You have $4,000 to spend on entertainment this year (lucky you!). The price of a day trip (T) is $40 and the price of a pizza and a movie (M) is $20. Suppose that your utility function is U(T, M) = T3/4M1/4. a. What combination of T and M will you choose? b. Suppose that the price of day trips rises to $50. How will this change your decision?
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You have $4,000 to spend on entertainment this year (lucky you!). The price of a day trip (T) is $40 and the
price of a pizza and a movie (M) is $20. Suppose that your utility function is U(T, M) = T3/4M1/4.
a. What combination of T and M will you choose?
b. Suppose that the price of day trips rises to $50. How will this change your decision?
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- You have $3,000 to spend on entertainment this year (lucky you!). The price of a day trip (T) is $40 and the price of a pizza and a movie (M) is $20. Suppose that your utility function is U(TM) T1/3M2/3. a. What combination of T and M will you choose? b. Suppose that the price of day trips rises to $50. How will this change your decision?EXERCISE 7 Aisha is considering how to allocate the next 6 hours of her free time. She could choose between leisure (L) and helping her neighbour with the house chores. If she decides to help her neighbour, she is going to get paid at £25 per hour, which she can then spend on her favourite pizza (P). Suppose the price of pizza is £12.50. Aisha's preferences for leisure and pizza are given by the following utility function: U(L, P) = 3L + P. (MU₁ = 3, MUp = 1). a) Write down Aisha's budget equation and draw the corresponding budget line. Clearly label the axes and calculate the coordinates of the points of intersection of the budget line with each axis. b) Calculate Aisha's marginal rate of substitution between leisure and pizza. Explain the concept of MRS and interpret the figure obtained. c) Find Aisha's optimal consumption bundle, both algebraically and graphically. Explain your reasoning. d) Would Aisha's optimal choice change if she could get a discount on her pizza purchases so…Economics Summer break is approaching! Suppose you derive utility from days spent traveling on vacation domestically, D, and days spent traveling on vacation in a foreign country, F. Your utility function over these two “goods” is: U(D, F) : 4D0.25F 0.75 Let your budget constraint be I(D, F) = pDD + pF F; where I is your income, pD is the price of domestic travel per day, and pF is the price of foreign travel per day. a. Determine the demand functions for domestic travel and foreign travel. Make sure you show your work – show the steps used. b. Suppose that you’ve saved $800 for your summer travel, the price of domestic travel per day is $25 and the price of foreign travel per day is $100. How many days of each type of travel will you embark on? c. Illustrate the indifference curve, budget constraint, and the utility maximizing bundle associated with (b). Make sure you show the level of utility, the budget constraint intercepts, and the optimizing equilibrium. Your answer
- 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.EXERCISE 6 If Ginna spends her entire budget, she could buy a chosen set of groceries and also buy 10 notebooks. If she spends only half of her budget, she could only buy a set of groceries and could not afford any notebooks. Suppose Ginna's budget is £150. Her preferences for groceries (G) and notebooks (N) can be described by the following utility function: U(G, N) = 30G + 2N (MUG = 30, MUN = 2). a) Find Ginna's optimal consumption bundle. Provide both algebraic and graphical solution. Explain your reasoning. b) Discuss how the price of a notebook should change for Ginna to change her optimal consumption choice. c) If the price of a notebook increases by 50%, how should the price of the groceries drop so that Ginna can be as well off as before this change in prices? d) Discuss the implications of the price change from c) on Ginna's optimal choice. In your discussion, include the analysis of the substitution and income effects as well as Ginna's demand for groceries and/or notebooks.If Ginna spends her entire budget, she could buy a chosen set of groceries and also buy 10 notebooks. If she spends only half of her budget, she could only buy a set of groceries and could not afford any notebooks. Suppose Ginna's budget is £150. Her preferences for groceries (G) and notebooks (N) can be described by the following utility function: U (G, N) = 30G + 2N (MUG = 30, MUN = 2). a) Find Ginna's optimal consumption bundle. Provide both algebraic and graphical solution. Explain your reasoning. b) Discuss how the price of a notebook should change for Ginna to change her optimal consumption choice. c) If the price of a notebook increases by 50%, how should the price of the groceries drop so that Ginna can be as well off as before this change in prices? d) Discuss the implications of the price change from c) on Ginna's optimal choice. In your discussion, include the analysis of the substitution and income effects as well as Ginna's demand for groceries and/or notebooks.
- 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?Pele enjoys coffee (C) and tea (T) according to the function U(C, T) = 6C + 8T (a) What does her utility function say about her MRS of coffee and tea? (b) Suppose the price of coffee (PC) and the price of tea (PT) are both $3. If Alana has $12 to spend on these products, i. How much coffee and tea should she buy to maximize her utility? ii. Draw a carefully labeled graph of her indifference curve map and her budget constraint. Put the quantities of coffee on the horizontal axis. Be sure to identify the utility maximizing point. (c) Would Alana buy more coffee if she had more income? Explain. (d) Suppose the price of coffee fell to $2. How would her consumption change?Suppose you had a budget of $20.00 and the prices of a burger and a slice of pizza are $4.00 and $2.00 respectively. What is the marginal utility per dollar spent for the fourth burger?
- Summer break is approaching! Suppose you derive utility from days spent traveling on vacation domestically, D, and days spent traveling on vacation in a foreign country, F. Your utility function over these two “goods” is: U(D, F) : 4D0.25F 0.75 Let your budget constraint be I(D, F) = pDD + pF F; where I is your income, pD is the price of domestic travel per day, and pF is the price of foreign travel per day. a. Determine the demand functions for domestic travel and foreign travel. Make sure you show your work – show the steps used. b. Suppose that you’ve saved $800 for your summer travel, the price of domestic travel per day is $25 and the price of foreign travel per day is $100. How many days of each type of travel will you embark on? c. Illustrate the indifference curve, budget constraint, and the utility maximizing bundle associated with (b). Make sure you show the level of utility, the budget constraint intercepts, and the optimizing equilibrium.Question 3. Suppose that Janice only cares about tea (T) and coffee (C). Her utility function is U = 2T + 4C. The price of T is $1.50, and the price of C is $2.50. Janice has a budget of $15 for tea or coffee during the week. (a) Write down the consumers maximization problem. (b) What are the consumption quantities of T and C that will maximize Janice's utility?8. Pele enjoys coffee (C) and tea (T) according to the function Replace 'Pele' with Alana U(C, T) = 3C + 4T(a) What does her utility function say about her MRS of coffee and tea?(b) Suppose the price of coffee (PC) and the price of tea (PT) are both $3. If Alana has $12 to spend on these products,i. How much coffee and tea should she buy to maximize her utility? ii. Draw a carefully labeled graph of her indifference curve map and her budget constraint. Put the quantities of coffee on the horizontal axis. Be sure to identify the utility maximizing point.(c) Would Alana buy more coffee if she had more income? Explain. (d) Suppose the price of coffee fell to $2. How would her consumption change?