There are two goods, x and y. The consumers' utility is U=4x6y³. The price of x is Px=5, the price of y is Px=10. At interior optimum, the relationship between x and y is: options: y=2x y=0.25x y=0.5x y=x
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- 2Rubyhas just finished her economics exam and must decide whether to spend two hours going to the beauty parlour, having a couple of pizzas, or going to a movie. She can do one, all, or any two of these things. The question is, what should she do? The marginal utility of the beauty parlour serviceis 36 utils and the price is $6. The marginal utility of the two pizzasis 24 utils and the price is $4 for two pizzas. The marginal utility of going to the movie is 40 utils and the price is $10. Ruby's marginal utility of a dollar is 5 utils per dollar.Question 7 A consumer has a utility function 100-(x₁-4)4 -(x2-3)4 and a budget constraint of 9x1+3x2 <200. How much of good 2 do they consume?
- You have 6 hours to study for 2 exams tomorrow. The relationship between the time studying and test scores is shown below. Economics Psychology Hours 0 1 2 3 134 4 5 6 Score 55 3 70 70 63 76 81 85 88 Hours 0 1 2 3 4 5 6 Score 55 16 70 73 75 75 66 76 a. Use the rule for determining optimal purchases to decide how many hours you should study each subject. Treat each point on an exam like 1 unit of utility and assume you are equally interested in doing well in economics and psychology. You should study economics for hours and psychology for hours.Refer to the graph below Quantity of Y 160 0 Multiple Choice The consumer's income is $1,000 Why doesn't the consumer choose the combination at point B O Quantity of X 200 O The marginal utility of Y exceeds the marginal uplity of X O The consumer is willing to give up more X for an additional unit of Y than must be given up given the relative prices of X and Y. The marginal utility per dollar spent on X exceeds the marginal utility per dollar spent on Y The consumer is willing to give up more Y for an additional unt of X than must be given up given the relative prices of X and YA utility function is given as U = √MB where B represents the quantity of books consumed and M represents magazines. This uülity is shown via indifference curves in the diagram to the right. Holding the number of magazines constant at 20 units, as we increase our consumption of books from 5 units to 10 to 15 and to 20 units, marginal utility with respect to books. is CIES Magazines (Y) 50- 45 40 35 30 25- 20- 15- 10- 5 0- 10 15 RSTV a quie 10 15 20 25 30 35 40 Books (X) 45 5 eboo SCOR scor scor score score
- 12) A consumer’s preferences are given by U(X,Y) = X0.6Y0.4. The price of X is 4, and the price of Y is 5. The consumer has an income of $2000.a) What is the utility maximizing choice of X and Y?b) How would the utility maximizing choice change if price of X falls to 3 because of a pricesubsidy?c) Given the answers to the previous parts plot a linear demand function for X.d) Show that the consumer would prefer the cash equivalent of the price subsidy in part b.The price of good "a" is $5 and the price of good "b" is $15. If the marginal utility of good "a" is 20 then the marginal utility of good "b" must be ________ to have an optimum combination of goods purchased. 80 20 60 4Diminishing Marginal Utility. Explain the law of diminishing marginal utility Discuss an instance where you have experienced this. Do consumers continue to purchase something even though its marginal utility is decreasing? Why or why not?
- *Calculate the marginal utility per dollar of going from eight to nine DVDs. * To increase total utility without increasing spending, should Skeeter change the amount of consumption of either good? No, Skeeter is already consuming at the optimal consumption bundle. Yes, Skeeter should choose more smoothies and fewer DVDs. Yes, Skeeter should choose fewer smoothies and more DVDs. Yes, Skeeter should choose more smoothies and more DVDs. * What is the total utility at the optimal consumption bundle?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.34) Suppose that left shoes and right shoes must be purchased separately. Ingrid needs an equal number of each type of shoe and has a budget of $100 for shoes. Left shoes always cost $1. If right shoes cost $19 each, how many of each will Ingrid buy? If the price of right shoes increases to $49 each, how will Ingrid react? Explain your answer by drawing the indifference curves-budget lines. 35) Johnny has $100 to spend on books and all other goods. Books cost $20 each and Johnny is at equilibrium consuming 3 books and $40 worth of other goods. Johnny's grandmom wants to give Johnny either a book or $20 for his birthday. Which gift does Johnny prefer? Explain using an indifference map and budget lines.