6. Milton consumes two commodities in a perfect market system. The price of x is $4 and the price of y is $1. His utility function is U(x, y) = xy. He is endowed with 76 units of good x and no y. Find his consumption of good y. a. 76 b. 157 с. 152 d. 162
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- Roisin consumes only two goods, X and Y, and her utility function is given by U = XY. Her income is €50 and the price of X is €10 and the price of Y is €5. In equilibrium Roisin will choose which combination of X and Y? (Partial units are possible) X = 5; Y = 20 X = 5, Y = 10 X = 10, Y = 10 X = 2.5, Y = 5Consider a consumer with well-behaved preferences and an income of $160. The price of good 1 is $12 and the price of good 2 is $16. At the consumption bundle (4,2), where 4 is the number of units of good 1 purchased and 2 is the quantity of good 2, the opportunity cost of consuming an extra unit of good 1 is ["", "", "", "", ""] units of good 2.Consider an individual whose preferences are represented by the utility function U(x1,x2) = min {3x1+x2 , x1+3x2}. For this individual, Calculate her optimal consumption bundle when she has an income of 24, and P1=1, P2=2. Calculate her optimal consumption bundle when she has an income of 24, and P1=1, P2=4. Calculate the income and substitution effects resulting from the change in price of Good 2 (on the level of Good 2 consumption!) Calculate her demand function X1* (P1, P2,m) Calculate her own price, cross price, and income elasticities at X1*(1, 2, 24) and at X1*(1, 4, 24). Based on these, can you say the goods 1 and 2 are (gross, or Marshallian) complements or substitutes?
- PROBLEM 3 – Slutsky Equation, Income Effect, Substitution Effect, and Total Effect There are two goods which quantities are to be denoted by x and y, while prices are denoted by px and py, respectively. There is a consumer whose income is to be denoted by I and utility by u. His expenditure function is known to be: *see image* Suppose the consumer already spend $90 on good x which cost $1 and good y which cost $1, and initially purchase 60 of good x and 30 of good y. i. If the price of good x increase to $2, how many will he purchase each of the goods? ii. How much of the decrease in his demand for good x is due to the fact that they have become relatively more expensive? How much is due to the fact that his overall purchasing power has decreased? [Hint: find first the initial utility before the price change and income level needed to reach those initial utility with new prices. Slope of the indifference curve is given by MRS = -2y/x] iii. Based on your answer, draw it in a graph…Bob views apples and oranges as perfect substitutes in his consumption, and MRS 1 for all combinations of the two goods in his indifference map. Suppose the price of apples is $2 per pound, the price of oranges is $3 per pound, and Bob's budget is $30 per week. What is Bob's utility maximizing choice between these two goods? A) 10 pounds of oranges and no apples B) 15 pounds of apples and no oranges C) 5 pounds of apples and 5 pounds of oranges D) 4 pounds of apples and 6 pounds of oranges E) none of the above10 . Consider a consumer with a utility function U = x1 + x2. Initially, the consumer was only purchasing good 2, but after the price of good 1 was reduced, the consumer switched all of her consumption into good 1. The total change in consumption of good 1 is due to the pure substitution effect (and the income effect is zero). True False 12. If a consumer has homothetic preferences (for two possible goods, good 1 and 2) we know that: They spend a fixed proportion of their income on each good (for given prices) O at least one good is an inferior good both goods must be normal all changes in consumption are derived from the pure substitution effect (that is, there are no income effects) both a and c
- Suppose a consumer’s utility function is u = x_1^(3/2) x_2^(3/2) . She spends her budget of £27 for two goods. The prices of both goods are p1 = 6 and p2 = 6 Now suppose that instead both goods are priced as follows: There is a discount of 50% on the price of good 1 on each additional unit in excess of 3 units, and there is a discount of 50% on the price of good 2 on each additional unit in excess of 3 units. Draw the new budget constraint and derive it analytically.Bob views apples and oranges as perfect substitutes in his consumption, and MRS = 1 for all combinations of the two goods in his indifference map. Suppose the price of apples is $2 per pound, the price of oranges is $3 per pound, and Bob's budget is $30 per week. What is Bob's utility-maximizing choice between these two goods?RM2 1. Assume Good X and Good Y are perfect complements and both are normal goods. Suppose the price of X increases while the price of Y remains unchanged. On a preference map, a. demonstrate the change in the optimal consumption bundle. b. On a separate graph, decompose the substitution effect and the income effect.
- q18- Which of the following statements about the budget constraint is true? The slope of the budget constraint is: (i) the rate at which a consumer can trade one good for another (ii) equal to the slope of the highest indifference curve (iii) constant Select one: a. (i) and (ii) b. (i) and (iii) c. (ii) and (iii) d. (i) only Clear my choiceMaria spends all of her income of $2,000 on food (F) and clothing (C). The prices per unit are: PF = $5 and PC = $20. d) Graph Maria’s budget line, with F on the vertical axis and C on the horizontal axis. (e) Maria (can, cannot) __________ afford to buy a combination of 200 F and 60 C because this combination of goods is located (outside, inside, on) __________ her budget line. (f) The slope of this budget line is _________. (g) The opportunity cost of one piece of clothing is ___ units of food. h) If Maria’s income rises to $3,000, the new intercepts of her budget line are _____ F and _____ C. (i) Graph this new budget line on your graph for item (d) above.Suppose a consumer’s utility function is given by U(X,Y) = X1/2*Y1/2. Also, the consumer has $72 to spend, the price of Good X, PX = $1, and the price of Good Y, PY = $1. Now suppose PX increases to $9 a)Of the total change in the quantity demanded of Good X, how much is due to the substitution effect and how much is due to the income effect? (Note: since there is an increase in the price of Good X, these values will be negative). b) On a piece of paper, draw on a graph the original budget constraint new budget constraint compensated budget constraint Also, on your graph, indicate the optimal bundle on each budget constraint. Label the optimal bundle on the original budget constraint X* and Y* Label the optimal bundle on the new budget constraint X** and Y** Label the optimal bundle on the compensated budget constraint XCand YC
