Given the assumptions of Hotelling's rule and constant...

Name: Problem 1, Chapter 14: Environmental Economics and Natural Resource Management, 3rd Edition
Uploaded: 2019-12-17T19:40:18-08:00
Duration: 4 min 59 s
Channel: Brett Boyer
Description: Given the assumptions of Hotelling's rule and constant extraction costs, what is the total value of a stock of 1 million "dry long ton units" of extractable iron ore if the current price is 40 cents per dry long ton unit and the extraction cost is 25 cents per dry long ton unit?

Given the assumptions of Hotelling's rule and constant extraction costs, what is the total value of a stock of 1 million "dry long ton units" of extractable iron ore if the current price is 40 cents per dry long ton unit and the extraction cost is 25 cents per dry long ton unit?

Key Concepts

Hotelling's Rule

A principle in resource economics that states the net price (market price minus extraction cost) of a non-renewable resource should increase over time at a rate equal to the interest rate. This rule is used to guide decisions about when to extract the resource to maximize its value over time, assuming that delaying extraction can generate additional financial returns.

Constant Extraction Costs

This assumption implies that the cost needed to extract each unit of a resource remains unchanged over time regardless of how much is extracted or how depleted the resource becomes. It simplifies the analysis of resource valuation and extraction timing under Hotelling’s rule by keeping the cost component fixed.

Net Price Differential

The difference between the current market price of a resource and its extraction cost. This margin represents the immediate profit per unit and is central to evaluating the economic value of the resource stock, since it factors into the incentive for extraction versus delaying for future gains.

Resource Stock Valuation

A method of assessing the total value of a resource deposit by multiplying the net profit (market price minus extraction cost) per unit by the total number of extractable units. Under the assumptions of Hotelling’s rule and constant extraction costs, this provides a straightforward calculation of the present value of the entire resource stock.

Transcript

00:01 Okay, so the problem gives us a marginal cost function.

00:06 Here, i've called the marginal cost function c prime of x, because for all the economics formulas, you can really think of the word marginal as saying derivative.

00:15 So in this case, it's the derivative of the cost function that i'm calling c of x, and then an initial cost, so a cost for zero units of $100 ,000.

00:27 Here, we are first asked to find the cost of extracting the first 50 -tenths, of ore from the mine, and then we're asked for the cost for the next 50 tons.

00:36 So in both the cases, we're going to use the net change theorem, which i've indicated on the right side kind of up in the corner.

00:43 So for the first 50 tons, it's pretty straightforward.

00:46 We just need the value c of 50, which will be the cost of extracting 50 tons.

00:54 And so going by what the formula says, we have that as c of zero plus the integral from 0 to 50, and now this marginal cost function was given in thousands of dollars per ton.

01:09 So what i'm going to do is multiply the whole thing by 1 ,000 to make it come out as dollars.

01:15 So it matches what co0 is.

01:17 So for that, we will get 600 plus 8x dx.

01:27 So this is going to be 100 ,000 plus 600x.

01:35 Evaluated from 0 and 50 plus 8 over 2 x squared evaluated at 0 and 50.

01:45 Now these two zeros cancel because when you plug in 0 for the x in either of those terms, it's just going to equal 0.

01:56 So we don't have to evaluate those...