Marginal Utility, Consumer Choice

revealed preference - finding preferences based on choices 

• instead of making choices based on preferences
• if consumer chooses more expensive basket over another, then chosen market basket is more preferred
• creates a more defined indifference curve >> more rankings
• changing budget lines >> more defined preference area

marginal utility (MU) - measures additional satisfaction from an additional unit of good 

• generally diminishes as more good is consumed
  • ex. the 4th or 5th hamburgers aren't quite as satisfying as the 1st
• same utility on all points of indifference curve
• MU increase w/ 1 good >> MU decrease w/ other good
• MU_A/MU_B = MRS = P_A/P_B
• marginal utility is same for each good >> utility maximization (equal marginal principle)
• U_A / P_A = U_B / P_B
  • P_A/P_B = U_A/U_B = MRS
  • now you can find the MRS even if price isn't given (or is a variable in your calculations instead of constant)

In buying goods x and y, a consumer has utility function U = 1.5x + 2y and an income of $60, where good x costs $2, and good y costs $3. Find the MRS and the amount of each the consumer would buy if he wanted to maximize his utility 

• budget constraint >> I = P_xx + P_yy
  • 60 = 2x + 3y
• MRS = U_x/U_y
  • U_y = 2
  • U_x = 1.5
  • MRS = 1.5/2 = 0.75
• note that in this case, P_x/P_y = 2/3, different from the MRS
  • this indicates a corner solution, where the maximum amount possible of 1 good is consumed
• consumer will buy 30 of good x
  • gives utility of 45
  • buying 20 of good y gives utility of 40
  • no other combination gives a higher utility

cost-of-living indexes - ratio of present cost to past cost 

• accounts for inflation, price growth (ie CPI )
• ideal cost-of-living index - cost of a given level of utility now compared to before
• Lasapeyres index - amount of money needed to purchase past market basket now divided by cost before
  • deals w/ purchases as opposed to preferences
  • usually overstates true cost-of-living index
  • assumes that consumers don’t change consumption patterns
• Paasche index - like Lasapeyres index, but deals w/ current market baskets (opposed to past)
  • will understate true cost-of-living index
  • assumes that consumers used current habits in the past
• chain-weighted index - unlike fixed-weight index (Laspeyres/Paasche)
  • accounts for changes in quantities of goods