# Economics Homework Ten - Model

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

- Some sort of effect, whether negative or positive, on a party other than the buyer or seller. (Michelle)

- Externalities are the results of a good or service that can have benefits or drawbacks for a person not involved with the transaction. (Anna)

- The positive or negative effect of a transaction on persons other than the buyer and seller. (Aran)

- Externalities are the costs or benefits that happen to people who are outside the transaction. (Isaac)

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

- Marginal revenue is zero because it cannot be positive or negative. Because revenue is at its maximum so you can't increase it any, so marginal revenue can't be positive. Same for negative. If it were negative it would reduce the output by one unit and have the effect of increasing the total revenue. That isn't possible because total revenue is at its maximum so then marginal revenue must be zero. (Seth)

3. What is your favorite question on the midterm exam that *you answered incorrectly*, and why is it your favorite?

- Question 30 regarding cross-elasticity is the one I find most interesting. Cross-elasticity is a very difficult concept, yet it is an extremely important concept to know in Economics. (Amanda)

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.

- A positive externality might be the printing press; its inventor, Gutenberg, never became rich and actually had all his equipment taken in a lawsuit, but his invention created an enormous benefit for society. A negative externality might be the noise created when aircraft take off from an airport: people living nearby have to endure the sound although they did not pay for a ticket. (Duncan)

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

- Private firms are not likely to provide public goods because no one is willing to pay for them! Since no one can be excluded from the benefit of a public good, even if they don't pay for it, no one is going to want to pay for it if they don't have to. (Trisha)

- It would be a bad idea because if one person bought it, then any number of people could enjoy it without paying. (Mark)

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. They are substitutes because as the price of one good goes up, the other good, which is at a lower cost, will be purchased in place of it. Goods C and D are complements. They are complements because the negative elasticity shows that they goods are bought or used together. The increase in demand of good C will, also, increase the demand of good D. (Allie)

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

- Land - the firm must make a decision as to where they will provide their goods and services. They wouldn't want to sell where the demand for the good or service wasn't very high; they would choose a place with higher demand. (Lucia)

- Capital - money (Sarah)

- Labor - how many workers do you need (Anthony)

- Entrepreneurship - efforts of the owners and managers to bring the business to life (Tim)

8. Mathematically prove (or disprove!) the answer to the question on the midterm exam about P=30/Q.

- Teacher: Given that P=30/Q, then P times Q must equal 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.

- But a more rigorous mathematical proof based on the equation for elasticity is desired:

- 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.)

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

- A good that cannot in any way be excluded from someone. For example, a park. (Kate)

10. Find a question on the midterm that describes a situation that would be unusual in the real world, and explain why the scenario of the question is unrealistic.

- Question 21 on the girl’s midterm exam is an example of an unusual situation. Question 21 is a graph of perfect substitutes and in real life it is very unusual to have something that can perfectly substitute for another. Everything is different and one item that could make you as perfectly satisfied as another is almost unheard of. (Veronika)

- "#16: If a firm's total revenue were maximized then its marginal revenue must be zero." This is an impossible situation because a firm's revenue is never maximized; a firm can always produce one more unit to make more revenue. (Will)

11. Revisit the problem on the midterm about the price ceiling (with the graph), which asked how much the shortage would be. Provide the correct answer and explain why. (If you answered it correctly, then provide a similarly difficult substitute question for this.)

- The correct answer is shortage of 600. A shortage occurs because a price ceiling increases demand, without adjusting output- in fact, output will ... decrease, because producers are now making less money. Specifically, the shortage can be measured by measuring the quantity between where a line representing the price ceiling intersects the supply curve and demand curve. (Addison)