Applied Economics Cost-Benefit Analysis Problem
The development of online bookstores has had a dramatic on the way in which we buy books. The Amazon.com website started in 1995 as one of the first online bookstores. By 1999, books were the second largest market segment of internet sales, only surpassed by online computer sales. Currently the online book market is a billion dollar industry, with Amazon and Barnes and Noble the market leaders.
Buying books online provides a number of benefits to consumers. First, it provides convenience. Rather than requiring a trip to the store, online stores allow the customer to purchase their book from the privacy of their home at any hour they choose. Second, online sales have the potential to reduce the cost of book purchases. While there is added shipping cost of an online book sale, an online book dealer can save money through economies of scale, the warehousing of inventory, and savings in labor costs. Third, online bookstores increase product variety. While a large "brick-and-mortar" bookstore might be able to carry tens of thousands or, possibly, 100,000 unique titles, online book sellers can offer literally millions of book titles.
One tangible outcome of the increased variety is an increase in the sale of hard to find or obscure book titles. While the traditional brick-and-mortar store might be able to special order most books requested by a customer, they generally do not stock books that have very low sales volume. This generally means that the customer must know the book that he or she is wishing to order. In contrast, internet book sellers can maintain a "virtual inventory" of hard to find titles. If the online dealer does not have the book in inventory, they can still offer it through arrangements with third party distributors. Advanced electronic searches and personalized recommendations allow customers to be made aware of obscure titles for sale, even if the customer was not looking for that particular book.
For assignment you will estimate the dollar value that consumers place on the benefits from increased product variety and availability of obscure titles available through internet markets.
While much of our work throughout this course will use Marshallian demand and consumer surplus to estimate benefits, in this case one can estimate the theoretically-preferred equivalent variation measure. To do this you'll first assume an indirect utility function to derive an explicit formulation of equivalent variation. Next, you'll find data (along with a simplifying assumption or two) to empirically estimate that formulation.
1. Algebraically solve for a correct measure of consumer welfare from the increased product variety in online book sales. Please show your work.
Review the concept of equivalent variation, compensating variation, and consumer surplus in your class notes, Appendix 3A in the Boardman et al. textbook, and your microeconomic textbook to make sure that you understand the concepts. Wikipedia also offers a relatively simple description of both equivalent variation and compensating variation. In fact, Wikipedia gives a pretty good summary for many of the concepts below. Note that we use "m" for income (rather than "y" or "w") and we denote the expenditure function, below, as m(p,v) (rather than e(p,v) or e(p,u)).
Assume that the (single good) indirect utility function takes the form
v(p, m) = -A(p1+α/1+α)+(m1-δ/1-δ).
Where v(.) is utility, p are prices, and m is income.
a. Solve for the Marshallian demand function using Roy's identity.
b. Using your Marshallian demand function.
i. Calculate the own price elasticity of demand.
ii. Calculate the income elasticity of demand.
c. Solve for the expenditure function, m(p,v). Using the indirect utility function, given above, solve for income, m, in terms of prices, p, and utility, v. (Note: The expenditure function is not going to be as simple as the Marshallian demand.).
d. Solve for the Hicksian demand curve using Shephard's lemma. (Note: You won't use the Hicksian demand below, but it is good to know how to calculate it.)
e. Solve for the equivalent variation of a price change using your expenditure function. Show all of your work. These steps should help you do this:
- Set up the subtraction problem using the expenditure functions, m(p, v). Remember that the equivalent variation uses the utility level after the change, v1 (not the utility level before the change, v0).
- Recall that m(p1, v1) is going to be the same as m(p0,v0) because the individual is on a new utility curve with the new prices, but income hasn't changed. So set m(p1, v1) = m. (To convince yourself of this look at the class notes diagram of equivalent variation and where budget constraints intercept the y-axis.)
- Remove v1 by subtracting m(p1, v1)1-δ and adding m1-δ inside your equation for m(p0, v1). All you have done here is added and subtracted the same thing because we know that m(p1, v1) = m. The reason that you subtract m(p1, v1)1-δ but add m1-δ is to make things easier later.
- Using the Marshallian demand function from above, solve for A as a function of p, x, and m. Be careful here! Because the equivalent variation has both initial prices, p0, and prices after the change, p1, you are going to have to keep track of whether A is a function of p0, x0, and m or p1, x1, and m. When solving for the A next to p0, solve for it in terms of p0, x0, and m. When solving for the A next to p1, solve for it in terms of p1, x1, and m.
- Since we are solving for the welfare effect of the introducing a new product, the initial quantity, x0, was zero. Therefore, set p0·x0,=0.
