Bill is the only person on an island, and he has an endowment of 20 units of coconuts (C) and 5 units of water (W). His utility function is: U(C,W) = In(C) +2 ln(W) a) Find the marginal utility of C and W. b) Find the marginal rate of substitution when Bill consumes all of his endowment.
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- A and B consume only two goods, cider (C) and dumplings (D). A has an initial endowment of 10 bottles of C and 30 of D. Bob has an initial endowment of 50 bottles of cider and 50 dumplings. Alice’s utility function is uA(CA,DA) = 9ln(CA) + 10ln(DA), where CA and DA represent consumption of C and D, respectively. B’s utility function is uB(CB,DB) = CBXDB, where CB and DB denote B's consumption of C and D. a) Find the competitive equilibrium, i.e. the price ratio, of this exchange economy and the resulting equilibrium allocation. b) Find the expression of the contract curve for this economy and use your answer to check that the equilibrium allocation you found in (b) is indeed Pareto optimal.Julio loves gardening. His favourite plants are tulips and hydrangeas. His utility function is ' u(t,h)= t +100h -h^2 where t is the number of tulipsin his garden and h is the number of hydrangeas in his garden. suppose he has a 500 square feet for his garden. each tulip takes up 1 square foot of space and each hydrangeas takes up 4 square feet. he gets both plants for free.If he wanted to maximize his utility, how many tulips should he plant, what about hydrangeas? b) if his yard was only 144 square feet, how many tulips would he plant? How many hydrangeas? C) In order to plant both tulips and hydrangeas, how big does his garden need to be. carfeully explain.Penny likes to have peanut butter (B) with apples (A). The price of apples is $3 per pound and peanut butter costs $.50 per ounce. Penny's budget for peanut butter and apples is $3.60. Penny's utility function is U (A, B) = A/B. Penny's MRS is [ Select ] His income expansion path is described by [ [ Select ] . Thus, Penny will consume [Select ] ounces of peanut butter and [ Select ] pounds of apples.
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- 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…Suppose that your family has just decided to adopt a cat named Hailey. You have a monthly budget of $40 that you can choose to spend on either cat food or other consumption goods. Assume the price of a can of cat food is $5 for the first 2 cans, but then it drops to only $3 per can for each additional can. All other consumption goods will be treated as a composite good, so you can think of this as simply the cash left over to spend on other items after buying cat food. On the following graph, use the green points (triangle symbol) to graph your family's budget constraint. Note: Plot your points in the order in which you would like them connected. Line segments will connect the points automatically. OTHER CONSUMPTION (Amount per month) 50 45 40 35 30 25 20 15 10 5 Budget Constraint ?A consumer has set a budget of $400 for the consumption of good X and Y. The price of Good X is S"Px", and the price of good Y is S5. The consumer has a Utility function given by U(X,Y) = ху Find the optimal consumption choice of the individual and the utility obtained in terms of Px. Make a graph that illustrates the solution to the problem. Why do we use parameters?