There Are at Least Two Different Possible Approaches to the Problem

question 4

Essay

There are at least two different possible approaches to the problem of building a model of the costs of production of electric power.
I: Model I hypothesizes that per-unit costs (C) as a function of the number of kilowatt-hours produced (Q) continually and smoothly falls as production is increased, but it falls at a decreasing rate.
II: Model II hypothesizes that per-unit costs (C) decrease fairly steadily as production (Q) increases, but costs decrease at a much faster rate for hydroelectric plants than for other
kinds of facilities.
Given this information,
(a) What functional form would you recommend for estimating Model I? Be sure to write out a specific equation.
(b) What functional form would you recommend for estimating Model II? Be sure to write out a specific equation.
(c) Would $\overline { \mathrm { R } } ^ { 2 }$ be a reasonable way to compare the overall fits of the two equations? Why or why not?
Note: In the following question, you may want to change the absolute size of the coefficients, depending on the size of your school, but remember to change the size of the standard errors proportionally.

---

Definitions:

R Terminal

The R Terminal is typically found in automotive applications and refers to the terminal on an alternator or generator used for relay activation or tachometer connections, signaling the engine's RPM.

Maximum Output Test

A procedure designed to determine the highest level of performance that a system, component, or machine can produce under specific conditions.

Heavy-Duty Truck

A classification of trucks designed for the commercial transport of heavy goods, characterized by large payload capacities.

Engine Rpm

A measurement indicating how many times the engine's crankshaft completes a full rotation every minute, crucial for assessing performance.