Sharon Kartika

Utility

U = U(x), where x is the amount of good x. U(x) can take many forms such as x,x2,ln⁡(x)x, x^2, \ln(x) etc.

Marginal utility Additional utility of one additional unit of the good.

u=u(x)Mux=dudx=U′(x) u = u(x)\\ Mu_x = \frac{du}{dx} = U'(x)

Multiple goods

U=U(x,y)Mux=δuδx,Muy=δuδy U = U(x,y)\\ Mu_x = \frac{ \delta u}{ \delta x}, Mu_y = \frac{ \delta u}{ \delta y}

Plotting U(x,y)U(x,y).

Let U0=U(x0,y0)U_0 = U(x_0,y_0). The indifference curve is the locus of (x,y)(x,y) which gives the same level of utility. (looks somewhat like 1x\frac{1}{x})

Note that U(x0+δx,y0+δy)U(x_0+ \delta_x, y_0+ \delta_y) will give either more utility, less utility, or same amount of utility.

Indifference curve

Properties:

  1. Negatively sloped.

  2. Further an IC from the origin, higher is the level of utility.

  3. ICs cannot intersect.

The slope of IC is called the marginal rate of substitution

Substitute goods. tea, coffee

complementary goods. tea, sugar, milk

Degree of substitutivity Perfect complements <–-> Perfect substitutes.

IC of Perfect substitues is a straight line, with negatively slope. The slope can vary. What will be the IC of perfect complements?

Sharon Kartika. Last modified: January 04, 2024.