Suppose There Are 1 Billion Tons of Titanium Dioxide in the World

question 3

Essay

Suppose there are 1 billion tons of titanium dioxide in the world and two periods: sooner and later. What we use sooner, we can't use later. Titanium is sometimes used to build rocket ships and road bikes among other light and durable products. With Q representing the quantity of titanium used sooner, the marginal benefit (net of any costs) from titanium used sooner is MB_sooner = .6 billion - Q. The (net) marginal benefit from titanium used later, MB_later, is constant at .6 billion. That is, every unit of titanium used later has a marginal benefit of .6 billion.
a) Illustrate this situation with a two-period model (as shown in the textbook) that includes both marginal benefit curves, labeled MB_sooner and MB_later.
b) If we don't discount benefits received later, what is the dynamically efficient quantity to use sooner? _______.
c) If the present value of benefits received later is one-half of their value later, what is the dynamically efficient quantity to use in each period? Sooner ________ Later ________
d) If we have an infinite discount rate for benefits received later, what is the dynamically efficient quantity to use in each period? Sooner ________ Later ________

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Definitions:

Null Hypothesis

The default hypothesis that there is no significant difference or relationship between specified populations, any observed difference being due to sampling or experimental error.

Directional Alternative

A hypothesis that outlines the anticipated direction in the variation or association among variables.

T-statistic

A T-statistic is used in statistical testing to determine the significance of the difference between the means of two groups relative to the spread or variability of their scores.

Means

Statistical measures that represent the average value in a set of numbers, calculated by dividing the sum of all numbers by the count of numbers.