a. Propose a utility function that you think makes sense for a consumer to evaluate consumption in t=1 and t=2. b. What is the Marginal Rate of Substitution (MRS) between current and future consumption based on your utility function? c. Write down the (intertemporal) budget constraint. d. Now assume that you are very impatient: you very much prefer to consume today, rather than delaying your purchases to next year. How would you change the utility function to model this impatience? Do you this impatience is realistic as a model of human behavior?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
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