Lecture Assignment #5- Consumer Theory • Utility Theory ...
Lecture Assignment #5- Consumer Theory
Utility Theory - Measurable Satisfaction Indifference Theory- does not require satisfaction to be measurable: rating/ ranking system Utility theory o Maximizing Utility (Satisfaction) o Satisfaction Measurable “Jollies” o Not worry about budget/ constraint One good X Two Goods X+Y
Total Utility TU= TU (X) – how much of good x you have Q 0 1 2 3 4 5 6 7 -
TU “Jollies” MU 0 10 10 8 18 6 24 6 28 4 30 2 30 0 28 -2 Marginal Utility (MU) Extra Utility from an extra unit Equation: MU= ∆TU/∆X Diminishing Marginal Utility (reasonable: Over a fixed period of time)
Demand Schedule for Good X Px $0 $1 $2 $3 $4 $5 $6 -
Qx 6 5 4 3 2 1 0 Max is 6 because the marginal utility is zero Reason: Diminishing Marginal Utility Schedule
NOT LA #5 -
Consumer Surplus- Entire Areas above their price AND below the demand schedule
-
4th Unit- No additional Surplus Demand= ½ (4) ($4) = $8 P= 6-1Q P=2, What is Cs? Earliest unit is more valuable
Cont.... Two Good Utility Model
TU= TU (x, y) -
Read because helps jumping to conclusion
MUx, MUy, Px, Py MUx/Px = MUy/Py -
-
Maximize satisfaction Marginal utility per dollar spent on good x = MU of last dollar spent bit on good y If not equal, you’re nt satisfying maximize satisfaction Example:14j/$2 > 4j/$1; 7j/$ > 4j/$ o Buy more x; buy less y o MU of X/ Px = MUy/ Py o Optimal Solution o No better than that o Suppose Px decrease , the LHS? RHS; if that happens, buy more LHS to reduce equality, slope of Dx MUx/Px= MUy/Py Qxd – negatively slope o Law of Diminishing Marginal Utility
MU Equilibrium Equation MUX/ Px= MUY/ Py Looking at Demand Side.... -
Adam Smith “Paradox of Value” – Nations of Wealth -1776 o Value- 2 meaning – value in use or value in exchange o The things which have the greatest value-in-use have frequently little or no value- inexchange, those which have greater value in exchange have frequently little or no value-in-use Example: Water- Diamond Water: Value in exchange (price) is low because marginal utility is high Diamond: Value of exchange (price) is high because marginal utility is high Marginal Utility is driving source of this one LOW- MUW/ Pw= High- Mud/ Pd Total Utility is high for water and low for diamond TUw> TUd Market= MU Drives Decision (it is the key)
Indifference Theory
Preference Map does not measure Utility A>B , A=B. BB, B>C , C cannot > A More is referred to less
-
East= more of both goods West= no- less of both groups Negative Slope ∆Y/∆X < 0
Absolute Value |∆Y/∆X| = Slope of IC – Marginal rate of substitution MRS= X/Y
-
Give up Yj- change by total utility, Gain Xj- change in total utility = Total Change in Utility =0 ∆Y [∆TU/∆Y] + ∆X [∆TU/∆X] = 0 ∆YMUy + ∆XMUx = 0 ∆y/∆x= MUx/ MUy MRS X/y = |slope IC | = MUx/ MUy What are the units associate with MUx/ MU y , Answer is, No units of measurements because it is a ratio Why is it Convex?? Hahahah MRS x/y= |slope| of IC = MUx/MUy Marginal Rate of Substitution
Concept of Budget Line/ Constraint Constraint: P.P , income available to buy good A + good y BC: I (Income) = Px x X + Py – y -
Exp. On Good x - Exp. On Good Y
-
X Intercept= I/Px Y-Intercept= I/ Py
-
Slope of BL= (-) (I/Py)/ (I/Px) = (-) Px/Py Budget Line= Constraints (example: Point A, Consumers can’t buy) BL2, Px ↓, ( it is a pivot) Parallel Shift → Income ↑
Equilibrium A= Can’t Achieve B= Can, but you can do better C= Still do better Equilibrium: Max Satisfaction subject to subject
At Equilibrium: |Slope| of BC = |Slope| of IC Px/ Py = MUx/ MUy = MRS x/y Slope of Budget Line- Slope of IC Pick IC and not draw all of them
|Slope| of IC = |Slope| of BC MRS x/y = MUx/MUy= Px/Py Indifference Theory MUx/MUy= Px/Py } No Units of Measurement MUx/Px= Muy/Py } Jollies Equal- No! Not equal, 2 different units, relates to Model, Economically Cannot be same
LA #, Part Two Q 3.2
- very “-“ sloped D
-
A, B same spot on X ↓Px → B
Income Consumption Curve
ICC/ Income Consumption Curve- consumption at X, Y at various level of income and maximize satisfaction -
Lines are parallel Income ↑ in each case (only change); Income growing from B:L1 to BL2 to BL3
Task: X= Inferior and Y = Inferior
- Still both inferior good, cannot be drawn, not spending any income, if any 2 goods, they cannot be both inferior
Price Consumption Curve
*not the only way to draw it - Px↓ as BL1 ↑ - PCC represent combination of how much can be purchase of good x and good y, depending p rice of good x and constant income
Question 6- Translate it into a Demand Schedule !
