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:

Price-Earnings Ratio

A valuation metric indicating the ratio of a company's stock price to its earnings per share, used to evaluate the relative value of shares.

Return On Assets

A measure of a company's profitability, indicating how efficient it is at using its assets to generate earnings.

Statement Of Cash Flows

A report detailing how shifts in income and balance sheet figures impact cash and its equivalents.

Cash Balance

The amount of cash or cash equivalents that a company or individual has available at any given time.