Consumer Theory
Consumer Theory Knowledge Summary: 1. Total utility is the amount of joy we obtain from consuming a product Total utility (TU) is a function of the units we consume (Q), i.e., TU = F(Q) 2. Marginal Utility (MU) - Defined to be the utility we obtain from consuming a little bit more - It is the first derivative of TU regarding Q MU = dTU / dQ - Marginal utility is diminishing, i.e., the joy we obtain from consuming the first unit is greater than the joy we get from the second unit, etc 3. To obtain demand function: - We want to maximize the net benefit obtained from consuming product, i.e. we want to maximize the consumer surplus (CS) - CS = TU – Total expenditure = TU – TE - TU is a function of Q - TE = P x Q - CS = TU – TE - To maximize CS, we can set the first derivative of CS regarding Q to be zero. In this way, we can calculate the Q to consume in order to maximize the CS for a particular P - Mathematically, dCS/ dQ = 0 dTU/dQ – dTE/dQ = 0 We know that dTU/dQ = MU and dTE/dQ = d (P x Q) / dQ = P Thus, to maximize the net benefits, MU = P - P = MU is the demand function 4. Utility: the satisfaction or well-being that a consumer receives from consuming a good or service Total Utility: the full satisfaction resulting from the consumption of that product by a consumer Marginal Utility: the additional satisfaction resulting from consuming one more unit of that product Equation for marginal utility: dTU/dQ=P Law of Diminishing Marginal Utility: The utility that any consumer derives from successive units of a particular product consumed over some period of time diminishes as total consumption of the product increases (if the consumption of all other products is unchanged) Optimal purchase rule: the consumer should purchase units of the commodity until MU = price
Consumer Surplus: the value of the goods to the consumer above and beyond the market price (Area below demand curve and above price) Producer Surplus: the difference in the amount that a producer actually receives for a product and what they are willing to receive for it (area above supply curve and below price)
Summary of Questions to be asked: 1. Given utility function, derive the demand curve - Calculate MU = dTU / dQ - Set MU = P 2. Calculate the quantity to be consumed for a given price - Substitute the value of P to MU - Solve for the Q 3. Calculate the consumer surplus obtained from consuming a given amount of quantity - Calculate the Q to be consumed for a given P - Calculate TU = F(Q) - Calculate TE = P x Q - CS = TU - TE 4. Find the Consumer Surplus o Find the area of the triangle formed between the demand curve, equilibrium point and price o Note: When Price Elasticity of Demand (PED) is infinite, CS=0. When PED = 0, CS is infinite. When PES=0/infinite, CS=0/Infinite
5. Price per unit vs. flat rate o Find the maximum quantity the consumer will consume with the price per unit o Calculate the total utility gained from this quantity o Calculate the consumer surplus gained at the original price per unit o For the consumer to choose the flat rate it must be at least equal to the difference between the total utility (from step 2) and the consumer surplus (from step 3)
6. Find deadweight loss associated with tax o Find equilibrium price and quantity when consumer and producer surplus is maximized (when the market is allocatively efficient) o Calculate the new quantity demanded and price after the tax has been applied o Calculate deadweight loss by using the equation DWL = (0.5)(change in price * change in quantity demanded) o This is the same as the area of the triangle formed by the supply curve, the demand curve, and the line of the new quantity demanded
7. Price is given; find how many units of the good the consumer will purchase o Find marginal utility by finding the first derivative of the total utility equation o Set MU = price, and solve for X Related Common Exam Question: Questions from 2011 Midterm Question 8, 9, 10, 20 and 21 Answers: 16) First, find the quantity demanded at P = $1, Q = 24. Using the diagram provided, calculate the consumer surplus by calculating the area underneath the demand curve from the $1 price. CS = $54. The correct answer is (H).
17) The correct answer is (E).
18) The new quantity demanded after the tax is 10. DWL = (0.5)(2*14) = $14. The correct answer is (C). 19) U = 48(X+8)1/3 - 96. Marginal utility is dU/dX = 16(X+8)-2/3. If P = 1, then the consumer will set marginal utility equal to price (i.e., will follow the Optimal Purchase Rule) so that 1 = 16(X+8)-2/3 or X = 56. The correct answer is (F). 20) The consumer surplus can be found as the total utility minus the amount spent by the consumer = (48(56+8)1/3 - 96) - (1*56) = $40. The correct answer is (C).
