layout: true background-image: url(figs/tcb-logo.png) background-position: bottom right background-attachment: fixed; background-origin: content-box; background-size: 10% --- class: title-slide .row[ .col-7[ .title[ # Consumer Behavior ] .subtitle[ ## Choice under Uncertainty ## .center[&] ## Economics of Information ] .author[ ### Dennis A.V. Dittrich ] .affiliation[ ] ] .col-5[ ] ] --- ## Decisions under Uncertainty and Risk .row[ .col-7[ What is uncertain in an economy? * future price * future income * current and future actions of economics agents * future states of the world Economic agents try to quantify uncertainty by assigning probabilities to possible outcomes of an action or events. ] .col-5[ ### Uncertainty A situation in which an action has several possible outcomes and the objective probability of any event is unknown. ### Risk A situation in which an action has a number of possible outcomes and the objective probability of each event is known. ]] --- # Describing Risk .row[ .col-7[ To measure risk we need to know: * All possible outcomes * The probability of each outcome ] .col-5[ ### Probability A probability is a number between 0 and 1 that indicates the likelihood that a condition occurs at a given time. ]] --- # Lotteries .row[ .col-7[ Possible outcomes: 1. Not losing any contact lens (0 Euro) 2. Losing one contact lens (-100 Euro) 3. Lose both contact lenses (-200 Euro) Their probabilities: 1. 50% Not losing any contact lens (0 Euro) 2. 30% Losing one contact lens (-100 Euro) 3. 20% Lose both contact lenses (-200 Euro) ] .col-5[ ### Expected Value The weighted average of the payoffs or values associated with all possible outcomes. The probabilities of each outcome are used as weights. The expected value measures the **central tendency**, the payoff or value that we would expect on average. ]] .row[ .col-7[ The expected value: `$$EW=0.5\times 0 -0.3\times 100 -0.2\times 200 = -70$$` ]] --- class: practice-slide # Probability Distribution ![](img05/pdf.png) .col-7[ What measures would you use to describe the different distributions? ] --- # Describing Risk .row[.col-7[ ### Lotteries Possible events and their probabilities: * 50% Not losing any contact lens (0 Euro) * 30% Losing one contact lens (-100 Euro) * 20% Losing both contact lenses (-200 Euro) The expected value: `$$EW=0.5\times 0 -0.3\times 100 -0.2\times 200 = -70$$` ] .col-5[ ### The Variance The variance is the sum of the squared distances between the expected value and the outcome. * Variance measures the **variability** of the outcomes and thus is the risk. * Other measures of variability are e.g. * Spread * Quartiles * Mean absolute deviation * Standard Deviation ]] .row[.col-7[ The variance: `$$\sigma^2=0.5\cdot (0+70)^2+0.3\cdot (-100+70)^2+0.2\cdot (-200+70)^2$$` `$$=2450+270+3380=6100$$` ]] --- class: practice-slide # Lotteries Should I buy an insurance for contact lenses? .row[ .col-6[ **No insurance** ] .col-6[ **With insurance** (Costs 75 Euro, 75 Euro Reimbursement per lens): ]] .row[ .col-6[ 50% Not losing any contact lens (0 Euro) 30% Losing one contact lens (-100 Euro) 20% Losing both contact lenses (-200 Euro) Expected value = `\(-70\)`, Variance = `\(6100\)` ] .col-6[ 50% Not losing any contact lens (-75 Euro) 30% Losing one contact lens (-100 Euro) 20% Losing both contact lenses (-125 Euro) Expected value = `\(-92,5\)`, Variance = `\(256,25\)` ]] --- # Risk Profiles .row[.col-5[ Risk Averse Risk Neutral Risk Loving ] .col-7[ Consider a bet where a fair coin is tossed and brings a profit of 2 Euro and 4 Euro (depending if head or tail). The expected profit is 3 euros. Someone who * is indifferent between the gamble or having a payment of 3 euros is called **risk neutral**. * prefers the gamble is **risk loving**. * prefers having the payment of 3 euros is **risk averse**. ]] --- # Decisions and Risk Preferences .col-7[ How an economic agent makes decisions between risky choices will depend on his/her preferences towards risk. ### Three Basic Assumptions about Preferences 1. Preferences are **complete**. For any bundle of goods, the consumer can decide whether one of the two bundles is preferred, or whether he is indifferent between both. 2. Preferences are **transitive**. If the consumer prefers bundle A to bundle B, and bundle B to bundle C, then he