AGRB PRACTICE PROBLEMS FOR MICROECONOMICS:

Indicate whether the statement is True or False, and briefly explain why:

A) An increase in income will increase the demand for all goods.

B) If the demand for eggs decreases as the price of bacon increases, economists would consider eggs and bacon as complements, and the cross-price elasticity of demand between these goods is positive.

C) If the demand for potatoes increases as income decreases, the income elasticity is negative, and economists would consider potatoes as an inferior good.

D) If the own price elasticity of demand for beef is -0.5, it means that a 10-percent increase in the price of beef would reduce the quantity of beef purchased by 0.5%.

E) As the price of a product falls, holding all else constant, the quantity demanded of that product will increase. This is what economists call the law of demand and it holds for all types of goods.

F) The Law of Diminishing marginal utility means that consuming less of a good would increase its marginal utility.

Solve each Math and Calculus review question below and choose the correct option when appropriate.

1) Simplify ^0.5^0.5 / ^0.5^0.5

2) If the value of rises from 5 to 6, what is the percentage change?

4) Solve for if: 60 2 = 28 + 2

5) What is the slope of the graph of 2 + 3 = 10?

6) Which of the following functions is the steepest?

a) I b) II c) III d) I and II

(The given functions):

) = 10 + 2

) = 8 + 3

) = 6 4

7) Given the function () = 2 + 6, what is the x-intercept?

a) (0, -3)

b) (-3, 0)

c) (3, 0)

d) (0, 3)

10) Given the function () = + , choose the statement that is false:

a) An increase in c changes the intercept of the function but not the slope.

b) An increase in m changes the slope but not the intercept.

c) An increase in x increases the value of the function f(x) given that the slope is positive.

d) A decrease in c changes the slope of the function.

11) Solve the following system of simultaneous equations:

= 45 + 8

= 125 2

=

=

12) Solve the following system of simultaneous equations to find the value of :

10 + 2 = 100

= 5

14) Find y when = 200 for the two simultaneous equations below

= 400 15 +

= 5

15) Find the derivative of the following function at an arbitrary point

() = 32 ^2

16) Find the derivative of the following function at an arbitrary point

() = ^0.5

17) Find the second-order derivative of the following function:

()=^3 10^2 +40+40

18) Find the slope of the following function at = 3 () = 10 ^2

19) Is the following function increasing or decreasing in the immediate vicinity of = 2?

= 2^2 ^3

20) Consider a function defined by = , for all > 0, where is a positive constant. Test whether the function is a concave function.

a) It is a convex function

b) It is a concave function

c) The function is initially concave and then convex

d) The function is neither concave nor convex

21) Consider a function defined by () = 10 2^2, for all > 0. Test whether the function is a concave function.

a) It is a convex function

b) It is a concave function

c) The function is initially concave and then convex

d) The function is neither concave nor convex

22) At which value of is the following function optimized?

() = 50 2^2

=

23) Suppose that () = 10 2. Find the first-order condition of ().

24) Find the first-order derivative of the expression ^0.5^0.5 with respect to treating as a constant.

25) Find the first-order derivative of the expression 5^0.5^0.6 with respect to treating as a constant.

(ALL RELEVANT INFORMATION FOR THESE MADE UP PROBLEMS IS WITHIN THE QUESTIONS THEMSELVES!)

REFERENCES THAT MAY HELP (SORRY HARD TO PROVIDE MANY):

https://www.youtube.com/watch?v=Xts5oboHEuc

https://www.khanacademy.org/economics-finance-domain/ap-microeconomics/production-cost-and-the-perfect-competition-model-temporary/the-production-function/v/introduction-to-production-functions

(PLEASE TRY TO COMPLETE AS MUCH AS POSSIBLE, I APPRECIATE YOUR HELP VERY MUCH!)