Questions and Answers about Discounting Function

Comparing Responses for Inconsistent Discount Function

These are answers to questions we asked the professor, please try to follow her answers to get a sense of what she wants  when trying to see whether the discount function is inconsistent with the assumption that it decreases, should we compare the responses between the two sessions or across each session separately? Please check for each individual within each session. ii. In relation to the economist’s assumption that D(t) is decreasing - are we looking at the exponential discounting function that we learned in class wherein the discount rate of 1 - sigma signifies individuals get more patient with time?

If I did not say that you should assume a particular functional form, do not assume a particular form. For example, if I say that you should only think about a general assumption of D(t) decreasing in t, do not assume a particular functional form. iii. Should we look at one session in isolation for each ID to figure out whether the individual is stationary or not? (since the class slides assume t0 i.e. only the first time period)? Or do we look at both sessions and compare only the first time period or do we look at all time periods? In the slides you will find how to check for time invariance, consistency, and stationarity. In your answer, explain clearly how the data that you were given allows you to measure the particular property that you selected for your answer.

It is possible that some of the properties cannot be measured. iv. Should we talk about the properties of the general function form such as non-stationary, non-consistent (slide 30 from discounting) when we have to provide an intuition in part Yes, talk about the property that is violated and say how your choice of the functional form helps to capture this violation.

Does the essay have to be 2 pages single or double spaced? What is the minimum we are expected to write? What format does the essay have to be and can we use the readings from lectures as resources? I am expecting between 1 and 2 pages. Single-spaced 12pt Please use standard font that is easy to read. You can definitely use readings from the lectures as resources. Also, in question 2, you've asked us to use the original utility function for parts c-f. Do you mean the utility function given in the question itself or some other function?

Exponential Discounting Function and Decreasing Discount Rate

I have a question about the midterm exam regarding question 2. In part b, how exactly do we incorporate the reference point of 1000 in the function? Like im confused on how to approach that question. I have tried and looked at the lecture slides but I still struggled. In class we did a simpler straightforward question by just finding the utilities but here we need to modify the function to make it more realistic and I don't understand how to do that.

I wanted to provide a couple more clarifications. I did not address one very specific question that one of you sent, because I felt like it would be giving the answer away. The rest should be addressed with the clarifications below. Do let me know if it looks like I made a typo that is important for the understanding of the concepts (terrible jetleg here). 1) Use the explanation below together with slides 39-40 in the lecture notes on discounting. Time invariance Time invariance implies that if I decide between $x today and $(x+y) in a fixed amount of time, I will make the same decision no matter when I am asked. Example of two decisions that form a violation of time invariance: On Oct 30th, you chose $6 on Oct 30th over $8 a week from Oct 30th B. On Nov 30th, you chose $8 a week from Nov 30thover $6 on Nov 30th Note that on Oct 30thand on Nov 30th, I was asked to make exactly the same choice $6 now or $8 in a week, but I made different decisions on these two dates.

You can also think about application to ageing, if people become less or more patient as they age, then their preferences violate time invariance. Stationarity Stationary preferences imply that today your preference between $x sooner and $(x+y) later is always the same as long as the delay stays the same. No matter when in the future the rewards are received if the delay between the sooner and later reward is the same, you should be making the same decision now. Here, you do not vary when the decisions are made. You vary the sooner and later date when the rewards are received, keeping the delay between sooner and later fixed and keeping the date when you are making the decision fixed. Example of two decisions that violate stationarity: Today, you choose $6 in a week over $8 in two weeks. Today, You choose $6 in two weeks over $8 in three weeks. Notice that the delay between sooner and later in both decisions is the same = 1 week. I made both of the decisions on the same date. Time consistency Time consist chooser makes the same decisions when she plans for the future today and when that future arrives.

Example of two decisions that violate time consistency Today, I decide that I prefer $10 in three months over $6 in a month. In a month, I decide that I prefer $6 today over $10 in two months.The delay between the sooner and later is always the same = 2 months. Moreover, the sooner and later rewards are received on exactly the same dates in both of the decisions. However, the date on which I was asked to make the decision is different in A and B Should we “include the IDs for the students that do not change their preferences at all within a session?”if there is a decreasing discount function, that can capture this behaviour, then do not include these preferences. Should we “compare both the responses from sessions 1 & 2 for each student or if we address both sessions and their answers without comparing the two”. focus on within individual within each session separately. In 1b) you need to compare session 1 to session 2 for each participant.