Bill is the only person on an island, and he has an endowment of 20 units of coconuts (C) and 5 units of water (W). His utility function is: U(C,W) = In(C) +2 ln(W) a) Find the marginal utility of C and W. b) Find the marginal rate of substitution when Bill consumes all of his endowment.

Bill is the only person on an island, and he has an endowment of 20 units of coconuts (C) and 5 units of water (W). His utility function is: U(C,W) = In(C) +2 ln(W) a) Find the marginal utility of C and W. b) Find the marginal rate of substitution when Bill consumes all of his endowment.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Related questions

Q: (In this question we denote income by Y, not by W as in the lecture notes). The following figure…

A: Giffen goods are the special cases of inferior goods in which an income effects overweighs the…

Q: You have the Cobb-Douglas utility function u(x,y) = xy over apples (x) and plums (y) and you have…

A: To construct a set of feasible set of bundle we need to keep both the budget income and weight…

Q: If u(x. y) is a utility function, then v(u) = u is a function that fulfills the monotonic…

A: Utility is an essential concept in economics which means the capability to satisfy various wants and…

Q: a) Graphically derive Vivi’s demand for tea when her income is $60 and the price of crumpets is $2.…

A: The utility function for the above is the Rawlsian utility function. For such a utility function…

Q: Michael does not like to mix peanut butter and jelly in the same sandwich. However, he will consume…

A: May be define as a term that is the total satisfaction derived from the consumption of a particular…

Q: There are two goods, coffee and mineral water, available in arbitrary nonnegative quantities (so the…

A: In theory of economic, a budget constraint refers to possible combinations of goods and services…

Q: Suppose Kayla has preferences over cakes (c) and pints of ice cream (i) that can be characterized…

A: To determine how many pints of ice cream Kayla would be willing to give you in exchange for one…

Q: Bob enjoys cookies (x) according to the utility function U(x)=20x- 2 tx , where t is a parameter…

A: According to the envelope theory, if the exogenous variable changes, the direct effects of that…

Q: Find Indirect utility function of the following function U= max (X, Y) subject to the budget…

A: Maximize U = Max(X,Y) Subject to Px*X + Py*Y ≤M This is the problem with cornor solution, here at…

Q: Assuming that the student is rational, for how many hours is she renting a bike if she can only rent…

A: Student's equilibrium condition is MUx/MUy = Px/Py where, MUx = ∂U/∂x MUy = ∂U/∂y

Q: Summer break is approaching! Suppose you derive utility from days spent traveling on vacation…

A: Given: The utility function over two goods is: The budget constraint is: To Find: The demand…

Q: For the utility function U = Qx0.68Qy(1-0.68) and the budget 103 = 10Qx + 13Qy find the CHANGE in…

A: Utility maximization problem: With the given prices and the income, a consumer chooses his…

Q: Casper's utility function is 3x + y, where x is his consumption of cocoa and y is his consumption of…

A: The budget line shows the different combinations of two goods that a consumer can consume given the…

Q: Consider the consumer whose tastes and preferences for (X) and (Y) can be characterized by the…

A: The utility function can be written as follows: The budget constraint can be written as follows:

Q: Calculate the demand for goods for Mad Hatter Assume Mad Hatter has utility U = q1M * (q2M)^2. He…

A: The demand curve shows the inverse relationship between price and quantity demanded. The demand…

Q: Under option A, Nick's utility maximizing basket is D and R =U- Under option B, Nick's utility…

A: The above question is the problem of utility maximization subject to budget constraint so that an…

Q: A shady raccoon strands you on a deserted island with nothing but tree branches (B) and cherries…

A: In the consumer theory, a consumer maximizes his total utility or satisfaction by consuming at a…

Q: A consumer utility function is U = 1 log x1 + log x2. His budget constraint is given by 2x1 + 4x2 =…

A: The consumer is in equilibrium when he gets maximum satisfaction out of his expenditure. The…

Q: Maya is doing her undergrad at Queen's University. She loves donuts and chocolate chip cookies…

A: a) When the price of CCC (chocolate chip cookies) is $1, which is the same as the price of donuts,…

Q: For the utility function U = Qx0.48Qy(1-0.48) and the budget 188 = 11Qx + 11Qy find the CHANGE in…

A: Utility maximization problem: With the given prices and the income, a consumer chooses his…

Q: Assume you consume two goods, X and Y. Your utility function is U = 2X + 4Y. Let PX= $4, PY= $2, and…

