Science:Math Exam Resources/Courses/MATH101 C/April 2024/Question 18 (a)

MATH101 C April 2024

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Question 18 (a)

In a particular market, the demand and supply functions for a quantity $q$ of a good are given below: $$D(q)={\frac {1}{2^{q}}}+1,\qquad S(q)={\begin{cases}0&{\text{ for }}q\leq 10\\{\frac {q}{10}}-1&{\text{ for }}q>10.\end{cases}}$$ (a) Aside from its name, how can you tell that $D(q)$ is the demand function (and not the supply function)? Circle the best way to complete the sentence, "$D(q)$ is the demand function, because ..." A. $D(q)\geq 0$ for all q. E. it is not piecewise defined. B. $\lim _{q\to \infty }D(q)=0.$ F. it is increasing. C. it has an asymptote. G. it is decreasing. D. $\int _{-\infty }^{\infty }D(q)\mathrm {d} q=1.$ H. it is continuous.

Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you?

If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it!

Hint
Recall that the demand is the price per unit that customers are willing to pay when $q$ is the total number of units available in the market. What should happen to the demand as the number of units available in the market increases?

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Solution
As more of a product is available in the market, it is easier to obtain, so the price per unit that a customer is willing to spend goes down. Therefore, we should expect the demand to be non-increasing in $q$. Thus, the correct answer is G. We know that $D(q)={\frac {1}{2^{q}}}+1$ because that is the only non-increasing function out of the two options.