- Simplify your equation for equivalent variation.
f. Briefly explain the assumption you would need to make about δ to make this equation equal to EV = - (p1·x1/1+α).
g. Briefly explain what your assumption in part 1.f would imply about EV, CV, and consumer surplus.
2. Calculate a range for the welfare impacts from increased product variety in online book sales using the equation for equivalent variation given in part 1.f. above:
EV = - (p1·x1/1+α).
a. Find α using the Lerner Index and the publishing industry's gross margin
The Lerner index is a simple measure of a firm's market power, named after Abba Lerner for an article he published in 1934. This also happens to be the optimal pricing rule for a single product monopolist. In the case of books, particularly for obscure titles, publishers tend to set both the list price and wholesale prices of the books they publish. So, we can treat a publisher of any book title as a monopolist of that book.
We are going to be using the version of Lerner Index set equal to the negative inverse of the price elasticity of demand. Assume that α is your price elasticity of demand.
Write the Lerner's Index here and then solve for α. Show your work.
Obtain and report a range for the publisher's Lerner index. As turns out, the Lerner index is actually the same thing as the firm's "gross margin".
You can find two values for gross margin, use her estimate of the "publisher's margin." In the second link, use his estimate for traditional publishing markup "between publisher and reader." Both articles state these as percentages.
Use your two estimates of the Lerner index values to solve for two values for α. Note that the values should be negative. Report those values here.
b. Calculate the equivalent variation for additional product variety obtained by online bookstores, using statistics for Amazon for this calculation.
i. (3 points) For simplicity, assume that shoppers at traditional brick-and-mortar stores might have access to the top 100,000 best-selling book titles, and that online book sellers provide additional variety by more titles than this. Here is a 2014 estimate of the total number of print books titles available for sale on Amazon. To avoid double counting, use the total number of paperback titles as your estimate (assuming that all hardback, Kindle, and other formats are also available in paperback). Report the estimate of the number of paperback titles listed by Amazon in 2014.
ii. We have to weight these additional titles by their sales.
Assume that the average number of sales of a book, Q, is a declining exponential function of the sales rank, R, taking the form Q = β1·Rβ2 , Where β2 < 0.
Take the logarithm of this function and write it here.
Obtain and report an estimate of β2 using an article by Chevalier and Goolsbee posted on the class site. In Section II of this paper (pages 9-11), Chevalier and Goolsbee estimate the equation
ln(Rank -1) = c -θ ln(Sales)
Note that this is estimating rank as a function of sales, so you will need to invert the equation. In other words, solve for ln(Sales) as a function of ln(Rank). (You can ignore the minus one and assume that the left hand side is ln(Rank).)
Calculate your estimate of β2 using their second estimate of θ.
Calculate the proportion of sales for obscure titles not available at brick-and-mortar stores (that is, those with a sales rank above 100,000) as a percentage of total sales by calculating the ratio
r(x, N) = (R=x∫R=NQdR)/(R=1∫R=NQdR)
Where x=100,000 and N is the total number of titles offered by Amazon that you found in 2.b.i. above.
c. Calculate the total revenue for obscure book titles in 2015. That is, calculate the p1·x1 for your equivalent valuation estimate. (Note that there is a small inconsistency in the analysis at this point because we are using 2015 for this part and we used 2014 in part 2.b above. However, part 2.b was only used to calculate the percent of titles only available online, so it probably will not matter too much.)
Obtain and report the net sales revenue for all content sold directly to online channels in 2015 using data. The sales revenue for content sold online will be the product of the net revenue for the publishing industry in 2015 times the market share for online retailers. Report your estimate here.
Multiply this net sales figure times the percentage of sales that are obscure titles calculated in part 2.b.ii.3) above. Report your estimate here.
d. Calculate the equivalent variation of additional product variety from online bookstores using the total revenue from 2.c. above and the two estimates α from 2.a.ii above.
3. Calculate the equivalent variation for the introduction of e-books. One big advance in the book publishing world is the introduction of electronic books, or e-books. As it turns out, the calculation for the equivalent variation from the introduction of e-books is even simpler than the calculations that you did above because you don't need to subtract out sales from brick-and-mortar establishments. E-books are almost exclusively an online product.
a. Obtain the sales revenue for e-books in 2015
b. Calculate the equivalent variation for the introduction of e-books using your formula for equivalent variation, the net sales revenue from 3.a. above, and the two estimates α from 2.a.ii above. Show your work.
4. Write a paragraph or two explaining your results. Assume that you were asked to conduct this analysis for book publishing trade organization that is lobbying for government support of online book sales. How would you explain your results to a trade representative? Assume that this representative is a well educated individual but is not an economist. How would you explain what your estimate of equivalent variation is measuring? How should he or she interpret the dollar values that you estimated?
Attachment:- Assignment File.rar