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- 2. Suppose John's utility function is UX,Y) = 4VXY , where X is consumption of beer and Y is consumption of pizza. For this utility function, ( Calculus Kahuna say: MUx = 2VY/X and MUy = 2\X/Y ) a) What happens to the marginal rate of substitution between X and Y as consumption of X increases?2. What is the economic interpretation of the condition that the consumer at his optimum equates his marginal rate of substitution and the price ratio of the goods he consumes?1. What is the difference between ordinal utility and cardinal utility? Explain why the assumption of cardinal utility is not needed in order to rank consumer choices! 2. Can you explain why taking a monotonic transformation of a utility function doesn't change the marginal rate of substitution? 3. Assume that Rossi consumes only bananas and avocado. Fortunately, she likes both goods. The consumption bundle where Rossi consumes xl units of bananas per week and x2 units of avocado per week is written as (x1, x2). (a) In fact, Rossi's preferences can be represented by the utility function u(x1, x2) = 4/x1 + x2. The price for bananas is $1 per unit and the price for avocado is $2 per unit. Rossi has $24 to spend on the two goods. Write down Rossi's budget constraint and solve for her optimal consumption bundle. (b) Now Rossi has $10 more to spend on the two goods ($34 in total), and what is her optimal consumption bundle now? Compare your solution with the previous one. Can you say…
- If we have money, we buy goods and services to satisfy our needs. In economics, thesatisfaction that we get from the consumption of goods and services is called utility. Usea utility graph to explain what happen to the utility when you keep on increasing thenumber of units consumed. Also explain what happens to the utility when you keep onincreasing the number of units consumed. Also explain what happens to the additionalutility (i.e. additional satisfaction) when you increase your consumption by one unitSuppose that Dale consumes only coffee and cheese, both of which have diminishing marginal utility. For each of the following cases, determine whether Dale should 1Consume more coffee and less cheese, or2Consume less coffee and more cheese: 1.The marginal rate of substitution of cheese for coffee is 3 (i.e., the marginal utility of cheese is three times the marginal utility of coffee), while the price ratio is 2 (i.e., cheese costs twice as much as coffee). 2.The marginal rate of substitution of cheese for coffee is 1 (i.e., the marginal utility of cheese is equal to the marginal utility of coffee) while the price ratio is 2 (i.e., cheese costs twice as much as coffee). 3.The marginal rate of substitution is initially equal to the price ratio, but the price of coffee increases. 4.The marginal rate of substitution is initially equal to the price ratio, but the price of cheese decreases. 5.The marginal rate of substitution is initially equal to the price ratio, but Dale enters exam…Case: Consumer A receives utility from spending her income of $90 on concert tickets (T) at $20 each & popcorn (W) at $2 each as given by the utility function U (T, W). For this utility function, the MRS of tickets for pretzels is 2W/T. Question: What is the value of Consumer A's marginal rate of substitution (MRS) of concert tickets for popcorn when her utility is maximized? Explain the details of calculating the maximized utility value.
- Currently, Paula is maximizing utility by purchasing 5 TV dinners (T) and 4 Lean Cuisine meals (L) each week. Graph Paula’s initial utility-maximizing choice. Suppose that the price of T rises by $1 and the price of L falls by $1.25. Can Paula still afford to buy her initial consumption choices? What do you know about her new budget constraint? Use your graph to show why Paula will choose to consume more L and less T given her new budget constraint. How do you know that her utility will increase? Some economists define the ‘‘substitution effect’’ of a price change to be the kind of change shown in part c. That is, the effect represents the change in consumption when the budget constraint rotates about the initial consumption bundle. Precisely how does this notion of a substitution effect differ from the one defined in the text? If the substitution effect were defined as in parts, how would you define ‘‘the income effect’’ to get a complete analysis of how a person responds to a…Assume that Sara has $800 per month to divide between playing golf and playing paint ball . Assume Golf costs $40 and paintball costs $80 . Suppose Sara plays golf eight times per month and plays paintball six times per month . a. Draw Sara’s budget constraintb. Assume Sara has new expenses and can spend $320 only this month. Draw the new budget constraintc. As a result of a decrease in income Sara decides to play 11 rounds of golf and two games of paintball . what kind of a good is paintball ? what kind of a good is golf?d. Assume Sara has $400, the price of paintball is still $40 , but the price of Golf doubles , draw the new budget constraint3. Suppose Mary enjoys Pepsi and Coke according to the functionU(P;C) = 4C + 5P. What does her utility function say about her MRS of Coke for Pepsi? What do her indi§erence curves look like? What type of goods are Pepsi and Coke for Mary? If Pepsi and Coke each cost $1 and Mary has $20 to spend on these products, how many units of each product should she buy in order to maximize her utility? Show this utility maximiz- ing combination combination of Pepsi and Coke on the graph. how would her consumption and utility maximizing bundle of Coke and Pepsi change if the price of Coke decreases to 50 cents. 4. Vera is an impoverished graduate student who has only $100 a month to spend on food. She has read in a government publication that she can assure an adequate diet by eating only peanut butter and carrots in the Öxed ratio of 2 pounds of peanut butter to 1 pound of carrots, so she decides to limit her diet to that regime. a) If peanut butter costs $4 per pound and carrots cost $2 per…
- 3. Finding the optimal combination of two goods - $2. Suppose that Larry buys Larry enjoys consuming both cheese and fruit. Each pound of cheese costs Pc = $1, and each pound of fruit costs PF 300 pounds of cheese and 200 pounds of fruit per year. The following graphs show his marginal utility curves for cheese and fruit. At his current consumption level, Larry's marginal utility from consuming the last pound of cheese he bought is MUC S 30 utils per pound, and his marginal utility from consuming the last pound of fruit he bought is MUF = 30 utils per pound. 60 40 30 IL 20 10 400 500 600 50 40 A 30 B C D 20 10 0 0 100 Is Larry currently maximizing his utility? Combination 200 300 CHEESE (Pounds per year) 300, 30 (Pounds per Year) 200 400 300 No; he could buy less cheese and more fruit, not spend any more money, and be better off. O No; he likes fruit and cheese more than other goods, so he should buy more of both. O No; he could buy more cheese and less fruit, not spend any more money,…Suppose that you are trying to determine whether or not your friend Rajiv views a pound of cheese as a necessity, a luxury, or in between a necessity and a luxury. Rajiv has a weekly income of s50 to spend on either cheese or other consumption. The price of cheese is $10 per pound, and the vertical axis is treated as a composite good representing dollars spent on other consumption. On the following graph, use the blue line (circle symbol) to graph Rajiy's budget constraint (BC). Then, place the black point (plus symbol) on the graph to indicate the best bundle in this case. Note: Dashed drop lines will automatically extend to both axes. 100 90 вс, 70 Initial Best Bundle 00 50 40 BC, 30 20 New Best Bundie 10 2. 6. 10 CHEESE (Pounds per week) Now, suppose that Rajiv's weekly income increases to $100. Use the green line (triangle symbol) to graph the new budget constraint (BCa). Then, place the grey point (star symbol) on the graph to indicate the new best bundle. According to the…1. What will be her total utility from both leisure and income when working 25 hours per week? 2. Does it make sense from the perspective of utility for Terry to increase her work hours? (Think about the total utility calculations.). Why or Why not?