also prefers bundle A to bundle C. 3. Consumers always **prefer more to less**. Principle of local non-satiation. ] --- # Independence Axiom .row[.col-7[ For `\(\alpha \in (0,1)\)` `$$A\succsim B \Longleftrightarrow \alpha A +(1-\alpha)C \succsim \alpha B +(1-\alpha)C$$` If preferences are transitive, complete, continuous and the independence axiom holds, then we can represent them by expected utility functions. **Expected utility** functions are also called **von-Neumann-Morgenstern-utility** functions. ] .col-5[ ### Expected Utility Expected utility is the sum of the utilities associates with all possible outcomes, weighted by the probability that each outcome will occur. `$$EU= p_1u(X_1)+p_2u(X_2)+\cdots +p_nu(X_n)$$` It is assumed that agents maximize their expected utility. ]] --- # Risk Aversion .row[.col-6[ A risk averse agent has a concave utility function. * Utility increases with increasing consumption, but at a decreasing rate * The expected utility of a risky action is lower than the utility derived from the weighted sum of the individual outputs. ### Concave Function `$$U(\alpha x_1+(1-\alpha )x_2)\geq \alpha U(x_1)+(1-\alpha )U(x_2)$$` ] .col-6[ ![](img05/riskaverse.png) ]] --- ## Risk Aversion ### Certainty Equivalent and Risk Premium .row[.col-7[ ![](img05/riskaverse.png) ] .col-5[ ### Risk Premium The risk premium is the amount that an individual is willing to pay in order to avoid taking a risk. ### Certainty Equivalent A guaranteed amount that someone would accept, rather than taking a chance on a higher, but uncertain, amount. ]] --- .row[.col-6[ ## Risk Neutrality A risk-neutral individual has a linear utility function. * The utility increases with increasing consumption, at a constant rate. * The expected utility of a risky action is equal to the utility from the weighted sum of all possible outcomes. * Risk-neutral individuals choose the option with the highest expected value. * The risk premium of a risk-neutral individual is always 0. ] .col-6[ ![](img05/riskneutral.png) ]] --- .row[.col-6[ ## Risk Loving A risk-loving individual has a convex utility function. * The utility increases with increasing consumption level, at increasing rates. * The expected utility of a risky action is higher than the utility from the weighted sum of all possible outcomes. * The risk premium of a risk-seeking individual is negative, i.e. s/he would even pay something in order to take a risk. ### Convex Function `\(U(\alpha x_1+(1-\alpha )x_2)\leq \alpha U(x_1)+(1-\alpha )U(x_2)\)` ] .col-6[ ![](img05/risklove.png) ]] --- class: practice-slide ## Who wants to be a millionaire? .col-9[ Let's say you're a candidate at "Who wants to be a millionaire?" You are at 250,000 and you are asked if you want to go to the 500,000 Euro question. You have your 50-50 Joker and can reduce the number of possible answers from four to two. If you are answering the next question correctly, you stand at 500,000 Euro, if you're wrong, your profit is reduced to 32,000 Euro. Suppose you have no idea what the right answer is and have to guess. What is the expected value? _"If you are risk averse, you'd finish the game at 250,000 Euro."_ True? False? Maybe? ] --- # Reducing Risk: Insurance .col-7[ ### Pooling of Risk The sharing of risk / risk pooling is based on the law of large numbers: If an independent event has a probability `\(p\)` of entering each of `\(N\)` possible cases, then the event will occur `\(p\)` times the cases for very large values of `\(N\)`. As the number of bad cases is approximately known, the loss can be divided among all the insured, even before the damage occurs. ] --- # Insurance .row[.col-6[ ### Actuarially Fair Insurance Premium Insurance premium for an insurance police that in expectation results in zero profit and zero loss for the insurer. ] .col-6[ ### Reservation Price for an Insurance The reservation price for an insurance is the certainty equivalent of the insured situation. If the certainty equivalent is higher than the insurance premium, the decision maker will buy the insurance. ]] .row[.col-7[ The insurance market is a market for _conditional_ goods. ]] ??? ## Insurance: Conditional Consumption .col-7[ Suppose there are two _conditional_ goods: 1. Wealth in good times: `\(W_g\)` 2. Wealth in bad times: `\(W_b\)` * Good times will