Final answer:
An unexpected increase in inflation to 10% rather than the expected 5% would erode the real wages of UAW workers, despite the nominal wage increase. There is no direct evidence provided that suggests this would lead to a decrease in the unemployment rate as other economic factors also play a role.
Step-by-step explanation:
If the United Auto Workers (UAW) negotiated a wage increase from $30.00 to $31.50 per hour for 2018 based on an expected 5% inflation rate, but the actual inflation rate turned out to be 10%, the real value of UAW workers' wages would decrease, assuming wages do not further adjust to the higher inflation. This is because the purchasing power of the higher wages would be eroded by the higher than expected increase in the price level. Therefore, the assertion that the unemployment rate will decrease is not directly supported by the information provided.
Whether unemployment decreases or not depends on other factors not provided in the question, such as the overall health of the economy, labor demand, and company strategies. Generally, unexpected high inflation can lead to uncertainty for both businesses and consumers, which could influence hiring and investment decisions. However, there is no direct causal link in the information given between the pay rise, the unexpected inflation, and a reduction in unemployment.