A: A perfect substitutes function of utility is a particular kind of utility function in economics that…

Q: Roisin consumes only two goods, X and Y, and her utility function is given by U = XY. Her income is…

A: Condition for equilibrium combination: Marginal Rate of Substitution = Price Ratio MRS = MUx/Muy =…

Q: Suppose the consumer is endowed with 10 units of orange and consumes 5 units of apple. The price of…

A: Endowment factor depicts how individuals will generally esteem things that they own more…

Q: Malcom only consumes 2 goods - Good A and Good B. His budget constraint is 4A+2B=400, which means…

A: Let us consider that the amount of A consumed is denoted by "A" and the amount of B consumed is…

Q: In Problem 6, Elmer's utility function is U(x, ) = min{x, y²}. If the price of x is $20, the price…

A: From the utility function, we know x and y are complements Thus, x=y2 When y= 8 x = (8)2 = 64if 8…

Q: Adam's Utility at Optimal Consumption Bundle Given Adam's utility function U = 4x0.8y 0.2 And the…

A: The notion in issue is related to the utility maximization paradigm in economics, which assumes that…

Q: A consumer has a utility function U(X,Y ) = X1/2 Y1/2 . Prices of the goods are pX = £10 and pY =…

A: The utility is the satisfaction that is derived from the consumption of the goods or services. The…

Q: Julian is interested in only two goods: good X and good Y and has M dollars to spend (and always…

Q: find the CHANGE in optimal consumption of X if the price of X increases by a factor of 1.5.

A: Utility is the total satisfaction that the consumer derives from the consumption of good.The…

Q: There are two goods, coffee and mineral water, available in arbitrary nonnegative quantities (so the…

A: Given, There are two goods, coffee and mineral water, available in arbitrary nonnegative quantities…

Q: Şeyma has the following utility function: U(x,y) = x'/²y+/2 and faces the budget constraint: M = P,x…

A: Maximizing, U(x,y)=x1/2y1/2 subject to, M=Pxx+Pyy Now, y=1PyM-Pxx Using the above equation in…

Q: A consumer can consume three goods, x₁, x2, and x3. In the markets where she buys them, she is a…

A: Utility, in economics, implies the usefulness or happiness a consumer can get from a service or…

Q: Beans and doughnuts: The consumer receives positive benefits from the consumption of beans (B) and…

A: Optimal consumption bundle: The optimal consumption bundle is such that at that bundle the…

Q: Kai spends his income on lime (L) and ginger water (G). Lime is priced at $2, while ginger water…

A: PL = 2 , PG=1 and I = 30

Q: A and B consume only two goods, cider (C) and dumplings (D). A has an initial endowment of 10…

A: Utility:The utility is want satisfying power of a commodity. It can be expressed in cardinal and…

Q: (1) Draw an Edgeworth box and show the initial allocation of goods, to be labelled e. Indicate the…

A: Here the lower left hand side corner is the point of origin for David and the top right hand corner…

Q: You enjoy consuming apples (A) and oranges (O). Suppose that your by Your marginal utility function…

A: The consumer will reach at equilibrium when the slope of a budget line is equal to the slope of an…

Q: Matthew Hamming is stranded on an island. He has decided that he will spend exactly 10 hours a day…

A: Utility function The utility function is a study that measures the combination of two goods. under…

Q: Summer break is approaching! Suppose you derive utility from days spent traveling on vacation…

A: Utility function over these two goods; U(D,F)= 4D0.25F0.75 Budget constraint; I(D,F)= PdD+ PfF D=…

Q: Alex's utility is U (TAYA) = min {TAYA), where A, and YA are his consumptions of I goods and y…

A: An extremely important concept in microeconomics is the Walrasian equilibrium, which symbolizes the…

Question

Bill is the only person on an island, and he has an endowment of 20 units of coconuts (C) and 5
units of water (W). His utility function is:
U(C, W) = In(C)+2 ln(W)
a) Find the marginal utility of C and W.
b) Find the marginal rate of substitution when Bill consumes all of his endowment.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, economics and related others by exploring similar questions and additional content below.

