Introduction to mathematics
1. (a) The population of Mountainland was 45.7million in 2008 and 46.3 million in 2009. What was the percentage change (rate of growth) in population from 2008 to 2009? (b) The rural population of Mountainland was 18.3 million in 2008 and 17.7 million in 2009. What was the percentage change? (c) The data below show Mountainland’s real GDP (real output produced) for the period 2008-2010. Calculate the rate of growth in real GDP in (i) 2008-9 and (ii) 2009-10.
|Year |Real GDP (in billion $) |
|2008 |5.6 |
|2009 |5.7 |
|2010 |5.5 |
2. You are interested in buying a book that cost £30 but discover that its price has increased by 20%. What is the book’s new price?
3. For each of the following pairs of variables, explain (i) whether there is likely to be a positive or negative relationship between them, and (ii) which is the dependent and which is the independent variable. (a) income and saving
(b) number of DVDs purchased and price of DVDs
(c) level of salary and number of years of working experience (d) the temperature and the number of swimmers on the beach
4. The following table contains data on the relationship between saving and income. Rearrange these data into a meaningful order and graph them on the accompanying grid. What is the slope of the line? The vertical intercept? Interpret the meaning of both the slope and the intercept. Write the equation which represents this line. What would you predict saving to be at the $12,500 level of income?
| | |
|Income |Saving |
|(per year)` |(per year) |
| | |
| | |
|$15,000 |$1,000 |
|0 |-500 |
|10,000 |500 |
|5,000 |0 |
|20,000 |1,500 |
5. Construct a table from the following data shown on the accompanying graph. Which is the dependent variable and which the independent variable? Summarize the data in equation form.
6. Suppose that C = a + bY, where C = consumption, a = consumption at zero income, b= slope, and Y = income. a.Are C and Y positively related or are they negatively related? b.If graphed, would the curve for this equation slope upward or downward? c.Are the variables C and Y inversely related or directly related? d.What is the value of C if a =10, b =.50, and Y = 200? e.What is the value of Y if C = 100, a = 10, and b = .25?
7. In the accompanying graph, is the slope of curve AA’ positive or negative? Does the slope increase or decrease as we move along the curve from A to A’? Answer the same two questions for curve BB’. Chapter 1 Limits, alternatives and choices
1. Indicate whether each of the following statements applies to microeconomics or macroeconomics: a.The unemployment rate in the United States was 5.2 percent in January 2005. b.A U.S. software firm discharged 15 workers last month and transferred the work to India. c.An unexpected freeze in central Florida reduced the citrus crop and caused the price of oranges to rise. d.U.S. output, adjusted for inflation, grew by 4.4 percent in 2004. e.Last week Wells Fargo Bank lowered its interest rate on business loans by one-half of 1 percentage point. f.The consumer price index rose by 2.7 percent in 2004.
2. (a) What is society’s economizing problem? (b) What is the meaning of opportunity cost? (c) How does the concept of opportunity cost relate to the definition of economics? (d) Which of the following decisions would...