multi variable functions Flashcards
define an indifference curve
a curve showing all the bundles where the different combinations of goods give the same utility to the consumer
define an isoquant
a curve showing all the different combinations of inputs that yield the same amount of output
which of these are considered functions and which are not ?
a. one to one
b. many to one
c. one to many
a. function
b. function
c. not a function
in this equation; which of the variables are independent and which are dependent ?
z = f(x,y) = x + y
z - dependent
x,y - independent
what is the domain of a function ?
the independent variables or the inputs (x,y)
what is the range/co-domain of a function ?
the dependent variables or the outputs (z)
what is a level curve ?
the plane that is cut into a dome when the optimum, under constraints, has been reached
what is a production function ?
a function that tells firms what level of production is obtainable with certain/different amounts of resources
what is a utility function ?
a function that models the levels of utility available for different amounts of goods
what is a cobb-douglas function ?
a particular form of function that it :
(x^a).(y^b)
a+b=1 - constant returns
>1 - increasing
<1 - decreasing
what is a profit function ?
a function that shows the profit obtainable from a business.
profit = price.quantity - (IR.capital + wagerate.labour)
how do you find the marginal product of capital and labour ?
you differentiate the production function to get a new function
what is marginal product of an input ?
it is how much output increases when the one input is increased
how do you find if the marginal product if diminishing,constant or increasing ?
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
what is the diminishing or increasing or constant marginal returns ?
it is how much more or less this unit added or took away from the overall total than the last unit did.
how can you tell if a curve is convex ( minimum point ) or concave ( maximum point ) ?
the second derivative > 0 - convex ( min )
the second derivative < 0 - concave ( max )
how do you find an isoquant ?
re arrange the production function to make K or L the subject of the equation
what is young theorem ?
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
what is arc elasticity ?
change Q / change in P . price / quantity
what is point elasticity ?
dq/dp . p/q
which elasticity do we mainly use ?
a. arc
b. point
b. point
when Qa = f(Qa,Qb,Y)
what is and how do you calculate own price elasticity ?
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 .
when Qa = f(Qa,Qb,Y)
what is and how do you calculate cross price elasticity ?
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.
when Qa = f(Qa,Qb,Y)
what is and how do you calculate income elasticity ?
3Y = dQa/dY . Y/Qa
conclusions;
- 3Y > 0 NORMAL
- 3Y < 0 INFERIOR
income elasticity is how responsive Qd is to a change in income.
how do you know is a function has constant elasticity ?
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
how is total revenue calculated ?
price.quantity
