# Economics Model Answers Ten - 2013

Economics Homework - [1 - 2 - 3 - 4 - 5 - 6 - 7 - 9 - **10** - 11 - 12]

1. In your own words, try to give a better definition of "externalities" than provided by this Lecture.

- A positive or negative effect by a transaction on someone other than the buyer or seller.

- "Externalities are positive or negative effects, not including the buyer and seller, created by a transaction." (by student CM)

2. Explain what "derived demand" is, and provide an example.

- "Derived demand" means that the demand for inputs to a firm, such as the factors of production, is dependent or "derived" from the demand for final finished goods or services that the firm is selling to the public.

- "A derived demand is when a business owner makes a decision on how much it will cost to run his business and how much demand is for his goods so he can decide how many workers to hire." (by student TH)

3. What is your favorite question on one of the quizzes that *you answered incorrectly*, and why is it your favorite?

- (answers vary among students)

4. Give an example of a positive externality, and an example of a negative externality. The example does not have to be limited to a business.

- The printing press inventor by Gutenberg had an enormous positive externality, enabling all of society to benefit from the new books that were printed (especially the Bible). Gutenberg himself did not become rich from his marvelous invention. A negative externality is any kind of pollution, such as smoke from a smokestack that makes it unpleasant to live downwind from it.

5. Explain why private firms in the free market are unlikely to try to provide public goods.

- It is impossible (or very difficult) to exclude the free use of public goods by people who not pay for them, such as Central Park in New York City. Charging admission to Central Park to limit who can use the massive park would be virtually impossible.

- Private firms cannot make money off something if the public can just use it for free. So private firms in the free market are unlikely to try to provide a public good.

6. Review question: the cross-elasticity of A with respect to B is positive, and C with respect to D is negative. What is the relationship (complement or substitute?) of goods A and B with each other, and C and D with each other? Explain.

- Goods A and B are substitutes, because when the price of one of them goes up, the other good sees its demand increase because it can be used instead.

- Goods C and D are complements. The Law of Demand says that the as the price of Good C increases, its demand decreases. But because Goods C and D have negative elasticity, the demand for Good D decreases also when the price of Good C increases, which shows that Goods C and D are used together as complements (like cars and tires for cars).

7. List the four factors of production and give a very brief explanation of each.

- Land. Land is needed for most firms. For example, gas stations and all retail stores need land in order to sell their goods to customers. Even providers of services, such as call centers to handle customer requests over the phone, need land at which to be able to have an office for talking on the phone.

- Capital. Capital is money, which all firms need to pay expenses. But notice that not all firms need much capital to start. A new car company would need perhaps $1 billion to start, but a new comedian does not need much money to start.

- Labor. Firms need workers, and that is called "labor". Even a new comedian needs labor - his own time to tell jokes.

- Entrepreneurship, which is the efforts by the owners and new workers to make a new firm a success.

### Honors

Answer 3 out of the following 4 questions:

8. Explain why marginal revenue must be zero when total revenue is maximized.

- When total revenue is maximized, then no additional revenue is possible. Increasing output at that point must have marginal revenue of zero.

- "Marginal revenue must be zero when total revenue is maximized because marginal revenue is the additional revenue gained by selling one more unit. And total revenue is the revenue earned from all of your sales. If total revenue is maximized, that means you are earning all you can earn and selling all you can sell. Therefore, (since you can't sell anymore), you can't have marginal revenue (since that is revenue earned for selling one more unit)." (by student MY)

- "Marginal revenue must be zero when total revenue is maximized by the definitions of marginal and total revenue. Marginal revenue is the extra revenue generated by another unit of output, while total revenue is the revenue of a firm for its current output. If total revenue is maximized, any further increase in output would not result in increased revenue; therefore, marginal revenue is zero." (by student NL)

9. Provide, in your own words, the best definition of "public good" that you can.

- A public good is a good which is either available to everyone in an area or available to no one, like music during a loud rock concert outside.

10. Identify a concept in economics that you found difficult to understand at first, but then explain how you were able to eventually understand it.

- (answers vary among students)

11. What is the price elasticity of demand for this demand curve: P=30/Q. Explain.

- Its price elasticity is 1 (unit elasticity).

- An easy way to understand this is to realize that because P=30/Q, it must be true that P times Q equals 30 for all P and all Q. But revenue is P times Q, and thus revenue is always constant no matter what the price is. Changing the price does not change the revenue, and thus this is unit elasticity.

- A more rigorous mathematical proof based on the equation for elasticity is as follows:

- P
_{ed}=(%change in Q)/(%change in P)

- P

- If the new P and Q are denoted by P
_{2}and Q_{2}, and the old P and Q are denoted by P_{1}and Q_{1}, then:

- If the new P and Q are denoted by P

- P
_{ed}=((Q_{2}-Q_{1})/Q_{1})/((P_{2}-P_{1})/P_{1})

- P

- But the above formula is simply an approximation, and the higher precision provided by calculus is needed to prove this rigorously. So we rewrite the above equation using calculus, such that P
_{ed}equals:

- But the above formula is simply an approximation, and the higher precision provided by calculus is needed to prove this rigorously. So we rewrite the above equation using calculus, such that P

- where you can think of "dQ" as replacing a tiny change in Q (i.e., Q
_{2}-Q_{1}) and "dP" replacing a tiny change in P (i.e., P_{2}-P_{1}) in the above equations. "dQ/dP" is the "differential" of Q with respect to P (i.e., the tiny change in Q based on a tiny change in P).

- where you can think of "dQ" as replacing a tiny change in Q (i.e., Q

- We can now solve the differential equation for P
_{ed}by substituting in Q=30/P:

- We can now solve the differential equation for P

- differentiating in the first half and substituting P=30/Q in the second half yields:

- substituting in Q=30/P and P=30/Q yields:

- and thus P
_{ed}= -1. By convention, because price elasticity of demand for one good is always negative, the negative sign is dropped and we have our answer: price elasticity is 1. (Price cross-elasticity of demand may be positive or negative, depending on whether the two goods are substitutes or complements.)

- and thus P