occur with probability `\(\pi\)` * The expected utility is then: `$$EU=\pi U(W_g)+(1-\pi)U(W_b)$$` * Given the initial endowment `\(W\)` the individual will maximize this expected utility Suppose the person can buy 1 Euro assets at price `\(p_g\)` and 1 Euro assets in bad times at price `\(p_b\)` * the budget constraint is then: `$$W=p_gW_g+p_bW_b$$` * The price ratio `\(p_g/p_b\)` shows the trade-off between assets in good and bad times. ] ??? # Conditional Consumption: Price .col-7[ If the markets for conditional goods are _thick_ then market participants can agree on a value for `\(\pi\)`, and prices will be actuarially fair `$$p_g=\pi$$` `$$p_b=1-\pi$$` The price ratio will reflect the (betting) odds: `$$\frac{p_g}{p_b}=\frac{\pi}{1-\pi}$$` A (risk-averse) utility maximizer will attempt to achieve a situation in which s/he can consume in bad times as much as in good times. `$$W_g^*=W_b^*$$` The wealth will therefore be identical -- regardless the state of the world ] ??? ## Conditional Consumption: Risk Aversion .col-7[ Utility maximization requires MRS=MRT `$$\frac{\dfrac{\partial EU}{\partial W_g}}{\dfrac{\partial EU}{\partial W_b}}=\frac{p_g}{p_b}\\ \frac{\pi U^\prime(W_g^*)}{(1-\pi)U^\prime(W_b^*)}=\frac{p_g}{p_b}$$` Consequently, `$$\frac{U^\prime(W_g^*)}{U^\prime(W_b^*)}=\frac{p_g}{p_b}\frac{1-\pi}{\pi}$$` If the market is fair `\(p_g=\pi\)` and `\(p_b=1-\pi\)`: `$$\frac{U^\prime(W_g^*)}{U^\prime(W_b^*)}=1\\ W_g^*=W_b^*$$` ] ??? ## Full insurance under fair prices <img src="img05/insurance1.svg" width="68%" /> --- # Insurance: Example .col-7[ Suppose a person has wealth of 100,000 Euro including a car which is worth 20,000 Euro. There is a 25% chance of car theft. 1. 75% Wealth = 100,000 = `\(W_g\)` 2. 25% Wealth = 80,000 = `\(W_b\)` Let's also suppose that this person has a logarithmic utility: `\(U=\ln (x)\)` `$$EU=0.75U(W_g)+0.25U(W_b)\\ =0.75 \ln 100,000+0.25\ln 80,000\\ =11.45714$$` ] --- # Insurance: Example .col-7[ The budget constraint with prices of the conditional goods are: `$$\pi W_g+(1-\pi)W_b=p_gW^*_g+p_bW^*_b$$` The expected amount of wealth is 95000 Euro `$$0.75\cdot 100000+ 0.25\cdot 80000=95000$$` The expected utility is: `$$U(95000)=\ln 95000 = 11.46163$$` To obtain this utility, the individual must convert 5,000 Euro good times' wealth into 15,000 Euro bad times' wealth. In case of damage, the insurance must assure 3 Euro payment per Euro insurance premium. A fair insurance contract allows this! `$$\frac{p_g}{p_b}=\frac{0.75}{0.25}=3$$` ] --- # Insurance with retention .col-7[ Suppose the policy costs 4700 Euro, but includes a retention of 1200 Euro. In case of damage, the first 1200 Euro have to be borne by the insured. 1. `\(W_g=100000-4700=95300\)` 2. `\(W_b=80000-4700+18800=94100\)` `$$EU=0.75\ln 95300 + 0.25\ln 94100 = 11.46162$$` This insurance still has a higher expected utility than the situation without insurance (11.45714) but less than the full insurance (11.46163). ] --- # Insurance .col-7[ Most insurance companies are not actuarially fair. * Switching costs * Administrative costs * market return on capital employed * It is therefore better not to insure small losses * Through deductibles, the insurance is often disproportionately more favorable Against large losses (significant proportion of lifetime income) you should protect yourself! * Health insurance (with retention) * Insurance for invalidity * Liability ] --- class: practice-slide # Optional Warranties .col-8[ A tablet computer costs 325 Euro; the optional one-year warranty, which will replace the tablet computer at no cost if it breaks, costs 79 Euro. What does the probability `\(p\)` of the tablet computer breaking need to be for the expected value of purchasing the optional warranty to equal the expected value of not purchasing it? ] --- # Buying Risky Assets ![](img05/riskyasset.svg) --- # Buying Risky Assets .row[.col-6[ Suppose there are two firms, A and B. The share price for company A and for company B is 10 Euro. There are two states of the world that are equally likely to occur. 