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[ ## Application of Rational Choice and Demand Theories ] .author[ ### Dennis A.V. Dittrich ] .affiliation[ ] ] .col-5[ ] ] ??? ## Financing of Private Schools .col-7[ A private school system runs alongside a state funded system in most countries. In some countries, e.g. the U.K. and the U.S. private schools receive no government funding. In some countries, e.g. Germany and Denmark, private school receive some government funding. In others, e.g. Sweden, private schools receive full funding. Question: What is the effect of such different financing of schools of resources devoted to education? ] .pull-left[ ![](img04/Chapter051.png) ] .pull-right[ ![](img04/Chapter052.png) ] ??? The family has a pretax income of Y, out of which it must pay `\(P_e\)` in school taxes. It is entitled to 1 unit of tuition-free public education. In lieu of public education, it may purchase at least 1 unit of private education at the price of `\(P_e\)` per unit. Its budget constraint is thus A'BCE, and its optimal bundle is B, which contains 1 unit of public education. Unlike the current system, the voucher system allows parents to provide small increases above 1 unit of education at the price of `\(P_e\)` per unit. The budget constraint is now A'BD, and the family shown now chooses bundle G, which contains more than 1 unit of education. --- # Consumer Surplus .row[ .col-9[ ![](img04/Chapter053.png) ] .col-3[ **Consumer surplus**: A euro measure of the extent to which a consumer benefits from participating in a transaction. In a graph: Area between demand curve and price. ]] --- class: practice-slide ## Loss in Consumer Surplus from an Oil Price Increase ![](img04/Chapter054.png) .col-8[ By how much would the consumer surplus shrink if the price of petrol rose from 3$/gal to 4$/gal? ] ??? `\(6*(4-3)+1/2 = 6.5\)` --- # Two-Part Tariffs .row[.col-7[ The purchase of some goods and services can be divided into two decisions -- and therefore into two prices. ]] .row[.col-6[ Amusement park * Admission fee * Price for each journey and for food in the park Tennis club * Membership fee * Fee for each use of the tennis field ] .col-6[ Renting a big computer * Basic fee * Fee for each unit of processing used Razor * Price for the razor * Price for the razor blade ]] --- # Two-Part Tariff .col-7[ The pricing decision involves defining an entry fee `\(T\)` and a usage fee `\(P\)`. Choosing the tradeoff between a free entry with a high usage fee, and between a high entry fee and a usage fee of zero. **Two-part tariff with a single consumer** ] .row[.col-7[ ![](img04/2part1.png) ] .col-5[ The usage fee `\(P^*\)` is set such that `\(MC = D\)`. The entry fee `\(T^*\)` equals the total (remaining) consumer surplus. ]] --- ## Two-Part Tariff with Two Consumers .row[.col-7[ ![](img04/2part2.png) ] .col-5[ The price `\(P^*\)` is set higher than `\(MC\)`. `\(T^*\)` is set following the value of the consumer surplus resulting from demand `\(D_2\)`. `$$\pi = 2T^*+(P^*-MC)(Q_1+Q_2)$$` Profits are more than twice as large as the area ABC. ]] --- ## Two-part tariff with many consumers .row[.col-7[ No precise method for the determination of `\(P^*\)` and `\(T^*\)`. The tradeoff between the entry fee `\(T^*\)` and the usage fee `\(P^*\)` must be considered. Low entry fee: high sales and decreasing profits with lower prices and more visitors. ]] .row[.col-7[ To determine the optimal combination, one must chose several combinations of `\(P\)` and `\(T\)`. The profit function to maximize is `$$\pi = \pi_T+\pi_Q = n(T)T +\{P-MC\}Q(n(T))$$` The total profits is the sum of the profits from the entrance fee and the profits from the sales. They both depend on `\(T\)`. Rule * Similar demand: chose `\(P\)` near MC and high `\(T\)`. * Different demand: chose high `\(P\)` and low `\(T\)`. ] .col-5[ ![](img04/2part3.png) ]] --- .row[.col-5[ .col-11[ ![](img04/fra51542_0503.jpg) ]] .col-7[ ## A Tax-Rebate Policy - Welfare comparison The government may want to tax a good like petrol to reduce demand, and pollution. The tax on its own would lower consumers income. But, the tax revenue should find its way back to consumers directly or indirectly. So, will consumers still decrease consumption if the tax is rebated? #### The Substitution Effect of a tax-rebate policy * Even if a consumer is given a direct rebate for a tax on petrol she decreases her consumption of petrol. The tax rebate leads to an **Income-Compensated Demand Curve** * If petrol is a normal good, the effect of the rebate is to offset the income effect of the price increase. It does nothing to alter the substitution effect. * If