Microeconomics
21st Edition
ISBN: 9781259915727
Author: Campbell R. McConnell, Stanley L. Brue, Sean Masaki Flynn Dr.
Publisher: McGraw-Hill Education
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Question
Chapter 7.A, Problem 2AP
To determine
The indifference curve and total utility.
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Students have asked these similar questions
Suppose Charlie has a utility function U(1, 2) = min{20, 5æ2} and that initially
the price of x2 is 5 and the price of 21 is 1, and that initially in the optimal bundle
Charlie consumes 20 units of æ1. If the price of 1 then changes to 3, what is the
new optimal amount of a1?
None of the other answers are correct
O 12
15
O 10
4.
To determine the utility maximizing consumption of two products one uses the formula that is
called the rule for maximizing utility:
OP1/P2-MU1/MU2 which also is stated as MU1/PU1-MU2/P2..
OExplains the Diamond-Water Paradox.
O Calculates the utility maximizing consumption of the two goods.
All of the above are correct.
None of the above are correct.
3- Suppose there are two agents Ahmet and Berk in an economy, and both consume two goods X and Y. Also assume that price of X is 2 YTL and Y is the numeraire good, thus price of Y is 1 YTL. Ahmet and Berk has the following utility functions:UAhmet (XA,YA)= 5ln(XA)+ln(YA)UBerk (XB,YB)= XB0,5 YB0,5a. Now assume that both X and Y are private goods. Write down the optimality condition for both agents. Then, write down the optimal level of X as a function of Y for both agents.
Chapter 7 Solutions
Microeconomics
Ch. 7.1 - Prob. 1QQCh. 7.1 - Prob. 2QQCh. 7.1 - Prob. 3QQCh. 7.1 - Prob. 4QQCh. 7.A - Prob. 1ADQCh. 7.A - Prob. 2ADQCh. 7.A - Prob. 3ADQCh. 7.A - Prob. 1ARQCh. 7.A - Prob. 2ARQCh. 7.A - Prob. 1AP
Ch. 7.A - Prob. 2APCh. 7.A - Prob. 3APCh. 7 - Prob. 1DQCh. 7 - Prob. 2DQCh. 7 - Prob. 3DQCh. 7 - Prob. 4DQCh. 7 - Prob. 5DQCh. 7 - Prob. 6DQCh. 7 - Prob. 7DQCh. 7 - Prob. 8DQCh. 7 - Prob. 9DQCh. 7 - Prob. 10DQCh. 7 - Prob. 1RQCh. 7 - Prob. 2RQCh. 7 - Prob. 3RQCh. 7 - Prob. 4RQCh. 7 - Prob. 5RQCh. 7 - Prob. 1PCh. 7 - Prob. 2PCh. 7 - Prob. 3PCh. 7 - Prob. 4PCh. 7 - Prob. 5PCh. 7 - Prob. 6PCh. 7 - Prob. 7P
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- Daniele has an income of 100 and he has to spend it to buy pencils and pens. To him, the two goods are perfect substitutes, i.e. u(x₁,x2)= X₁ + X2. If pens are twice as expensive as the pencils, what would be his optimal bundle? O Buy only Pens O Any combination maximises his utility O Buy only Pencils O Buy same amount of pens and pencils O Buy twice as many pencils as pens O No answer.arrow_forwardConsider the following indifference curve. The marginal rate of substitution between points C and D is roughly equal to Price (dollars per pizza) $40 30 20 50 Quantity of pizzas per week 100 O 2 O 0.5 O 1.5arrow_forwardRosalia buys only two goods X₁ and x₂. Her utility function is Cobb-Douglas. Her optimal choices have which of the following properties? O One of the goods is an inferior good and the other is a normal good. O Her purchase of x₁ depends on her income and on the prices of both goods, p₁ and p2. O Her purchase of x₁ does not depend on income. O Her purchases for neither good depends on income. O Her purchase of x2 depends only on her income and on the price of that good, p2.arrow_forward
- Suppose that the following utility function is given U(X,Y) = x/3y1/2, Which of the following is correct? O We have convex preferences since Law of diminishing Marginal Rate of Substitution holds and indifference curves are bowed inward towards the origin We have convex preferences since Law of diminishing Marginal Utility holds and indifference curves are bowed outward from the origin O We have convex preferences since Law of diminishing Marginal Rate of Substitution fails to hold and indifference curves are bowed inward towards the origin O We have non-convex preferences since Law of diminishing Marginal Rate of Substitution holds and indifference curves are bowed inward towards the originarrow_forward4.13 CES indirect utility and expenditure functions In this problem, we will use a more standard form of the CES utility function to derive indirect utility and expenditure functions. Suppose utility is given by U(x, y) = (x° +y®)'/8 [in this function the elasticity of substitution o = 1/(1 – 6)]. a. Show that the indirect utility function for the utility function just given is V = I(p, + p,)¬/", where r = 8/(ò – 1) = 1 – 0. b. Show that the function