1. In state 1, the share price of company A increases to 100 Euro and the share price of the company B to 20 Euro. 2. In state 2, the share price of the company A increases to 20 Euro and the shares of the company B to 100 Euro. The decision maker has to invest 100 Euro. If one only buys shares of Company A, one can buy 10 shares In state 1, one earns 900 Euro, and in state 2 one earns 100 Euro ] .col-1[] .col-5[ Expected profit `$$0.5\times 900 + 0.5\times 100 = 500$$` Variance: `$$\sigma^2=0.5(900-500)^2+0.5(100-500)^2\\ =160000$$` ]] --- # Diversification .row[ .col-5[ If one only buys shares of company B, one can buy 10 shares. In state 1, one earns 100 Euro, and in state 2 one earns 900 Euro ] .col-1[] .col-5[ If one buys 5 shares of company A and 5 shares of company B, in state 1 one earns 500 Euro, and in state 2 one earns 500 Euro `$$5\times 100+5\times 20 -100 = 500$$` ]] .row[.col-5[ Expected profit `$$0.5\times 900 + 0.5\times 100 = 500$$` Variance: `$$\sigma^2=0.5(900-500)^2+0.5(100-500)^2\\ =160000$$` ] .col-1[] .col-5[ Expected profit `$$0.5\times 500 + 0.5\times 500 = 500$$` Variance: `$$\sigma^2=0.5(500-500)^2+0.5(500-500)^2\\=0$$` ]] --- # Diversification .col-7[ By diversifying the portfolio, one can convert the high-risk expected profit of 500 Euro in a sure gain of 500 Euro. This works here so well because the shares of both companies were perfectly negatively correlated. Typically, you will not find a perfectly negatively correlated assets. But as long as the investments are not perfectly positively correlated, the risk can be reduced through diversification. Diversification into related values that have a high positive correlation will reduce the risk only slightly. ] --- ## Asymmetric Information: Quality Uncertainty .row[.col-6[ A used car sales man knows more about the car than the buyer An insured person may know more about his risk then the insurance ] .col-6[ ### Experience Goods quality is difficult to observe in advance ### Post-experience Goods / Credence Goods it is difficult for consumers to ascertain the quality even after they have consumed them ]] --- ## Problems caused by Asymmetric Information .row[.col-6[ If two parties (buyer and seller) involved in a transaction have limited information, one of them may have an advantage Asymmetric information leads to opportunistic behavior * The informed agent may profit from the uninformed agent * Sometimes, with asymmetric information all are worse off than with complete information ] .col-6[ ### Moral Hazard Opportunistic behavior of an informed person; he profits when a less informed person cannot observe an **action**. * quality and quantity of work effort ### Adverse Selection Opportunistic behavior of an informed person; he profits when a less informed person cannot observe some **characteristics** of a good or service. * quality of a used car, experience goods, health ]] --- class: practice-slide .col-8[ Why do _almost new_ used cars sell for so much less than brand new ones? ] --- ## Quality uncertainty kills high-quality goods .col-7[ Often buyers do not know the quality of a good before their purchase decision (experience goods) The lack of complete information increases the risk and hence decreases the value of the good to the prospective buyer Example: low-quality used cars (lemons) may drive high-quality used cars out of the market * Owners of lemons are more likely to sell their cars `\(\hookrightarrow\)` leads to adverse selection .caption[George A. Akerlof, The Market for "Lemons": Quality Uncertainty and the Market Mechanism, The Quarterly Journal of Economics, Vol. 84, No. 3 (Aug., 1970), pp. 488-500] ] ??? %---# Choice of Quality and Adverse Selection} %Assume a seller can choose the quality of his products to be either low or high. % %What quality will he produce and sell? % %Additional assumptions: %\begin{itemize} %* Buyers are willing to pay 1400 Euro for a high-quality product and 800 Euro for a low-quality product %* Buyer cannot identify the quality of a product before their purchase decision %* The marginal costs of production are %\begin{itemize} %* 1100 Euro for a high-quality product %* 1000 Euro for a low-quality product %\end{itemize} %\end{itemize} %} % %---# Choice of Quality and Adverse Selection} %Assume, only high-quality products are produced %\begin{itemize} %* Buyers pay 1400 Euro and sellers realize a profit of 1400 - 1100 = 300 Euro per unit %* Buyers cannot identify the quality before their purchase decision, sellers therefore have an incentive to produce low-quality products and