Deck 2: Key Mathematical Tools

Question 1

What is the quantity q at which the profit function given by 200q - q² is maximized?

A)20
B)40
C)60
D)80
E)100

Answer 1

100

Question 2

A cost function is given by C(q) = 100 + 3q + 5q², where q is the quantity produced.What is the first derivative dC(q)/dq of the cost function with respect to q?

A)dC(q)/dq =3
B)dC(q)/dq = 3 + 10q
C)dC(q)/dq = 100 + 10q
D)dC(q)/dq = 10q
E)None of the above

Answer 2

dC(q)/dq = 3 + 10q

Question 3

Consider a market with a demand curve given by q = 120 -P and a supply curve of q = 2P.Solving for q and P yields

A)q = 10, P = 30
B)q = 20, P = 40
C)q = 80, P = 40
D)q = 50, P = 25
E)q = 30, P = 15

Answer 3

q = 80, P = 40

Question 4

If there is a 10 per cent change in y given a 5 per cent change in x, what is the elasticity of y given the change in x?

A)10
B)2
C)1/2
D)5
E)None of the above

Question 5

Consider a demand curve represented by P = 100 - 2q, where P is price and q is the quantity demanded.What is the price when the quantity demanded is 20?

A)100
B)80
C)60
D)40
E)20

Question 6

What is the quantity q at which the profit function given by 240q - 4q² is maximized?

A)30
B)40
C)50
D)60
E)70

Question 7

Consider a demand curve represented by P = 10 - 2q, where P is price and q is the quantity demanded.What is the slope of the line?

A)10
B)2
C)-2
D)-1/2
E)P

Question 8

If there is a -20 per cent change in y given a 5 per cent change in x, what is the elasticity of y given the change in x?

A)2
B)-.025
C)-1/2
D)-4
E)3

Question 9

Consider a market with a demand curve given by P = 150 - q and a supply curve of P = 2q.Solving for q and P yields

A)q = 60, P = 30
B)q= 120, P = 60
C)q = 90, P = 60
D)q = 40, P = 80
E)q = 50, P = 100

Question 10

Consider a straight-line demand curve that cuts the P axis at P = 10 and cuts the q axis at q = 20.What is the equation for this demand curve?

A)P = 20 - q
B)P = 10 - 2q
C)P = 20 - 2q
D)P = 10 - 1/2q
E)None of the above.