derived in part (a) is homogeneous of degree zero in prices and income. c. Show that this function is strictly increasing in income. d. Show that this function is strictly decreasing in any price. e. Show that the expenditure function for this case of CES utility is given by E = V(p', + p,)''". f. Show that the function derived in part (e) is homogeneous of degree one in the goods' prices. g. Show that this expenditure function is increasing in each of the prices. h. Show that the function is concave in each price.arrow_forwardWhich one of the following statements about preferences is true? O Quasilinear tastes can be defined, such that if (x1, x2) > (Y1₁. y2), then (tx1, tx2) > (ty1₁, ty2) O Homothetic preferences have the same MRS on a ray from the origin, whereas quasilinear preferences have the same MRS on a vertical ray. The MRS for perfect complements is 0 on the vertical part of the indifference curve, -∞ on the horizontal part of the indifference curve and undefined at the kink. O If goods X and Y are perfect substitutes (with X measured on the horizontal axis) and the MRS MUX> Px, then the consumer will optimize by consuming only good Y. MUY Py O The Engel curve for a normal good will bend backwards, whereas the Engel curve for an inferior good will slope upwards. O No answer.arrow_forward
- 5. Which one of the following statements is definitely correct for the marginal rate of substitution MRS(x1,x2) = dxX2/dx1 of some continuous preferences over bundles of x1 and x2 with prices p, and p2, respectively? a) If the preferences over x1 and x2 are strictly monotone, MRS(x1,x2) 0. c) For strictly monotone preferences, at a corner solution (x;,x;), MRS(x¡,x;) = P1/P2. d) For strictly monotone and strictly convex preferences, if at a point (x1,x2) on the budget line MRS(x1,x2) > P1/P2, then the optimum bundle (x, x;) lies where x X2.arrow_forwardAssume a piece of jewelry, and 3 consecutive drops in its price, from ??1 to ??2, from ??2 to ??3 and from ??3 to ??4. Alia’s preferences are such that her demand is relatively elastic between ??1 and ??2, relatively inelastic between ??2 and ??3, and that she perceives that piece of jewelry as a Giffen good between prices ??3 and ??4. How would her priceconsumption curve look like in an indifference curves framework with well-behaved preferences? Clearly label your graph.arrow_forwardBe fast Suppose there are three (3) consumers in a market for bottles of perfume; Mutumbu, Jasanu and Julius The individual demand for perfumes for each of these consumers is given as 10 bottles for Mutumbu, 15 bottles for Jasanu and 25 bottles for Julius at $60 per bottle for perfume. Thus, the market demand for perfumes if the market price is $60 is: (a)40 bottles (b)60 bottles (c)80 bottles (d) None of the abovearrow_forward
- Draw the following scenario: Assume a piece of jewelry and 2 consecutive drops in its price. Also consider Alia’s demand to be relative elastic in the price range from ? 1to ? 2, and that she perceives jewelry as a Giffen good in the price range from ? 2to ? 4. Draw her price-consumption curve with well-behaved preferences. Clearly label your graph. The graph may be something like this:arrow_forward5. 24.A large Coca-Cola vendor recently hired some economic analysts to assess the effect of a price increase in its 16-ounce bottles from $1.00 to $2.00. The analysts determined that, on average, the vendor's customers spend about $15.00 on soda (Coke and all other brands) each week, and the average price for other 16- ounce soda bottles is $1.00. The analysts also utilized some focus groups to determine the preferences of the vendor's customers. They used this analysis to build the following graph: Bottles of Budget line with price of $1.00 Other Soda Budget line with price of $2.00 Bottles of Coke Suppose Xo = 9 and X1 = 7. Should the vendor expect to sell 7, more than 7, or less than 7 bottles of Coke after raising the price to $2.00 if Coke is a normal good?arrow_forwardSuppose we observe that an individual's demand for good 1 is: 1/(2p,+p2) (where I- income). From this we can conclude that: Goods 1 and 2 are perfect complements O The price of good 1 is higher than the price of good 2 Two answers are correct O Goods 1 and 2 are perfect substitutes Three answers are correct No answer is correct Goods 1 and 2 are normal goods O These goods may be perfect substitutes or perfect complements, it depends upon the utility functionarrow_forward
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