The United States and China can produce TVs at $200 and 2000 yuan each. One day of labor is needed to produce a TV in the United States and 10 days of labor are needed to produce a TV in China. Each country also produces the nontraded good, car washing. In each country, one car can be washed in one day. The exchange rate is 10 yuan = $1. Assume people in each country spend half their income on TVs and half on car washes. Compute the consumer price index (CPI) for each country given by the square root of the TV price times the car wash price. Convert the Chinese CPI to dollars at the 10 yuan = $1 exchange rate. What is the ratio of the U.S. to Chinese CPI?

Question

Quizplus · Accepted Answer

The CPI for the United States is: 
(sqrt($200 x 1) x $1) + (sqrt($5 x 1) x $1) = $20 + $2.24 = $22.24

The CPI for China is: 
(sqrt(2000 yuan x 10 yuan) x 1 yuan) + (sqrt(500 yuan x 1 yuan) x 1 yuan) = 200 yuan + 22.36 yuan = 222.36 yuan 
Converted to dollars at the exchange rate, the CPI for China is $22.24.

The ratio of the U.S. to Chinese CPI is: 
$22.24/$22.24 = 1, or approximately 3.16 when rounded to two decimal places.

The United States and China Can Produce TVs at $200