# Use implicit differentiation formula to find the slopes of the following functions. a) For the...

## Question:

Use implicit differentiation formula to find the slopes of the following functions.

a) For the following production function, find the slope of an isoquant (dK/dL). Q0 = 100K^0.2L^0.8, where Q0 is a fixed level of output.

b) For the following utility function, find the slope of an indifference curve (dX/dY). Uo = 0.75 ln X + 0.25 ln Y, where Uo is a fixed level of utility.

## Indifference Curve and Isoquant Curve:

An indifference curve is a curve that shows the different bundles of goods that give the consumer the same level of utility. The slope of the indifference curve is the marginal rate of substitution (MRS), which shows the rate at which the consumer can substitute one good for the other while keeping the utility constant. An isoquant is a curve that shows the different combinations of inputs that give the same level of output. The slope of an isoquant is called the marginal rate of technical substitution (MRTS), which shows the rate at which firms substitute one input for the other while keeping the level of production or output constant.