Questions from 2008 Midterm Question 13, 14 and 15 Answers 13) U = 100X - (4/3)X3/2. Marginal utility is dU/dX = 100 - 2X1/2. If P = 40, then the consumer will set marginal utility equal to price (i.e., will follow the Optimal Purchase Rule) so that 40 = 100 - 2X1/2 or X = 900. The correct answer is (F).
14) The consumer surplus can be found as the total utility minus the amount spent by the consumer = 100(900) - (4/3)(900)3/2 – (40 ∗ 900) = $18,000. The correct answer is (F). 15) For full solution, see question 16 from the 2009 Midterm. The correct answer is (I).
Questions from 2009 Midterm Question 15, 16, 17, 18 and 19 Answers
Consumer Surplus: the value of the goods to the consumer above and beyond the market price (Area below demand curve and above price) Producer Surplus: the difference in the amount that a producer actually receives for a product and what they are willing to receive for it (area above supply curve and below price)
Summary of Questions to be asked: 1. Given utility function, derive the demand curve - Calculate MU = dTU / dQ - Set MU = P 2. Calculate the quantity to be consumed for a given price - Substitute the value of P to MU - Solve for the Q 3. Calculate the consumer surplus obtained from consuming a given amount of quantity - Calculate the Q to be consumed for a given P - Calculate TU = F(Q) - Calculate TE = P x Q - CS = TU - TE 4. Find the Consumer Surplus o Find the area of the triangle formed between the demand curve, equilibrium point and price o Note: When Price Elasticity of Demand (PED) is infinite, CS=0. When PED = 0, CS is infinite. When PES=0/infinite, CS=0/Infinite
5. Price per unit vs. flat rate o Find the maximum quantity the consumer will consume with the price per unit o Calculate the total utility gained from this quantity o Calculate the consumer surplus gained at the original price per unit o For the consumer to choose the flat rate it must be at least equal to the difference between the total utility (from step 2) and the consumer surplus (from step 3)
6. Find deadweight loss associated with tax o Find equilibrium price and quantity when consumer and producer surplus is maximized (when the market is allocatively efficient) o Calculate the new quantity demanded and price after the tax has been applied o Calculate deadweight loss by using the equation DWL = (0.5)(change in price * change in quantity demanded) o This is the same as the area of the triangle formed by the supply curve, the demand curve, and the line of the new quantity demanded
7. Price is given; find how many units of the good the consumer will purchase o Find marginal utility by finding the first derivative of the total utility equation o Set MU = price, and solve for X Related Common Exam Question: Questions from 2011 Midterm Question 8, 9, 10, 20 and 21 Answers: 16) First, find the quantity demanded at P = $1, Q = 24. Using the diagram provided, calculate the consumer surplus by calculating the area underneath the demand curve from the $1 price. CS = $54. The correct answer is (H).
17) The correct answer is (E).
18) The new quantity demanded after the tax is 10. DWL = (0.5)(2*14) = $14. The correct answer is (C). 19) U = 48(X+8)1/3 - 96. Marginal utility is dU/dX = 16(X+8)-2/3. If P = 1, then the consumer will set marginal utility equal to price (i.e., will follow the Optimal Purchase Rule) so that 1 = 16(X+8)-2/3 or X = 56. The correct answer is (F). 20) The consumer surplus can be found as the total utility minus the amount spent by the consumer = (48(56+8)1/3 - 96) - (1*56) = $40. The correct answer is (C).
Questions from 2008 Midterm Question 13, 14 and 15 Answers 13) U = 100X - (4/3)X3/2. Marginal utility is dU/dX = 100 - 2X1/2. If P = 40, then the consumer will set marginal utility equal to price (i.e., will follow the Optimal Purchase Rule) so that 40 = 100 - 2X1/2 or X = 900. The correct answer is (F).
14) The consumer surplus can be found as the total utility minus the amount spent by the consumer = 100(900) - (4/3)(900)3/2 – (40 ∗ 900) = $18,000. The correct answer is (F). 15) For full solution, see question 16 from the 2009 Midterm. The correct answer is (I).
Questions from 2009 Midterm Question 15, 16, 17, 18 and 19 Answers
