Question 1 Yoko has the utility function U(x, y) = 2r(y + 3). The price of x is £2 and the price of y is £1. Income is £10. i. How much x does Yoko demand? How much y? ii. If her income doubles and prices stay unchanged, will Yoko's demand for both goods double? Show all your calculations by any method including the Lagrange multiplier if needed.

Question 1 Yoko has the utility function U(x, y) = 2r(y + 3). The price of x is £2 and the price of y is £1. Income is £10. i. How much x does Yoko demand? How much y? ii. If her income doubles and prices stay unchanged, will Yoko's demand for both goods double? Show all your calculations by any method including the Lagrange multiplier if needed.

Exploring Economics

8th Edition

ISBN:9781544336329

Author:Robert L. Sexton

Publisher:Robert L. Sexton

Chapter10: Consumer Choice Theory

Section: Chapter Questions

Problem 3P

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Question 2 David spends his budget on chocolate and chip. His utility function is given by ?(?1,?2)= 2?1?2, where ?1 is the number of chocolates he consumers per week, and ?2 is the number of chips he buys per week. A chocolate costs 10 SEK, and a chip costs 20 SEK. David’s weekly budge for consuming on these two goods is 120 SEK. (1) What is David’s budge line? Draw the budget line on a graph with chocolate amounts on the horizontal axis and chip amounts on the vertical axis. Write explicitly at which points budget line crosses the axis. (2) What is David’s marginal utilities for the two goods, respectively? What is his marginal rate of substitution between the two goods? (3) What is David’s optimal choice? Calculate the numerical answer for the optimal bundle. Also draw an indifference curve for David on the same graph as question(1) and show the optimal bundle.
1) Elaine wants to keep a good balance of soup and Jujyfruit (a delicious fruit flavored candy) in her diet. Her preferences over bundles of soup and Jujyfruit are represented by the quasi-linear utility function U(S,J) = J0.5 + S, where S and J denote the quantities of soup and Jujyfruit, respectively (Assume fractional quantities of each good can be consumed). Let Ps & Pj denote the prices of the goods and Y denote Elaine's monthly income for spending on these goods. For this exercise, treat soup as the x-axis good. a) Find Elaine's Marshallian demand for soup and Jujyfruit. Is soup a normal or an inferior good? Justify your answer using calculus. Also, calculate the derivative of Marshallian demand for Jujyfruit with respect to income and briefly explain what this implies about the relationship between the demand for Jujyfruit and income for Elaine. b) Now, assume Pj = $5 and Ps Marshallian demanded quantities of Jujyfruit and soup given these prices and income. Use your answers…
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Xavier has preferences between food eaten today and food eaten tomorrow of the form. U(today, tomorrow) = 0.51 * ln(today) + 0.49 * ln(tomorrow) He has $100,000 to spend. Food today costs $20 per pound; food tomorrow costs $19 per pound. 9. How many pounds of food does he consume today? 10. How many pounds of food does he consume tomorrow? (Please evaluate to get number values as solution)
1. Suppose someone's budget is $780, and it is fully spent on buying Product A. The price of this product is $26. Calculate the price change of Product A if there is a 1.3 times increase in the quantity available to purchase. Enter your answer in the box below, use a minus sign to show a decrease in price, and round to the nearest whole number if necessary. 2. Consider the spending choices of the following consumer: Emily's income is spent on colas and orange sodas, as well as other goods. She considers colas to be a normal good and orange sodas to be a normal good. What will happen to Emily's purchases of these goods if her income decreases? Select the best answer. She will buy more colas and fewer orange sodas.She will buy fewer colas and fewer orange sodas.She will buy more colas and more orange sodas.She will buy fewer colas and more orange sodas. Is the following statement true or false? Select the best answer. The price ratio of coffee to cookies is 1.5, so the marginal utility…
Question 3 (Demand). Carlos really likes pizza. His utility function for Little Caesar's (xi) and Woodstock's (x.) is given by: U(xi, x2) = x;+2x2 The price of x,is $10 and Carlos spends $50 on pizza. a) Graph the demand curve for x1, with pi (the price of x) on the y-axis and x, on the x-axis. (Hint: There will be a range of prices where the demand for x, will be 0). Explain you graph. Page 2
1. Muhammad enjoys going to the aquarium (x) and playing basketball (y). His preferences on x and y are described by his utility function: U(x, y) = 100x23y3. He has a budget of £120 per week to spend on playing basketball and going to the acquarium. Knowing that p,=10 and py=10: ,2/3,1/3 (A) Find the optimal combination of x and y so that Muhammad maximizes his utility subject to the budget constraint. Show this graphically. (B) Consider now that the price of going to the aquarium increases to £20, the price of playing basketball is now £15 and the income did not change. How does this modify Muhammad's optimal bundle? Show this graphically. (C) Compare the optima in (A) and (B): has the valuation of y in terms of x changed? Explain.
DEFINE Limit of consumption options
Assume that you have a budget of Taka 4000 that can spend on two goods like: coke and burger. Suppose coke costs Taka 100 per unit and burger costs 400 per unit. Suppose also that your utility function is given by the equation U(B, C) = 20BC. Write your budget equation. What combination of coke and burger should you buy to maximize utility?
Questions 4 (Choice & Demand). Suppose a consumer's utility function is given by: U(xi, x2 ) = x" a) What is the consumer's demand for x, as a function of income and prices? What is the consumer's demand for x; as a function of income and prices? Use Lagrange method or your intuition. b) What percentage of income does the consumer spend on x;? What percentage of income does the consumer spend on x2?
With diminishing marginal utility, how do consumers decide how much to consume? Students are expected to give a detailed answer to this question. You must include an explanation about what diminishing marginal utility means in your answer. Concepts such as "budget constraint", "more is better", "utility". "marginal utility", and "marginal utility per dollar spent" must be used in your answer. No graph or calculation is required in this question.
Q- Marginal utility can never be negative. True/False