-
If smart student, ↑ income
Utility Theory - Measurable Satisfaction Indifference Theory- does not require satisfaction to be measurable: rating/ ranking system Utility theory o Maximizing Utility (Satisfaction) o Satisfaction Measurable “Jollies” o Not worry about budget/ constraint One good X Two Goods X+Y
Total Utility TU= TU (X) – how much of good x you have Q 0 1 2 3 4 5 6 7 -
TU “Jollies” MU 0 10 10 8 18 6 24 6 28 4 30 2 30 0 28 -2 Marginal Utility (MU) Extra Utility from an extra unit Equation: MU= ∆TU/∆X Diminishing Marginal Utility (reasonable: Over a fixed period of time)
Demand Schedule for Good X Px $0 $1 $2 $3 $4 $5 $6 -
Qx 6 5 4 3 2 1 0 Max is 6 because the marginal utility is zero Reason: Diminishing Marginal Utility Schedule
NOT LA #5 -
Consumer Surplus- Entire Areas above their price AND below the demand schedule
-
4th Unit- No additional Surplus Demand= ½ (4) ($4) = $8 P= 6-1Q P=2, What is Cs? Earliest unit is more valuable
Cont.... Two Good Utility Model
TU= TU (x, y) -
Read because helps jumping to conclusion
MUx, MUy, Px, Py MUx/Px = MUy/Py -
-
Maximize satisfaction Marginal utility per dollar spent on good x = MU of last dollar spent bit on good y If not equal, you’re nt satisfying maximize satisfaction Example:14j/$2 > 4j/$1; 7j/$ > 4j/$ o Buy more x; buy less y o MU of X/ Px = MUy/ Py o Optimal Solution o No better than that o Suppose Px decrease , the LHS? RHS; if that happens, buy more LHS to reduce equality, slope of Dx MUx/Px= MUy/Py Qxd – negatively slope o Law of Diminishing Marginal Utility
MU Equilibrium Equation MUX/ Px= MUY/ Py Looking at Demand Side.... -
Adam Smith “Paradox of Value” – Nations of Wealth -1776 o Value- 2 meaning – value in use or value in exchange o The things which have the greatest value-in-use have frequently little or no value- inexchange, those which have greater value in exchange have frequently little or no value-in-use Example: Water- Diamond Water: Value in exchange (price) is low because marginal utility is high Diamond: Value of exchange (price) is high because marginal utility is high Marginal Utility is driving source of this one LOW- MUW/ Pw= High- Mud/ Pd Total Utility is high for water and low for diamond TUw> TUd Market= MU Drives Decision (it is the key)
Indifference Theory
Preference Map does not measure Utility A>B , A=B. BB, B>C , C cannot > A More is referred to less
-
East= more of both goods West= no- less of both groups Negative Slope ∆Y/∆X < 0
Absolute Value |∆Y/∆X| = Slope of IC – Marginal rate of substitution MRS= X/Y
-
Give up Yj- change by total utility, Gain Xj- change in total utility = Total Change in Utility =0 ∆Y [∆TU/∆Y] + ∆X [∆TU/∆X] = 0 ∆YMUy + ∆XMUx = 0 ∆y/∆x= MUx/ MUy MRS X/y = |slope IC | = MUx/ MUy What are the units associate with MUx/ MU y , Answer is, No units of measurements because it is a ratio Why is it Convex?? Hahahah MRS x/y= |slope| of IC = MUx/MUy Marginal Rate of Substitution
Concept of Budget Line/ Constraint Constraint: P.P , income available to buy good A + good y BC: I (Income) = Px x X + Py – y -
Exp. On Good x - Exp. On Good Y
-
X Intercept= I/Px Y-Intercept= I/ Py
-
Slope of BL= (-) (I/Py)/ (I/Px) = (-) Px/Py Budget Line= Constraints (example: Point A, Consumers can’t buy) BL2, Px ↓, ( it is a pivot) Parallel Shift → Income ↑
Equilibrium A= Can’t Achieve B= Can, but you can do better C= Still do better Equilibrium: Max Satisfaction subject to subject
At Equilibrium: |Slope| of BC = |Slope| of IC Px/ Py = MUx/ MUy = MRS x/y Slope of Budget Line- Slope of IC Pick IC and not draw all of them
|Slope| of IC = |Slope| of BC MRS x/y = MUx/MUy= Px/Py Indifference Theory MUx/MUy= Px/Py } No Units of Measurement MUx/Px= Muy/Py } Jollies Equal- No! Not equal, 2 different units, relates to Model, Economically Cannot be same
LA #, Part Two Q 3.2
- very “-“ sloped D
-
A, B same spot on X ↓Px → B
Income Consumption Curve
ICC/ Income Consumption Curve- consumption at X, Y at various level of income and maximize satisfaction -
Lines are parallel Income ↑ in each case (only change); Income growing from B:L1 to BL2 to BL3
Task: X= Inferior and Y = Inferior
- Still both inferior good, cannot be drawn, not spending any income, if any 2 goods, they cannot be both inferior
Price Consumption Curve
*not the only way to draw it - Px↓ as BL1 ↑ - PCC represent combination of how much can be purchase of good x and good y, depending p rice of good x and constant income
Question 6- Translate it into a Demand Schedule !
-
If smart student, ↑ income
