multi variable functions

Question 1

define an indifference curve

Answer 1

a curve showing all the bundles where the different combinations of goods give the same utility to the consumer

Question 2

define an isoquant

Answer 2

a curve showing all the different combinations of inputs that yield the same amount of output

Question 3

which of these are considered functions and which are not ?

a. one to one
b. many to one
c. one to many

Answer 3

a. function
b. function
c. not a function

Question 4

in this equation; which of the variables are independent and which are dependent ?

z = f(x,y) = x + y

Answer 4

z - dependent

x,y - independent

Question 5

what is the domain of a function ?

Answer 5

the independent variables or the inputs (x,y)

Question 6

what is the range/co-domain of a function ?

Answer 6

the dependent variables or the outputs (z)

Question 7

what is a level curve ?

Answer 7

the plane that is cut into a dome when the optimum, under constraints, has been reached

Question 8

what is a production function ?

Answer 8

a function that tells firms what level of production is obtainable with certain/different amounts of resources

Question 9

what is a utility function ?

Answer 9

a function that models the levels of utility available for different amounts of goods

Question 10

what is a cobb-douglas function ?

Answer 10

a particular form of function that it :

(x^a).(y^b)

a+b=1 - constant returns
>1 - increasing
<1 - decreasing

Question 11

what is a profit function ?

Answer 11

a function that shows the profit obtainable from a business.

profit = price.quantity - (IR.capital + wagerate.labour)

Question 12

how do you find the marginal product of capital and labour ?

Answer 12

you differentiate the production function to get a new function

Question 13

what is marginal product of an input ?

Answer 13

it is how much output increases when the one input is increased

Question 14

how do you find if the marginal product if diminishing,constant or increasing ?

Answer 14

if you double differentiate the production function or just differentiate the marginal product function. then you plug some of the input combinations in and see how the output total changes

Question 15

what is the diminishing or increasing or constant marginal returns ?

Answer 15

it is how much more or less this unit added or took away from the overall total than the last unit did.

Question 16

how can you tell if a curve is convex ( minimum point ) or concave ( maximum point ) ?

Answer 16

the second derivative > 0 - convex ( min )

the second derivative < 0 - concave ( max )

Question 17

how do you find an isoquant ?

Answer 17

re arrange the production function to make K or L the subject of the equation

Question 18

what is young theorem ?

Answer 18

the theory that the second derivative by one variable of the first derivative of the other variable is equal to the second derivative by the other variable of the first derivative by one variable . basically if you differentiate by one variable and then differentiate again by the other variable it gives the same answer no matter what the order of the two variables is. d’‘z/dxdy = d’‘z/dydx

you are deriving by the second d on the denomenator

Question 19

what is arc elasticity ?

Answer 19

change Q / change in P . price / quantity

Question 20

what is point elasticity ?

Answer 20

dq/dp . p/q

Question 21

which elasticity do we mainly use ?

a. arc
b. point

Answer 21

b. point

Question 22

when Qa = f(Qa,Qb,Y)

what is and how do you calculate own price elasticity ?

Answer 22

3Pa = dQa/dPa . Pa/Qa

conclusions ;

• 3Pa > 1 ELASTIC
• 3Pa < 1 INELASTIC

own price elasticity is how responsive Qd,a is to a change in the price of good a .

Question 23

when Qa = f(Qa,Qb,Y)

what is and how do you calculate cross price elasticity ?

Answer 23

3Pb = dQa/dPb . Pb/Qa

conclusions ;

• 3Pb > 0 substitutes
• 3Pb < 0 complementary

cross price elasticity is how responsive Qd,a is to a change in the price of good b.

Question 24

when Qa = f(Qa,Qb,Y)

what is and how do you calculate income elasticity ?

Answer 24

3Y = dQa/dY . Y/Qa

conclusions;

• 3Y > 0 NORMAL
• 3Y < 0 INFERIOR

income elasticity is how responsive Qd is to a change in income.

Question 25

how do you know is a function has constant elasticity ?

Answer 25

ONLY IF IT IS IN THE FORM: Q = mP^3

because dQ/dP = 3mP^3-1
and therefore 3 = dQ/dP . P/Q = 3mP^3-1 . P/mP^3 = 3

Question 26

how is total revenue calculated ?

Answer 26

price.quantity