petrol is an inferior good the rebate still offsets the income effect of the price rise. But, this makes the demand fall more than without the rebate. ]] --- # Compensating variation .row[ .col-8[ ![](img04/fra51542_0507.jpg) ] .col-4[ **Compensating variation**: the amount of money a consumer would need to compensate for a price change ] ] --- .row[ .col-5[ .col-11[ ![](img04/fra51542_0508.jpg) ]] .col-7[ ### The Demand Curve Measure of Compensating Variation ...a slightly more accurate measure of welfare changes than consumer surplus changes that takes account of the income effect. The **compensating variation** of a price rise is the area under an income-compensated demand curve. For a normal good, the compensating variation will be larger than the change in the consumer surplus. ] ] --- class: practice-slide .col-8[ Is the income-compensated demand curve steeper or flatter than the ordinary demand curve for an inferior good? ] ??? Flatter. An increase in income leads to less demand. --- ### Income-compensated demand for an inferior good <img src="img04/ex-inferior.png" width="100%" /> --- # The Discounted Utility Model .col-7[ Time * We now incorporate time into our model because not all outcomes occur at the time of the decision. * Example: The rate of interest influences whether or not consumers take out a loan. Simple and Compound Interest * Simple interest is computed using the following formula: `$$L=PR$$` `\(L\)` is amount owed, `\(P\)` is the principal, `\(R=1+r\)`, where `\(r\)` is the rate of interest. * Compound interest is computed using the following formula: `$$L=PR^t$$` ] --- class: practice-slide ## Interest .col-8[ You borrow $1000. Which credit card will cost the most to pay back? ] .col-11[ ![](img04/c8-009-1.png) ] ??? ``` ## [1] 247.2 ``` ``` ## [1] 387.5 ``` ``` ## [1] 248.2 ``` ``` ## [1] 213.5 ``` ``` ## [1] 296.5 ``` ``` ## [1] 332.5 ``` ``` ## [1] 294.5 ``` --- .row[ .col-6[ ![](img04/c8-009-1.png) ```r 1000*.1992 + 48 ``` ``` ## [1] 247.2 ``` ```r 1000*.1375 + 250 ``` ``` ## [1] 387.5 ``` ```r 1000*.1992 + 49 ``` ``` ## [1] 248.2 ``` ] .col-6[ ```r 1000*.1775 + 36 # lowest total fee ``` ``` ## [1] 213.5 ``` ```r 1000*.1975 + 99 ``` ``` ## [1] 296.5 ``` ```r 1000*.1825 + 150 ``` ``` ## [1] 332.5 ``` ```r 1000*.2225 + 72 ``` ``` ## [1] 294.5 ``` ]] --- class: practice-slide .col-8[ You put 100 Euro into a savings account. Your bank promises an annual rate of 5%. What is your balance after 1 year? 10 years? 50 years? ] --- class: practice-slide .col-8[ You put 100 Euro into a savings account. Your bank promises an annual rate of 5%. What is your balance after 1 year? 10 years? 50 years? `$$P\times(1+r)^t=FV$$` ```r 100*(1.05)^1 ``` ``` ## [1] 105 ``` ```r 100*(1.05)^10 ``` ``` ## [1] 162.8895 ``` ```r 100*(1.05)^50 ``` ``` ## [1] 1146.74 ``` ] --- # Exponential Discounting .col-7[ People discount the future and hence prefer their rewards sooner than later. Example: Tom prefers to have $100 today rather than $100 next year. A person's time preference represents the extent to which they discount the future. Exponential discounting is designed to capture this phenomenon. Let `\(u>0\)` be the utility you get from getting a Euro now. Getting a Eruo tomorrow is worth slightly less to you. Hence, we multiply it by a discount factor `\(\delta\)` between 0 and 1: `\(\delta u\)` Getting a dollar the day after tomorrow is worth even less. Thus, we multiply it by an additional `\(\delta\)`: `\(\delta^2 u\)` ] --- # Exponential Discounting .row[.col-7[ If we are interested in the entire utility stream `\(u=<u_0,u_1,u_2,\dots>\)`, the discounted utility from the point of view of time zero is given by the following expression: `$$U_0(u)=\delta^0u_0+\delta^1u_1+\delta^2u_2+\ldots$$` This is the delta function. ]] .large[.row[.col-7[ Suppose `\(\delta = 0.9\)` and you are making a decision at `\(t=0\)`. What is the value of each choice? What about `\(\delta=0.1\)`? ] .col-5[ ![](img04/c8-022-1.png) ]]] ??? ```r 1 * 0.9^0 ``` ``` ## [1] 1 ``` ```r 3 * 0.9^1 ``` ``` ## [1] 2.7 ``` ```r 4 * 0.9^2 ``` ``` ## [1] 3.24 ``` ```r 1 * 0.9^0 + 3 * 0.9^1 + 4 * 0.9^2 ``` ``` ## [1] 6.94 ``` --- # Exponential Discounting .col-11[ ![](img04/c8-025-1.png) ] --- # The Intertemporal Choice Model .row[.col-6[ How would rational consumers distribute their consumption over time? Two time periods: current and future. Two alternatives (goods): current consumption (C1) versus future consumption (C2). ] .col-6[ ![](img04/fra51542_0514.jpg) ]] --- # Present value .row[ .col-6[ ![](img04/fra51542_0515.jpg) ] .col-6[ **Present value**: the present value of a payment of `\(X\)` euros `\(t\)` years from now is `\(X(1 + r)^t\)`, where `\(r\)` is the annual rate of interest. **Present value of lifetime income**: the horizontal intercept of the intertemporal budget constraint ] ] --- .row[.col-9[ ![](img04/fra51542_0516.jpg) ] .col-3[ ### Intertemporal Budget Constraint with Income in Both Periods, and Borrowing or Lending at the Rate `\(r\)` ] ] --- ## Marginal rate of substitution over time .row[ .col-6[ ![](img04/fra51542_0517.jpg) ] .col-6[ ...is the number of units of consumption in the future a consumer would exchange for 1 unit of consumption in the present. The marginal rate of substitution (**MRS**) declines as one moves downward along an indifference curve. ] ] --- ## The Optimal Intertemporal Allocation ![](img04/fra51542_0518.jpg) --- # Patience and Impatience ![](img04/fra51542_0519.jpg) --- class: practice-slide .col-8[ Assume that the interest rate falls. Do you you consume more or less today? ] ??? The **income effect**... * A borrower has more income after an interest rate fall. So, her income effect is to consume more in both periods. * A saver has less income after an interest rate fall. So, her income effect is to consume less in both periods. The **substitution effect** after a fall in the interest rate is always to increase current consumption and reduce future consumption. --- **The effect of a fall (or rise) in the interest rate depends on whether the consumer is a borrower or a saver.** .row[.col-8[ The **income effect**... * A borrower has more income after an interest rate fall. So, her income effect is to consume more in both periods. * A saver has less income after an interest rate fall. So, her income effect is to consume less in both periods. ] .col-4[ The **substitution effect** after a fall in the interest rate is always to increase current consumption and reduce future consumption. ]] .col-8[ ![](img04/fra51542_0520.jpg) ] --- .row[ .col-6[ ![](img04/fra51542_0522.jpg) ] .col-6[ ### Permanent Income, not Current Income is the Primary Determinant of Current Consumption **Permanent income**: the present value of lifetime income. ] ] --- .row[ .col-6[ ![](img04/c9-007-1.png) ] .col-6[ ## Time (In)consistency The **standard model of exponential discounting** fails to capture the manner in which people's preferences appear to change over time. One's behavior is time consistent if their preferences over two options do not change just because time has passed. ] ] --- # The Beta-Delta Function .col-7[ The utility `\(U_0(u)\)` of utility stream `\(u=<u_0,u_1,u_2,\ldots>\)` from the point of view of time zero is: `$$U_0(u)=\delta^0u_0+\beta\delta^1u_1+\beta\delta^2u_2+\ldots$$` This the beta-delta function. We assume that `\(0<\beta\leq1\)`. Note that `\(\beta\)` is not raised to higher powers for more distant rewards. ### Impulsivity vs. Impatience The parameter `\(\delta\)` can be said to capture a person's **impatience**. The parameter `\(\beta\)` can be said to capture a person's **impulsivity**. ] --- # Preferences over Profiles .row[ .col-4[ Some people also like to distribute pleasant and unpleasant events over time. If so, they are said to exhibit a _preference for spread._ People might also have preferences over shapes of utility profiles. They might prefer increasing profiles, and/or like to end on a high note. ] .col-8[ Watch Daniel Kahneman's TED-talk on [_The riddle of experience vs. memory_](http://www.ted.com/talks/daniel_kahneman_the_riddle_of_experience_vs_memory.html) <div style="max-width:854px"><div style="position:relative;height:0;padding-bottom:56.25%"><iframe src="https://embed.ted.com/talks/daniel_kahneman_the_riddle_of_experience_vs_memory" width="854" height="480" style="position:absolute;left:0;top:0;width:100%;height:100%" frameborder="0" scrolling="no" allowfullscreen></iframe></div></div> ]] --- # Peak / End Rule .row[ .col-7[ When people assess a past experience, they pay attention above all to two things: how it felt at the peak and whether it got better or worse at the end. ]] .row[.col-5[ * The peak-end rule represents one way to evaluate the desirability of utility streams. * Here, individuals care about the peak and the end of the utility stream, as opposed to the discounted utility. ] .col-7[ ![](img04/c9-001.png) ]] --- ## Preferences over Profiles and UX Design .col-7[ ![](img04/progress+bar+pauses.png) A study found that progress bars with accelerating progress were strongly favored over decelerating progress. This means that progress bars _with the fastest progress occurring near the end of the process_ were perceived faster than progress bars _with pauses near the process conclusion_. ]