Managerial Economics (Chapter 5)
Chapter 5: Question 3: Suppose that two units of X and eight units of Y give a consumer the same utility as four units of X and two units of Y. Over this range: a. If the consumer obtains one more unit of X, how many units of Y must be given up in order to keep utility constant ∆Y∆X=2-84-2= - 62= -3 ~ Utility unchanged, if consumer exchanges 3 units of Y for 1 unit of X. b. If the consumer obtains one more unit of Y, how many units of X must be given up in order to keep utility constant? ∆Y∆X= 4-22-8= 26= -13 ~ Utility unchanged, if consumer exchanges 1/3 units of X for 1 unit of Y. c. What is the marginal rate of substitution? X = 2, Y = 8 X = 4, Y = 2 ∆Y∆X=MRS -( 8-2 )( 2-4 )= - 62=3
8 6 4 2 1 2 3 4 5 Question 7: Suppose a customer has indifference map shown below. The relevant budget line is LZ. The price of Y is $10.
60 50 L 40 B 30 20 10 A M 0 10 20 30 40 50 60 70 80 a. What is the consumer’s income? Quantity Y = 50 50 × $10 = $500 Price Y = $10 b. What is the price of X? Quantity X = 40 40 × Px = 500 Price X = ? Px = 500 / 40 Income = 500 Px = $12.50 c. Write the equation for the budget line LZ. Budget line LZ Py = $10 Px = $12.50 M = $ 500 PxX + PyY = y 12.50x + 10y = 500 or y = 50 – 1.25x
d. What combination of X and Y will the consumer choose? Why? Consumer choose 20 units of X and 25 unit of Y. Indifferent curve II is tangent to budget line LZ. No other combination costing $500 provides more utility than X = 20, Y = 25 e. What is the marginal rate of substitution at this combination? MRS= PxPy= $12.50$10=1.25 f. Explain in terms of the MRS why the consumer would not choose combinations designated by A or B. Combination A : MRS is the consumer
8 6 4 2 1 2 3 4 5 Question 7: Suppose a customer has indifference map shown below. The relevant budget line is LZ. The price of Y is $10.
60 50 L 40 B 30 20 10 A M 0 10 20 30 40 50 60 70 80 a. What is the consumer’s income? Quantity Y = 50 50 × $10 = $500 Price Y = $10 b. What is the price of X? Quantity X = 40 40 × Px = 500 Price X = ? Px = 500 / 40 Income = 500 Px = $12.50 c. Write the equation for the budget line LZ. Budget line LZ Py = $10 Px = $12.50 M = $ 500 PxX + PyY = y 12.50x + 10y = 500 or y = 50 – 1.25x
d. What combination of X and Y will the consumer choose? Why? Consumer choose 20 units of X and 25 unit of Y. Indifferent curve II is tangent to budget line LZ. No other combination costing $500 provides more utility than X = 20, Y = 25 e. What is the marginal rate of substitution at this combination? MRS= PxPy= $12.50$10=1.25 f. Explain in terms of the MRS why the consumer would not choose combinations designated by A or B. Combination A : MRS is the consumer