The correct answer is B. improve.
The economy is beginning to look up now means that it is improving. This can be seen in a number of ways, such as an increase in GDP, a decrease in unemployment, and an increase in consumer spending.
Option A, remain static, is incorrect because the economy is clearly improving. Option C, look clear, is incorrect because the economy is still facing some challenges, such as high levels of debt. Option D, go down, is incorrect because the economy is clearly improving.