Apple vs. Saturn Case

The Wealth of Nations

Course 33520-81

Prof. Chang-Tai Hsieh

Summer 2012

Problem Set #2

Joseph Bauer

Nick Geeza

Scott Duba

Jake Hubbard

I pledge my honor that I have not violated the Honor Code during this examination or case write-up

Part A

1) Suppose that there are two firms in Mexico, firm 1 and firm 2. Initially both firms have the same productivity: A1=1 and A2=1. Both firms produce output according to the following production function: Y = AL (1-y)

a) W = (1-y)(2*1^2)^(1/2) = .70711, the number of workers employed in each firm: 500

b) Output of each firm: Y=A* L^(1-y) = 1 * 500^(.5) = 22.36

c) Total GDP (sum of the output produced by the two firms) in Mexico: 44.7214

2) Now suppose that firm 2 raises its productivity from A2=1 to A2=10, but the productivity of firm 1 does not change. How does the improvement in productivity of firm 2 change total GDP in Mexico?

* W = (1-y)((1*1^2)+(1*10^2))^(1/2) = 5.025

* The number of workers employed at firm 1: L=(((1-y)*A)/W)^(1/y) = 10 workers

* The number or workers employed at firm 2: L=(((1-y)*A)/W)^(1/y) = 990 workers

* Output of each firm: Y=A* L^(1-y) = Output of firm 1: 3.1623 and output of firm 2: 314.64

* Total output in Mexico: 317.8050

3) Now suppose that Mexico has a universal health care system that is finance by a surtax of 50% on the sales of firms with more than five hundred workers (firms with less than five hundred are exempt). What is the effect of the improvement of productivity of firm 2 from A2=1 to A2=10 under this scenario? Why is your answer different from your answer in B?

Firm two would want to use the combination of a smaller workforce (under 500 workers to remain exempt from the health care tax) and its improved productivity to generate output. If the firm continued to use the 990 workers to generate 314.64 in output, they would subsequently have to pay 157.32 in tax, resulting in net output of 157.32. If...