4- utility Flashcards
what is the slope of the indifference curve?
it is the marginal rate of substitution
what occurs to the marginal rate of substitution along the indifference curve?
there are diminishing marginal rate of subsitution
in the case of perfect substitutes what is the marginal rate of substitution?
it is constant
in the case of perfect complements, what occurs to the MRS curve?
the MRS changes from negative infinity to 0
what can the slope of the indifference curve be considered to measure?
the marginal willingness to pay as the MRS measures the amount of good 2 that one is willing to pay for a marginal amount of extra consumption of good 1
what are the requirements for a consumers preference to be represented by a utility function?
given that the consumers preferences are well behaved and satisfy the six axioms then they can be expresed as a utility function
what is the equation of the utility function for perfect substitutes?
u(x1,x2) = ax1 + bx2
what is the slope for a perfect substitute utility function?
-a/b
what is the equation for the utility function of perfect complements?
u(x1,x2) = min{ax1,bx2} where a and b are positive numbers that indicate the proportions in which the goods are consumed
what is the equation for a quasi linear utility function where it is only linear for x2?
u(x1,x2) = f(x1) + x2
how does the quasi linear utility function shift for each indifference curve?
for quasi linear utility function each indifference curve is a vertically shifted copy of the others
what is the equation for a cobb douglas utility function?
u(x1,x2) = x1^a * x2^b with a and b being greater than 0
what trait is constant throughout all cobb douglas indifference curves?
cobb douglas indifference curves are always well behaved
what is the relationship between the marginal rate of substitution and the slope of the indifference curve?
dx2/dx1 = -MU1/MU2
how does the MRS change when x2 changes but x1 is constant for a quasi linear utility function of the form u(x1,x2)=f(x1) +x2 ?
MRS does not depend upon 𝑥2 so the slope of indifference curves for a quasi-linear utility function is constant along any line for which 𝑥1 is constant.
