a) Choose a value for parameter "a" by yourself. Graphically illustrate the budget line of the consumer and draw some example indifference curves. Then, find the consumption bundle that maximizes the consumer's utility. b) List the possible outcomes for different values of parameter "a".
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- Ceja has utility function U=A2*B2 , where A equals the number of apples she eats each week, while B is the number of bananas she eats each week. Ceja has $20 to spend on fruit each week. The price of an apple is $1, while the price of a banana is $0.25. Find out the combination of Apples and Bananas that maximize Ceja’s satisfaction. If price of Banana is increased by $.25, what will be the new combination of A and B that would maximize her utility? Show graphically and drive the demand curve for BananasConsider a hypothetical consumer named Hayden who is shopping for bread and brie. The graph with bread and brie on the axes presents the utility‑maximizing combinations of bread and brie that Hayden chooses when the price of bread is $1.00$1.00 per loaf and the price of brie is $4.00$4.00 and $6.00$6.00 per wheel, respectively. The other graph shows Hayden's demand curve for brie. The two points and associated values in the graph for bread and brie combinations correspond to points A and B in the graph of the demand curve for brie. What are the specific prices and quantities of brie associated with points A and B on Hayden's demand curve? price of brie at point A: $$ quantity demanded at point A: price of brie at point B: $$ quantity demanded at point B:Suppose that you are given $20,000 to split between two people, Jane and Fred. The income and marginal utility for each of them is shown in the following table. Amount to Jane Amount to Fred MU of Jane's Last Dollar Spent MU of Fred's Last Dollar Spent $ 5,000 $ 15,000 80 65 $ 7,000 $ 13,000 70 70 $ 9,000 $ 11,000 60 75 $ 11,000 $ 9,000 50 80 $ 13,000 $ 7,000 40 85 Instructions: Enter your answers as a whole number. If you want to maximize their combined utility, how much of the $20,000 should go to Jane? How much should go to Fred? Amount to Jane = $ Amount to Fred = $
- Reese thinks peanut butter and chocolate are great when separate, but when they combine they are even more epic. In other words, Reese likes to eat either peanut butter or chocolate, but when he eats them together, he gets additional satisfaction from the combination. His preference over peanut butter (x) and chocolate (y) is represented by the utility function: u(x, y) = xy + x + y Suppose that now Reese loses almost his entire income, so that he is left with only one dollar, i.e. his new income is I0 = 1. If prices are still px = 2, py = 4, what is his new optimal consumption of x and y (Hint: Remember that consumption of both goods must be weakly positive, i.e. x∗ ≥ 0 and y∗ ≥ 0) (a) x∗ = 0.5, y∗ = 0(b) x∗ = 0.25, y∗ = 0(c) x∗ = 0.75, y∗ = 0.25(d) x∗ = 0.75, y∗ = 0(e) x∗ = 0.5, y∗ = 1How does the utility-maximization model help highlight the income and substitution effects of a price change. Provide an example please.Consider a couple's decision about how many children to have. Assume that over a lifetime a couple has 100,000 hours of time to either work or raise children. The wage is $10 per hour. Raising a child takes 10,000 hours of time. a. Make a graph with the budget constraint showing the trade-off between lifetime consumption and number of children. (Ignore the fact that children come only in whole numbers!) Show indifference curves and an optimum choice. b. Suppose the wage increases to $15 per hour. Show how the budget constraint shifts. Using income and substitution effects, discuss the impact of the change on number of children and lifetime consumption. c. We observe that, as societies get richer and wages rise, people typically have fewer children. Is this fact consistent with this model? Explain.
- Discuss how the utility-maximization model helps highlight the income and substitution effects of a price change.Reese thinks peanut butter and chocolate are great when separate, but when they combine they are even more epic. In other words, Reese likes to eat either peanut butter or chocolate, but when he eats them together, he gets additional satisfaction from the combination. His preference over peanut butter (x) and chocolate (y) isrepresented by the utility functionz; u(x, y) = xy + x + y Suppose now that Reese’s income is high relative to the prices of peanut butter andchocolate (more concretely, imagine I > px and I > py). What is Reese’s Marshalliandemand for peanut butter, x^∗(Px, Py, I)?Q19 Let's assume that Justin Trudeau, who lives in Ottawa, is purchasing corn (C) and dandelion (D) in utility-maximizing amounts. If the price of corn (C) is $4 and the price of dandelion (D) is $2, then: Multiple Choice the marginal utility of dandelion is the same as that of corn. Justin Trudeau will buy only corn. the marginal utility of corn is twice that of dandelion. the marginal utility of corn is four times that of dandelion. the marginal utility of dandelion is twice that of corn.
- Suppose that each week Fiona buys 16 peaches and 4 apples at her local farmer's market. Both kinds of fruit cost $1 each. From this we can infer that: If Fiona is maximizing her utility, then her marginal utility from the 16th peach she buys must be greater than her marginal utility from the 4th apple she buys. Fiona is not maximizing her utility. If Fiona is maximizing her utility, then her marginal utility from the 16th peach she buys must be equal to her marginal utility from the 4th apple she buys. The law of diminishing marginal utility does not hold for Fiona.Reese thinks peanut butter and chocolate are great when separate, but when they combine they are even more epic. In other words, Reese likes to eat either peanut butter or chocolate, but when he eats them together, he gets additional satisfaction from the combination. His preference over peanut butter (x) and chocolate (y) is represented by the utility function: u(x, y) = xy + x + y Which of the following is NOT true about Reese’s preference? (a) The MRS decreases when x increases.(b) The preferences are homothetic.(c) The marginal utility of y is higher when x = 10 than when x = 5.(d) For any a > 0, Reese prefers the bundle (x =a/2 , y = a/2 ) over either the bundle (x = a, y = 0) or (x = 0, y = a).Clarke County High School has $60,000 to spend on computers and other goods so its budget equation is C + X = 60,000, there C is expenditure on computers and X is expenditure on other things. The high school’s preferences can be represented by the utility function ?(?, ?) = ??2, where the marginal rate of substitution is −?/2?. Currently, the high school’s optimal bundle is $20,000 of computers, and $40,000 of everything else.a. Graphically show the school’s budget line, with computers on the x-axis and all other goods on the y-axis. Label intercepts and the current optimal bundle and sketch an indifference curve.b. The State Education Commission wants to encourage “computer literacy” in schools, and so has proposed the following plan: Give a grant of $20,000 to each school in the state, which the school can use only for computers. If the state adopts the plan, add the school’s new budget constraint to the graph above, making sure to label the line and the appropriate intercepts. What…