sell them for the price of a high-quality product increasing their profit to 400 Euro per unit %* The production of only high-quality products is not an equilibrium %\end{itemize} % %Is producing only low-quality products an equilibrium? %} % %---# Choice of Quality and Adverse Selection} %Assume, only low-quality products are produced %\begin{itemize} %* Buyers pay 800 Euro and sellers (would) realize a loss of 800 - 1000 = -200 Euro per unit %* The production of only low-quality products is not an equilibrium %\end{itemize} % %Is there an equilibrium in which both qualities are produced and sold? %} % %---# Choice of Quality and Adverse Selection} %Assume, a fraction `\(q\)` of all products are of high quality %\begin{itemize} %* Buyers are willing to pay at most the expected value of the product %\[EV=1400q+800(1-q)=800+600q\] %* Sellers (of high-quality products) need to earn at least the cost of production (of high-quality products) %\[800+600q\geq 1100 \Rightarrow q\geq 1/2\] %* At least half the products have to be of high quality %\end{itemize} %} % %---# Choice of Quality and Adverse Selection} %\begin{itemize} %* Problem: Sellers of high-quality products could increase their profits by selling low-quality products instead. %* If all sellers think so no one will produce high-quality products %* Since there are no high quality products buyers are only willing to pay 800 Euro %* There is no equilibrium in which both qualities are sold %* There is not any equilibrium in which the products are sold %\end{itemize} %\centering Adverse Selection can destroy markets!\par %} --- # Effects of Asymmetric Information .col-7[ ### Price discrimination Because of misconceptions (beliefs) about the quality of (branded) products, price discrimination is possible. * Several brands for the same product. * Pharma industry: generics and ``originals'' from the same manufacturer. ### Market power Ignorance about the prices gives firms market power. * Consumers who do not know the market prices, pay higher prices. ] --- # Effects of Asymmetric Information .col-7[ The insurance market: health insurance * Is it possible for insurance companies to insure high-risk and low-risk individuals separately? * If this wouldn't be possible, only high-risk individuals would buy the insurance. * Due to adverse selection the health insurance would not be profitable. Solution: ? ] --- class: practice-slide ## Solution to Adverse Selection .col-8[ Why can producers still offer high-quality goods even though adverse selection leads to a crowding out of high quality products? ] --- ## Solution to Adverse Selection: ### Reputation and Standards .col-7[ Why can producers still offer high-quality goods even though adverse selection leads to a crowding out of high quality products? Answer: Reputation & Standards. * Why do tourist often eat at McDonald's instead of trying the local cuisine? * Holiday Inn (a hotel chain) used to run ads with the slogan _no surprises_, thereby directly addressing the problem of adverse selection. * eBay implemented an electronic reputation system to facilitate trust and therefore trade ] --- ## Solution to Adverse Selection: ### Harmonize Information .row[ .col-6[ ### Screening Action of the uninformed party to gain the information of the informed party * test drive in the used car ] .col-6[ ### Signaling An action that sellers (agents) can use to provide information (a **signal**) about the quality of their products to their potential customers (principals). * product test report by an impartial agency to credibly signal quality of the product ### Strong Signal An effective signal has to be * costly * easy to obtain by the provider of high quality * hard to obtain by the provider of low quality ]] --- ## Warranties as Signals .col-7[ Warranties signal high quality and reliability It is cheaper to produce a low quality product. If a producer sells it without a warranty at the same price as a high quality product he has a higher profit. If you sell both low- and high quality products with life time warranties high quality products will cause lower server costs. Total costs may be lower than for a low quality product. Warranties are an effective signal for high quality since the costs of warranties to the producer of a low quality product are too high. ]