Similar questions

Problem 3 (10 points; 5 points for each part): Richard has a total utility function of: TU = 10q₁q₁²+24q2q2² +9192, where q₁ and q2 are goods. Richard is currently consuming at q₁ = 4 and q₂ = 6, which is also his utility maximizing consumption level. (Richard's optimal point is an interior solution). (a) How much additional utility would Richard receive if he were to increase his consumption of q2 from 6 to 7? (5 points). (b) How much q2 is Richard willing to pay (in terms of q2) in order to consume the 5th unit of q₁? (5 points).
Two students go out to lunch and decide to split the bill evenly between them. Each student has a quasi-linear utility function given by ui(fi , xi) = φi(fi) + xi , where φi(·) is strictly concave, fi is the amount of food consumed by student i, and xi is a composite numeraire good. Each student has a fixed budget of mi . EVALUATE THIS CLAIM: Both students eat too much!
If the consumer's budget constraint is given by 4P + 2B = 50 where P is Pizza and B is Burgers, the following bundles of Pizza and Burger would be on the budget constraint: P = 5; B = 10 P = 2; B = 21 P = 10; B = 20 %3D P = 2; B = 24
For the utility function U = Qx^0.84Qy^(1-0.84) rate between good X and good Y at Qx= 7 and Qy=19 find the trade-off
Karen has perfect complement preferences over toothbrushes B and toothpaste P, with the associated utility function U(B,P) = min (3B, 2P). Suppose the price of a toothbrush is $6, the price of toothpaste is $4 a tube, and she has $72 to buy her entire year's supply of toothbrushes and toothpaste. How many toothbrushes and tubes of toothpaste will she buy?
Two friends, Karol and Manuel, like to drink kombucha (x₁) and matcha (x₂). Both X₁ and X2 are expressed in ounces. The following utility function represents Karol's preferences: 1 1 2 2 u (x1, x2) = x1 x3 The following utility function represents Manuel's preferences: u (x₁, x2) = √√x1 + x2 Karol's income in dollars is denoted by mk, and Manuel's income is denoted by mm. Both face the same prices in the market, denoted by p₁ and p2, for kombucha and matcha, respectively. Both prices are expressed in dollars per ounce. Assume p₂=1 throughout the whole question. 1) Draw Karol's and Manuel's indifference curves in separate graphs and describe any important similarities or differences between the two.
Refer to figure. Suppose the consumer is endowed with 10 units of orange and consumes 5 units of apple. The price of the apple decreases and at the new price the consumer consumes 9 units of apple. The change in the demand for apples due to the endowment effect is equal to Optionsa) 3b) 4c) 1d) none of these
Suppose the function for the utility from good c is denoted as U(c)=2c2. Which of the following expressions indicates the marginal utility of c? 1/c2 1/square root of c All of the above are correct.
Bread and doughnuts: The consumer receives positive benefits from the consumption of beans (B) and donuts (K). Utility function of the consumer is the following: U(B,K) = 100∙B0.25 · K0.75 The price of beans (can) is ISK 2,000. but the price of a donut (box) is ISK 4,000. Consumption restrictions are placed on the consumer since his income is ISK 400,000. Put on all form donuts on the x-axis and beans on the y-axis. a) Show an equation for the bean's success rate for a single donut in light of the utility function. Draw the equivalence curve on a picture and explain what the equation is performance ratio is stated at each point on the equivalence curve. Explain with the concept of the efficiency ratio of the curvature of the equivalent curve. b) Find the most efficient consumption combination and draw on the diagram. c) The government decides to support the consumption of beans so its price drops to 1,000. Who is the most economical consumption combination based on the changed price…
For a consumer with a utility function u=3x^2y^2 when px=3 and py=4, find the consumption levels that maximize his utility under the $120 budget constraint. What is the maximum benefit?
Allen has a utility function U=xy², where x is the consumption of apples and y is the consumption of bananas. Price of apple is 1 and price of bananas is 4. Allen has 30 dollars in his pocket, so how many apples and bananas will he purchase to maximize his utility? options: 10 apples and 5 bananas. 3 apples and 10 bananas. 30 apples only. none of above.
Part A . Consider an economy with the following features. • There are 100 identical consumers that derive utility from consuming three different goods: software, computers, and good m. • Each consumer decision utility function is given by U (c, 8) = 4c¹/48¹/4+m, where e denotes the amount of computers that she consumes, s denotes the amount of software that she consumes, and m denotes the amount of good m that she consumes. cand s must be non-negative, but m can take any real value. • Computers are produced by 20 identical competitive firms with a total cost function given by 10c². • Software is produced by 40 identical competitive firms with a total cost function given by 20s². . QUESTION 1: What are the equilibrium prices for software and comput- ers in equilibrium? Part B • Suppose that there is a positive technology shock in the software industry so that that the new cost function of the software firms becomes 10s². Let C and S denote, respectively, the aggregate level of…