Please help me with this assignment that is more than an essay, it is a way to experience the estimation of the consumer's preferences, the single consumer demand, the aggregate demand, the elasticity, and the cross-price elasticity. Follow the instructions listed below. Main contents of your work to be presented in a short written 'paper' in which you present: An introduction that explains the reasons behind the choice of the goods in the consumers' basket; A description of the preferences obtained with some comments or evaluations of results and the representation of the indifference curves obtained with the interpolation procedure (please attach also the excel file with the answers to the questionnaire); The representation of the demands of the individual consumers and the aggregate demand; The computation of elasticities; Some general comments and conclusions. It will be evaluated according to these criteria: the rigor of the analysis; the originality in the goods and in the market choice; the clarity in the exposition.

The goal of the assignment is to estimate the own and cross price elasticity of two goods to charac- terize the demand of a simple market (made of two goods) you are interested in. You can imagine to be a

consulting firm doing market analysis, or the marketing department of a company that is considering how to deal with the competition. Choose an ideal small market made of only two goods. You can think of two potential substitutes (e.g. tea and coffee for breakfast) or potential complements (e.g. coffee and sugar); it is important that

you believe the two goods to be part of the SAME market (linked by a relationship either of complemen- tarity or of substitutability). You can use general goods (e.g. coffee, tea, milk, cars, computers), or general

differentiated goods (e.g. red vs. white cars, white vs. green tea), or branded differentiated goods (e.g. Apple vs. Samsung smartphone). Choose what you are curious about! Below is the explanation in the steps to follow to get the own and cross price elasticity of the two goods. You start by estimating the individual preferences over the two goods of a sample of consumers through online interviews. Then, you derive the individual demand for the two goods as a function of the two prices, and aggregate them to the market demand. Finally, you can compute the own and cross elasticity of demand and verify whether your starting assumption about the complementarity or substitutability of the goods is confirmed.

1. Estimate consumer preferences

make a short questionnaire to be addressed to at least 5 consumers selected according to the market target. The questions have the goal of estimating the indifference curves for each consumer. The goal of the questionnaire is to get at least three points on the same indifference curve to plot it in the two-variable graph. Be careful about the structure of the questions: guide the consumer to answer according to his/her perception of indifference (constant satisfaction/happiness level). Remember that to plot a curve (not necessarily a line) you need at least three points; the more points you have, the more you can be precise. Moreover, remember to ask a question about the income allocated to the consumption of the two goods. Example for the market of generic coffee and tea: Q1. How many cups of tea you consume (or would like to consume) everyday? Q2. How many cups of coffee you consume (or would like to consume) everyday? Q3. How much would you allocate everyday to consume coffee and tea? Q4. Imagine you have to reduce the consumption of coffee (one cup less than desired). How many cups of tea would help you stay as satisfied as before about your drinking? Q5. Imagine you increase your consumption of coffee (2 cups more than before). Would you reduce your consumption of tea? By how many cups? Administer the questionnaire by using an online platform (e.g. Survey Monkey or Google Forms) or personal interviews if you prefer.

For each consumer separately, use the points obtained to fit the indifference curve. Use an interpola- tion tool of your choice (e.g. Wolfram Alpha) and find the shape that you think is best suited (you

should probably avoid the linear and go with quadratic, cubic or exponential).

2. Derive the aggregate demand

Using the indifference curve estimated and the income declared by the consumer in the survey, find for each consumer his/her demand as a function of prices for the two goods separately through the constrained utility maximization problem. Pay attention to the optimality condition: since you don't have the utility function but the indifference curve expression, you can directly get the Marginal Rate of Substitution through the total derivative of the indifference curve. Sum up the individual DIRECT demands (the quantities, not the prices!) for each good to get the two aggregate demand functions D1(p1, p2) and D2(p1, p2).

3. Compute the own and cross elasticities

Now that you have D1(p1, p2) and D2(p1, p2), you can compute the elasticity of demand for each good with respect to its own price as D1,p1 =D1(p1, p2)/p1*p1/D1(p1, p2) , D2,p2 =D2(p1, p2)/p2*p2/D2(p1, p2)

and the cross elasticity as D1,p2 =D1(p1, p2)/p2*p2/D1(p1, p2) , D2,p1 =D2(p1, p2)/p1*p1/D2(p1, p2) Comment the four results considering both the sign and the magnitude. Draw your conclusions on the relationship between the two goods, also with reference to your expectations before the experiment.