Mathematical introduction - progression of a function, optimization, Lagrange fce, equilibrium problem. The theory of the consumer 1. Budget constraints - set of consumption options, budget constraints, substitution in exchange, change of constraints, ad valorem tax and benefits, relative prices (numeraire), quantity discount and surcharge, multiple constraints (time, consumption). 2. Preferences - rationality of the consumer, preference relations, axioms, indifference curves, extreme types of IC, saturation, marginal rate of substitution, correctly behaving IC, lexicographic preferences, discrete goods. 3. Utility - its measurement, utility function, undesirable and neutral goods, marginal utility, marginal rate of substitution, the elasticity of substitution, types of utility functions, perfect substitutes, perfect complements (Leontief), Cobb-Douglas function, CES function. 4. Consumer optimization - objective function and constraints, Lagrange multiplier, internal and corner optimization solutions, derivation of the demand function for individual types of utility functions, comparative statics, Engel curve and income elasticity of demand, supply price curve, price elasticity of demand, cross elasticity, manifested preference. 5. Substitution and income effect - Slutsky and Hicks substitution and income effect (numerically and graphically), Slutsky equation, Giffen goods. 6. Demand and duality - dual optimum solution, Marshall demand, Hicks (compensated) demand, indirect utility function, expenditure function, Sheppard's lemma, Roy's identity and relations in dual optimization, Slutsky equation, link to substitution and income effect, market demand. 7. Consumer surplus - reservation price, consumer surplus, compensating and equivalent variations. 8. Risk decision-making - risk and uncertainty, fair bet, expected benefit, budget and risk preference, optimization, risk aversion, risk preference, insurance principle, Bayes theorem, conditional probability. Theory of the firm 9. Technology - production functions in the short and long run, isoquants, marginal product, marginal rate of technical substitution, returns to scale, the elasticity of substitution, types of production functions - Cobb Douglas, Leontief, perfect substitutes, CES. 10. Profit maximization - economic profit, production factors and costs, iso-profit curve. Profit maximization in the short and long term, comparative statics, demonstrated profitability. 11. Costs - isocost, cost minimization, demand for production factors, expansion path, costs as a function of production - total costs, average costs, marginal costs, the relationship between costs and the production function, costs in the short and long term. 12. Supply - market environment, types of competition (monopoly, oligopoly, perfect, monopolistic), individual and market demand (from the company's point of view), supply in the short and long term, producer surplus, industry supply. General balance 13. General equilibrium - efficiency in production, Exchange, and market, Pareto efficiency, Edgewoth's Box diagram, PPF and UPF, product transformation, equilibrium price, and quantity determination, comparative statics (technological progress), Walras law.
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