BEPP 250 Study Guide Slides 1 - Managerial Economics Is the use of (micro)economic theory for the purpose of informing business/policy decision-making. - Body of knowledge that studies individual-level behavior and decision-making in order to provide tools (models), results and ideas to help us: - Understand observed phenomenon (positive economics) - Guide decisions (normative economics) - Key principles: - Optimization: Individual objectives + constraints → shape decisions and observed behavior - Equilibrium: observed outcomes ← interaction across individuals’ decisions, no incentive to change further, “system at rest” Slides 2 - Choice, Preference and Utility - Theory of consumer behavior: - Evaluate willingness to pay, predict demand, anticipate customer reaction, asses and improve public policy - Goal: Derive a demand function - We see making people choices from a choice set and we want to rationalize these choices, we analyze preferences and constraints - with this we create a utility function. - Preferences satisfy the following qualities: - Completeness - When facing a choice between two bundles a consumer can rank them, in the form that one is preferred over the other or they create equal utility - Transitivity - consumers' rankings are logically consistent, if a is preferred over b and b is preferred over c then a is preferred over c. - Monotonicity - All else same more of a good is better - Budget Constraint - Budget constraint limits a customer form choosing any bundle, this constraint defines our budget set - Budget Set - the set of feasible (affordable) bundles given price and income - I.e set of bundles where expenditure is less than or equal to how much we spend. - Budget Line → p1x1 +p2x2 = I - Utility Function - Preference relations and indifference curves at not practical in empirical setting, therefore we use a more convenient set of preferences. If an individual has preferences that satisfy completeness, transitivity and monotonicity we can represent this preference with a utility function. - - - - Preferences are basically a ranking over bundles. All information can be captured by a mathematical function that assigns a number for each bundle, such that the order of preferences is fully captured. Utility Maximization - Slides 3 - In order to solve the utility maximization problem we must link the IC to the utility functions. - Given the link between ICs and the utility function the most preferred affordable bundle is equivalent to finding (x, y) such that - u(x, y) = U is the largest and (x, y) satisfies the budget constraint. - I.e maximize utility subject tot the budget constraint - Optimal bundle - a point where the IC is tangent to the budget line - Mathematically this point of tangency is captured by equality of the slopes of the budget line and the IC at the optimal bundle. - Equations in notes - Slope of IC = Marginal rate of substitution (MRS) - MRS - (delta)y/(delta)x tells us how much we are willing to give up in terms of y in exchange for an increase in x, while keeping utility constant. This is also the slope between two points on the IC. - (delta)y/(delta)x is the first derivative dx/dy. This measures the tradeoff between y and x. Relating MRS and Marginal Utility - The increase in x given by Δx increased our utility, say by ΔxU per unit of x Similarly, the decrease in Δy decreased our utility, say by ΔyU per unit of y Being on the same IC means that after all these changes in x and y, at the end of the day our utility does not change: ΔU=0 - Slope of IC is equal to the negative ratio of marginal utility - equality of the slopes of the budget line and the IC at the optimal bundle. - Rearranging this gives us a particular optimality condition which we refer to as (B4Bs) the Equality of bang for bucks. Optimality and B4B Bang - for - buck (B4B) - benefit-cost ratio of the marginal (the very last) unit. - Thinking at the margin Optimal Behavior - As long as one good has a higher bang for buck that the other, allocate consumption here - If B4Bs are equal then you stop - If you hit some constraint, (you can't consume more or you can't give up negative quantities) then you stop. Demand Part 3: Demand Function - Slides 4 - Optimality condition - Interior Solution - Solution involves consuming strictly positive amounts of each good. - Mathematically: First order condition is both necessary and sufficient - Optimality condition→ equality of B4Bs - Corner solution - Solution entails spending all your income on the good with the highest B4B - Mathematically - non negativity constraint binds - Optimality condition→ B4Bx > B4By then its optimal to set y=0 - Take into account there could be additional constraints one must satisfy. - You will usually know what solution to look for - But you can notice by looking at the behavior of the marginal utilities. - Interior solution → marginal utilities go to infinity when consumption is 0 - Corner solution→ when marginal utilities are non-decreasing - Note for which values of parameters(prices, income) solution may be non-negative - Law of Demand : Demand for a good is decreasing in its own price, demand curve slopes downward - Elasticities (Linear Demand) - Own price elasticity - % change in quantity with respect to % in the good s price - Cross Price Elasticity - % change in quantity with respect to % in other products price Supply: Part 1 - Production Function - Theory of Firm Behavior, must know to: - Predict how much a firm is willing to supply at a given price - Understand Industry dynamics - Figure out how to change incentives to encourage/discourage supply - Learn how to derive the supply function, pairing with demand function we can predict market outcomes - Assumption: Firm choose quantities in order to maximize profits: - Profits (q) = Revenue (q) - Cost (q) - To figure out how much to supply (q), we first need to figure out how to produce a given quantity q with the goal of minimizing cost, 9z, y) -> Cost(q) - Key Questions - What inputs do we need and how do we combine them to produce output q? - → Production function: transform input bundle (x, y) to q - What is the optimal input bundle given input prices and required output q? - Sole cost minimization problem to get cost (q) - Production Function - A firm transforms inputs (factors of production) such as capital K and labor L into output q - Short vs Long- run - Whether inputs can be adjusted depends on decision time horizon: - Short-run: At least one input (fixed input) can’t be adjusted, suppose k, therefore only l is the input that can be varied - Long run: all inputs can be adjusted - Production function concepts - Measures of productivity - Returns to scale→ How much does output change if a firm increases all its inputs proportionally? - Marginal and average product - Law of diminishing marginal returns - Isoquants - Marginal rate of substitution - Marginal and Average Product - Decisions driven by marginal productivity - The average product of labor is the ratio of output to the amount of labor used - The marginal product of labor is the additional output produced by an additional unit of labor, holding all other factors constant. - Marginal product drive average product - Law of Diminishing marginal returns - As a firm increases its use of and input (holding all else constant), the marginal product of the input decreases. - Isoquants - AN isoquant is a set of input bundles that produce the same quantity of output. - The slope of the isoquant measures the tradeoff between inputs, i.e the Marginal Rate of Technical Substitution (MRTS) - We can derive an expression for MRTS as a function of the marginal products of 2 inputs Cost Minimization - Supply: Part 2 - Slides 6 - Isocost Line - collection of bundles that have the same cost - Optimality - we want to find the cheapest input bundle that will produce at least q units of output (bundle on or above the isoquant) - Slope of the isoquant = slope of the isocost (optimal bundle input for interior case) - Cost minimization in the long run - All inputs can be varied thus we need two equations - Optimality condition involving B4Bs - Production Constraint → f(x, y) = q (be wary different from budget constraint) - Short run Cost Function - Some inputs are fixed which adds an additional constraint to our cost minimization problem. - When one variable is fixed, we only have one unknown, x, so one equation is sufficient. Typically, this equation is the production constraint with the fixed input is imposed: Supply: Part 3 - Supply Function - Slides 7 - We assume firm chooses output q to maximize profit P(q) = R(q) - C(q) - We refer to economic profit = revenue - opportunity cost - Profit max problem - Optimal output q solve the profit maximization problem - Profit is maximized when marginal profit is 0 - Thus Marginal Revenue = Marginal Cost (proof in bible) - Assumption: Perfectly Competitive Markets - A perfectly competitive market is where firms and consumers act as price takers (no market power) - Firm cannot influence market outcomes - Firm takes market price p as given and fixed regardless of q - Perfectly elastic demand curve - Therefore, a price taking firm’s revenue is R(q) = pq - Since MR(q) = p a price taking firm maximizes profit by choosing q such that p = MC(q) - Operate or Shutdown? - A firm should operate as long as revenues cover its relevant costs. - You only pay variable costs when q>0 - Fixed costs are relevant if they can be recovered or not - Costs that can’t be recovered are called sunk costs those that can are called avoidable costs - Only avoidable costs are relevant to shutdown - Therefore, operate if: Revenues > Variable costs + Avoidable Fixed costs - Operating at a Loss - This rule does not mean a firm operates in positive numbers - pq - VC(q) - F > 0 - Which requires p>AVC(q) + AFC(q) = AC(q) - If sunk costs are large this can mean the firm operates at a loss, however its better to lose less money than shut down - Shutdown Price - Lowest price at which a firm will operate - P = AAC(q) Midterm #2 Lecture 10: Monopoly Market Power - Most extreme case of market power→ monopolist Monopoly→ Firm is only sell of a product that does not have close substitutes (consumers only alternative is to no consume, and there is 0 cross-price elasticity with any other product) - Monopolies are usually defined as having 70+% market power has effective control, these arise from innovative tech, cost advantages, network effects, etc - SSNIP Test - check if a small price increase leads to consumers switching to another product, i.e compute cross-price elasticity - For monopolistic firms it thinks about how q will affect p - Price is and function of q in the firm's profit maximization problem - For a firm with market power marginal revenue must me less than 0 - - When inverse demand is linear, you can find MR by doubling the slope - MR can be a function of elasticity Takeaways: - As demand becomes more elastic the profit maximizing price goes down - The monopolist only produces on the elastic part of demand e>1 - If demand is inelastic then increasing price leads to more revenue and less cost therefore profits of up - Are these bad - They are not legal but can be regulated (electric grids) - Welfare under a monopolist - When a firm has market power, it will produce less than the competitive quantity in order to keep price high. This is inefficient since there are consumers who have WTP>MC but are prevented from buying the goods. SO are they Bad? - Mad - monopolies supply through high prices, reduce CS and introduce DWL so it lowers welfare - This is a product of innovation routing form competition Lecture 12: Monopoly Price Descrimination(Third Degree) - Breaking the assumption that firms only price linearly Types of Price Descrimination - First degree: Firms with perfect knowledge with individual valuations charge personalized prices. - Welfare is maximized but there is no Consumer Surplus, aka perfect price descrimination. - Very hard to implement and quite unrealistic - Second Degree: Firms offer different product quality/quantity so that consumer self-select form the menu of products - Business class vs economy, bulk vs single - Third Degree: Firms set different prices for the exact same product in different markets based on observable characteristics Multiple markets strategy - Firms face different types of buyers (loq/highly elastic), you want to set a low price for the elastic and high for the inelastic. However for this to work: - Firms must have market power t be able to set the price - The fir must be able to distinguish consumers - Consumers cannot engage in arbitrage - Firms problem: to choose how much supply in each market to maximize profit - Optimality condition- MR=MC, Why? - Cuppose MC is come constant and le MR1(q2)>MR2(q2). Than we can increase profit by selling more to market 1 since it has a higher bang for the same buck Welfare implications - If price discimination is not allowed, firm has to choose between selling to obh markets or just to market that is less price sensitive - Trade offs - (+) Larger market since face both markets - (-) But in order to access more price sensitive market, have to lower the price below what you would optimally charge the market - Selling to both market can be profiabel it - Difference in elasticity is not big - More price sensitive market is much larger so you don't want to miss out. - Example in notes Welfare Implications - Allowing price discrimination increases profits (unless firm earns 0 profit in hihlhy sensitve market) - If is is optimal for a firm to exclude some market when restricted to a sinlge price then discrimination increases surplus -
