1   Multiple Choice (3pts each)

Q1. Rosa is trying to make a little money so that she can buy herself a new set of clothes before she goes to college. She decides to sell lemonade to make some money. The graph shows the prices at which she sold lemonade and how many glasses were sold.

How many glasses of lemonade did Rosa sell at a price of $3?

A. six glasses               B. seven glasses               C. eight glasses               D. nine glasses Q2. What is the partial derivative of k3 − 2l2 with respect to k?

A. 2k                B. 3k2                        C.3k3                       D. k

Q3. Let f(x) = (x − 1)2 + 3 and g(x) = −  1 北 . Then g(f(x)) is

A. −  1 − (北 1)2 +3                        B. −  1 − (北 1)2 −3                        C. ( −  1 北  − 1)2 +3               D. ( −  1 北 ) ((x − 1)2 + 3)

Q4. All of the following are measures of GDP except the total:

A. income from all production in the economy

B. expenditures on all final goods produced.

C. value of all final production.

D. expenditures of all businesses in the economy.

Q5. Two equivalent ways to view GDP are as the:

A. total payments made to all workers in the economy or the total profits of all firms and businesses in the economy.

B. total income of everyone in the economy or the total expenditure on the economy’s output of goods and services.

C. total expenditures n all goods produced in the economy or the total income earned from producing all services in the economy.

D. total profits of all firms and businesses in the economy or the total consumption of goods and services by all households in the economy.

Q6. To compute the value of GDP:

A. goods and services are valued at market prices.

B. the sales of used goods is included.

C. production for inventory is not included.

D. goods and services are valued by weights.

Q7. All of the following transactions that took place in 2009 would be included in GDP for 2009 except the purchase of a :

A. book printed in 2009, entitled The Year 3000.

B. ticket to see the movie 2001.

C. year 2010 calendar printed in 2009.

D.  2001 Jeep Cherokee.

Q8. When the bread is baked but put away for later sale, this is called:

A. waste.

B.  saving.

C. fixed investment.

D. investment in inventory.

Q9. Assume that a firm buys all the parts that it puts into an automobile for $10,000, pays its workers $8,000 to fabricate the automobile, and sells the automobile for $22,000. In this case, the value added by the automobile company is:

A. $4,000.

B. $12,000.

C. $14,000.

D. $22,000

Q10. An example of an imputed value in the GDP is the:

A. value-added of meals cooked at home.

B. housing services enjoyed by homeowners.

C.  services of automobiles to their owners.

D. value of illegal drugs sold.

Q11. The new chain-weighted measures of real GDP are an improvement over traditional mea-

sures because the prices used to compute real GDP are:

A. never far out of date.

B. always from the same base year.

C. imputed.

D. chained to the CPI.

Q12. If GDP (measured in billions of current dollars) is $5,465, consumption is $3,657, investment is $741, and government purchases are $1,098, then the net exports are:

A. $31               B. -$31                C. $131               D. -$131

Q13. If real GDP grew by 6 percent and the population grew by 2 percent, then real GDP per person grew by approximately          percent.

A. 2                   B. 3                   C. 4                   D. 8

Q14. The CPI is determined by computing:

A. an average of prices of all goods and services.

B. the price of a basket of goods and services that changes every year, relative to the same basket in a base year.

C. the price of a fixed basket of goods and services, relative to the price of the same basket in a base year.

D. nominal GDP relative to real GDP.

Q15. Assume that apples cost $0.50 in 2002 and $1 in 2009, whereas oranges cost $1 in 2002 and

$0.50 in 2009. If ten apples and five oranges were purchased in 2002, and five apples and ten oranges were purchased in 2009, the CPI for 2009, using 2002 as the base year, is:

A. 0.75.

B. 0.80.

C.  1.

D.  1.25.

2   Short Answer Questions

Q16. (2pts) Your savings this month fell by $20 from your regular savings of $ 50 till last month. Your savings are reduced by          percentage points.

Q17. (2pts) Simplify the following and find the exponent of x: 北5 北(北3)10

Q18. (2pts) Consider the system of linear equations

x + y = 9

x + 0.40y = 6

The value of x is          and the value of y is          .

Q19. (2pts) Consider the following non-linear equation

x +  = 3

What are the roots of x? The first root is          and the second root is          .

Q20. (8pts) Vac Inc.  manufactures a type of vacuum cleaner that sells for $200 a piece.  The production line of the vacuum cleaners has an overhead cost of $20, 000, and each vacuum cleaner costs $100 in manufacturing, shipping, and retailing.  Suppose there is no other revenue or cost. Let x denote the number of vacuum cleaners to be sold.

(1) (2pts) How many vacuum cleaners does the company need to sell to break even? (e.g., make zero profits). The answer is          .

(2) (2pts) How many vacuum cleaners does the company need to sell to make a $40, 000 profit? The answer is          .

(3) (2pts) How much profit will the company make if 500 vacuum cleaners are sold? The answer is          .

(4) (2pts) How much more profit will the company make for every 100 additional piece sold? The answer is          .

Q21. (9pts) Find the maximum and the minimum of f on specific domains D1  and D2  if they exist.

(1) (3pts) x3 + 3x on D1  = ( −∞ , ∞) and D2  = [1, 2].

(2) (3pts) x3 − 3x on D1  = [ −4, −2] and D2  = [0, ∞).

(3) (3pts) 1北2   on D1  = ( −∞ , ∞) and D2  = [1, 2].

Q22. (9pts) For each of the following functions, compute partial derivatives:

(1) (3pts) u(x,y) = 7x2y3

(2) (3pts) u(x,y) = (5x2 + 7y)(2x − 4y3 )

(3) (3pts) u(x,y) = 北(9)y(3)

Q23. (8pts) Consider the following objective function of two variables X and Y (note that this is like a utility function)

U(X,Y) = log(X) + log(Y)

The two variables must satisfy the following linear relationship (note that this is like a budget constraint)

20X + 10Y = 100

(1) (2pts) Use the constraint to solve for Y as a function of X . Sketch this equation with X on the horizontal axis and Y on the vertical axis. What is the slope of this line?

(2) (1pt) Replace Y the expression above into the objective function U and re-write the maximization problem, which now should only depend on X .

(3) (2pts) Find the optimal value of X .  To do this, take the derivative of the objective function found in part 2. with respect to X and make it equal to zero. Then solve for X .

(4) (2pts) Using the expression in 1 and the optimal value of X found in 3, find the optimal value of Y.

(5) (1pt) Using the optimal value of X and Y, find the value of the objective.

Q24. (4pts) A farmer grows a bushel of wheat and sells it to a miller for $1. The miller turns the wheat into flour and then sells the flour to a baker for $3. The baker uses the flour to make bread and sells the bread to an engineer for $6. When the engineer eats the bread, what is the value added by each person? What is the bread’s contribution to GDP?

(1) (1pt) The farmer’s added value is          .

(2) (1pt) The miller’s added value is          .

(3) (1pt) The baker’s added value is          .

(4) (1pt) The bread’s contribution to GDP is          .

Q25.  (9pts) Let’s recall the example from class. Suppose people only consume 3 different goods.

The following table shows the prices and quantities of each good consumed in 2006, 2007, and 2008.

(1) (3pts) Calculate nominal GDP in each of the three years.

(2) (3pts) Calculate the GDP deflator for each of the three years.