describe an industry structure in which companies compete on the amount of output they will produce, which they decide on independently of each other and at the same time. It is named after Antoine Augustin Cournot (1801–1877) who was inspired by observing competition in a spring water duopoly. It has the following features: There is more than one firm and all firms produce a homogeneous product, i.e., there is no product differentiation; Firms do not cooperate, i.
Profit (economics)In economics, profit is the difference between revenue that an economic entity has received from its outputs and total costs of its inputs. It is equal to total revenue minus total cost, including both explicit and implicit costs. It is different from accounting profit, which only relates to the explicit costs that appear on a firm's financial statements. An accountant measures the firm's accounting profit as the firm's total revenue minus only the firm's explicit costs.
Optimization problemIn mathematics, computer science and economics, an optimization problem is the problem of finding the best solution from all feasible solutions. Optimization problems can be divided into two categories, depending on whether the variables are continuous or discrete: An optimization problem with discrete variables is known as a discrete optimization, in which an object such as an integer, permutation or graph must be found from a countable set.
Mathematical optimizationMathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries.
Combinatorial optimizationCombinatorial optimization is a subfield of mathematical optimization that consists of finding an optimal object from a finite set of objects, where the set of feasible solutions is discrete or can be reduced to a discrete set. Typical combinatorial optimization problems are the travelling salesman problem ("TSP"), the minimum spanning tree problem ("MST"), and the knapsack problem. In many such problems, such as the ones previously mentioned, exhaustive search is not tractable, and so specialized algorithms that quickly rule out large parts of the search space or approximation algorithms must be resorted to instead.
OligopolyAn oligopoly () is a market in which control over an industry lies in the hands of a few large sellers who own a dominant share of the market. Oligopolistic markets have homogenous products, few market participants, and inelastic demand for the products in those industries. As a result of their significant market power, firms in oligopolistic markets can influence prices through manipulating the supply function. Firms in an oligopoly are also mutually interdependent, as any action by one firm is expected to affect other firms in the market and evoke a reaction or consequential action.
Convex optimizationConvex optimization is a subfield of mathematical optimization that studies the problem of minimizing convex functions over convex sets (or, equivalently, maximizing concave functions over convex sets). Many classes of convex optimization problems admit polynomial-time algorithms, whereas mathematical optimization is in general NP-hard.
ToolA tool is an object that can extend an individual's ability to modify features of the surrounding environment or help them accomplish a particular task. Although many animals use simple tools, only human beings, whose use of stone tools dates back hundreds of millennia, have been observed using tools to make other tools. Early human tools, made of such materials as stone, bone, and wood, were used for the preparation of food, hunting, the manufacture of weapons, and the working of materials to produce clothing and useful artifacts and crafts such as pottery, along with the construction of housing, businesses, infrastructure, and transportation.
Constrained optimizationIn mathematical optimization, constrained optimization (in some contexts called constraint optimization) is the process of optimizing an objective function with respect to some variables in the presence of constraints on those variables. The objective function is either a cost function or energy function, which is to be minimized, or a reward function or utility function, which is to be maximized.
Antoine Augustin CournotAntoine Augustin Cournot (ɑ̃twan oɡystɛ̃ kuʁno; 28 August 1801 - 31 March 1877) was a French philosopher and mathematician who also contributed to the development of economics. Antoine Augustin Cournot was born at Gray, Haute-Saône. In 1821 he entered one of the most prestigious Grandes Écoles, the École Normale Supérieure, and, according to Sandmo: in 1823 he took a license degree in mathematics at Sorbonne University. He then became the private secretary of a field marshal who required assistance in writing his memoirs.
Garden toolA garden tool is any one of many tools made for gardening and landscaping, which overlap with the range of tools made for agriculture and horticulture. Garden tools can be divided into hand tools and power tools. Hand tool Today's garden tools originated with the earliest agricultural implements used by humans. Examples include the hatchet, axe, sickle, scythe, pitchfork, spade, shovel, trowel, hoe, fork, and rake. In some places, the machete is common. The earliest tools were made variously of wood, flint, metal, tin, and bone.
Hand toolA hand tool is any tool that is powered by hand rather than a motor. Categories of hand tools include wrenches, pliers, cutters, , striking tools, struck or hammered tools, screwdrivers, vises, clamps, snips, hacksaws, drills, and knives. Outdoor tools such as garden forks, pruning shears, and rakes are additional forms of hand tools. Portable power tools are not hand tools. Hand tools have been used by humans since the Stone Age when stone tools were used for hammering and cutting.
Stackelberg competitionThe Stackelberg leadership model is a strategic game in economics in which the leader firm moves first and then the follower firms move sequentially (hence, it is sometimes described as the "leader-follower game"). It is named after the German economist Heinrich Freiherr von Stackelberg who published Marktform und Gleichgewicht [Market Structure and Equilibrium] in 1934, which described the model. In game theory terms, the players of this game are a leader and a follower and they compete on quantity.
Duality (optimization)In mathematical optimization theory, duality or the duality principle is the principle that optimization problems may be viewed from either of two perspectives, the primal problem or the dual problem. If the primal is a minimization problem then the dual is a maximization problem (and vice versa). Any feasible solution to the primal (minimization) problem is at least as large as any feasible solution to the dual (maximization) problem.
Power toolA power tool is a tool that is actuated by an additional power source and mechanism other than the solely manual labor used with hand tools. The most common types of power tools use electric motors. Internal combustion engines and compressed air are also commonly used. Tools directly driven by animal power are not generally considered power tools. Power tools are used in industry, in construction, in the garden, for housework tasks such as cooking, cleaning, and around the house for purposes of driving (fasteners), drilling, cutting, shaping, sanding, grinding, routing, polishing, painting, heating and more.
DuopolyA duopoly (from Greek δύο, duo "two" and πωλεῖν, polein "to sell") is a type of oligopoly where two firms have dominant or exclusive control over a market, and most (if not all) of the competition within that market occurs directly between them. Duopoly is the most commonly studied form of oligopoly due to its simplicity. Duopolies sell to consumers in a competitive market where the choice of an individual consumer choice cannot affect the firm in a duopoly market, as the defining characteristic of duopolies is that decisions made by each seller are dependent on what the other competitor does.
Machine toolA machine tool is a machine for handling or machining metal or other rigid materials, usually by cutting, boring, grinding, shearing, or other forms of deformations. Machine tools employ some sort of tool that does the cutting or shaping. All machine tools have some means of constraining the workpiece and provide a guided movement of the parts of the machine. Thus, the relative movement between the workpiece and the cutting tool (which is called the toolpath) is controlled or constrained by the machine to at least some extent, rather than being entirely "offhand" or "freehand".
Marginal revenueMarginal revenue (or marginal benefit) is a central concept in microeconomics that describes the additional total revenue generated by increasing product sales by 1 unit. Marginal revenue is the increase in revenue from the sale of one additional unit of product, i.e., the revenue from the sale of the last unit of product. It can be positive or negative. Marginal revenue is an important concept in vendor analysis.
Nash equilibriumIn game theory, the Nash equilibrium, named after the mathematician John Nash, is the most common way to define the solution of a non-cooperative game involving two or more players. In a Nash equilibrium, each player is assumed to know the equilibrium strategies of the other players, and no one has anything to gain by changing only one's own strategy. The principle of Nash equilibrium dates back to the time of Cournot, who in 1838 applied it to competing firms choosing outputs.
