The Calculus of Demand Calculus Appendix Figure It Out: Question 1 of 3 Antonio gets utility from burgers (B) and fries (F). His utility function is U(B, F) = √√√BF = B0.5 F0.5 Antonio's income is $20, and the price of fries is $2. Derive Antonio's demand for burgers. Use symbolic notation and fractions where needed. B =

The Calculus of Demand Calculus Appendix Figure It Out: Question 1 of 3 Antonio gets utility from burgers (B) and fries (F). His utility function is U(B, F) = √√√BF = B0.5 F0.5 Antonio's income is $20, and the price of fries is $2. Derive Antonio's demand for burgers. Use symbolic notation and fractions where needed. B =

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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3. Suppose Paul, a 3rd grader, has the following utility function over his lunch of Twinkles (t) and soda (s), utility = U(t, s) = √√ts (a) If Twinkles cost $0.10 cach and soda costs $0.25 per can, how must Paul spend the $1.00 from his parents in order to maximize his utility?
Show whether or not the following utility functions are monotonic transformation of each other u = X,X2: u = lnX,lnX, %3! u = X, + X2: u = (X, + X,) u = X, + X2: u = (X1 + X2)? Show whether or not the following utility functions are convex U = x,°X, U = x, + X,2 U = X, + X,X2X
The utility function for Morris is U = min {AM, T}, where M is pints of milk and T is cans of tuna. Morris has S90 to spend or tuna (prices at $2 per can) and milk (priced at $1 per pint). What is Morris's utility-maximizing consumption bundle? 1)M = 40 and T= 25 2)M= 15 and T= 65 3)M= 10 and T= 40 4)M= 30 and T= 30
Question #4 Mary's preferences over X andY correspond to the following utility function: U(X,Y) = XY. Suppose that her income is M=$80 and that the market price of X is Px=$2, while that of Y is Py=$4 a) Find and plot her budget line, clearly indicating the intercepts and the slope. b) The marginal utility of X is MUx=Y3, while that of Y is MUy=3XY2. Compute and show Mary's optimal consumption bundle on the same graph. c) Find her utility at her optimal consumption bundle, specifying the amount of satisfaction she derives from the last unit of each good purchased.
Assume that Bob's utility function over beer x and pizza y is U(x,y) = 4x+12y. Which of the following statements is false? a) If the price of pizza is 12 and the price of beer is 3, then we can't determine how much pizza relative to beer Bob purchases. b) If the price of pizza is 16 and the price of beer is 5, then Bob only purchases pizza. c) If the price of pizza is 15 and the price of beer is 5, the own price elasticity of the demand for pizza as well as beer is infinite. d) It the price of pizza is 15 and the price of beer is 4, Bob purchases only beer e) Pizza and beer are perfect substitutes.
Let U(x, y) = 3x + y be the utility function of a consumer, whohas a budget of I. As a function of I, find the consumer’s Walrasian demand when the prices are px = py = 1. The price of good x increases to 2, find the new Walrasian demand for the new prices px= 2 and py = 1. Decompose this change into an income and a substitution effect.
Suppose a consumer has a budget of $200 to spend on two goods, X and Y, whose prices are $20 and $10, respectively. If the consumer is observed to buy 5 units of X and 10 units of Y, where the respective Marginal Utilities of X and Y are, 50 and 40 utils, is the consumer in equilibrium? Explain why or why not. If the consumer is not in equilibrium under conditions in d), suggest another combination that would possibly achieve equilibrium. Explain your answer.
There are two goods, apples and bananas. The price of apples is PA = $2,and the price of bananas is PB = $3. A consumer has $120 to spend, and his utility function is U(A,B)=2A2B3 a) With apples on the x axis, the slope of the budget line is ________ b) At A=2, B=1, the marginal utility of A is and the marginal utility of B is ________ c) At the optimal bundle, the consumer buys apples and bananas ______
Let U(x, y) = 3x + y be the utility function of a consumer, whohas a budget of I. As a function of I, find the consumer’s Walrasian demand when the prices are px = py = 1. The price of good x increases to 2, find the new Walrasian demand for the new prices px = 2 and py = 1. Decompose this change into an income and a substitution effect.
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John’s preferences for Orange (O) and lemons (L) are represented by the funtion U(O, L)= O+2L. The oranges cost £2 and the lemons £1. Given that John’s monthly income is £30 answer the following questions: What type of goods are oranges and lemons for John? What is the proportion to which John is willing to exchange Oranges for Lemons? Illustrate and solve graphically John’s utility maximization problem. If his income increases every month by £10, how will John’s consumption choice be affected? Illustrate graphically the income expansion path and the Engel curve for each good. How will an increase in the price of Lemons to £6 affect John’s optimal consumption choice? (John’s income is £30) Graph John’s demand curve for each good. Assume that John wins a voucher of £20, redeemable only in Oranges. How would this affect John’s utility? (Assume that prices and income are as described initially) Assume that John is presented with two options: an Orange voucher of £20 or just £6 to spend…