Question

Informal Economic Discussion: Estimation of Demand: Winners of Wireless Auction to Pay $7 Billion

• The CEO of a regional telephone company picked up the March 14 New York Times and began reading on page D1:

The Federal Government completed the biggest auction in history today, selling off part of the nation's airwaves for $7 billion to a handful of giant companies that plan to blanket the nation with new wireless communications networks for telephones and computers...

• The CEO read the article with interest because his firm is scrambling to secure loans to purchase one of the licenses the FCC plans to auction off in his region next year. The region serviced by the firm has a population that is 7 percent greater than the average where licenses have been sold before, yet the FCC plans to auction the same number of licenses. This troubled the CEO, since in the most recent auction 99 bidders coughed up a total of $7 billion--an average of $70.7 million for a single license.
  • Fortunately for the CEO, the New York Times article contained a table summarizing the price paid per license in 10 different regions, as well as the number of licenses sold and the population of each region. The CEO quickly entered this data in to his spreadsheet, clicked the regression tool button, and found the following relation between the pride of a license, the quality of licenses available, and regional population size (price and population figures are expressed in millions of dollars and people, respectively):

ln P= 2.23 - 1.2 ln Q + 1.25 ln Pop

Based on the CEO's analysis:

• How much money does he expect his company will need to buy a license?
• How much confidence do you place in this estimate? Can you make this calculation with the information provided?

Answer 1

SOLUTION:

GIVEN THAT:

P= 2.23 - 1.2 ln Q + 1.25 ln Pop

• The Co-efficient of In Pop is 1.25 means the percentage Change in Price results in each 1 percent Change in Population.
• Here, the population in the relevant region is 7 percent (ie.,) Higher than the Average.
• This means,

1.25 = % Change in P / % Change in Pop   

1.25 = % Change in P / 7% - 0% Change in P

= 1.25 * 7%

= 0.0875 * 100

= 8.75%

• Based on the analysis, the CEO expects to pay in his region is 8.75%, which is higher than the Average Price paid in the March 14th Auction.
• As that price was $70.7 Million, the expected price needed to win the auction in his region but other things are equal = $76.9 Million.
• So, the CEO 's analysis expects that the demand for the licenses will be greater in his region due to the greater size of the market, which is ultimately serviced by the holders of the licenses.