Consider a utility function with one consumption good q1 and one type of leisure q2 c) Show mathematically and diagrammatically the decomposition of total effect.
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Q3. Consider a utility function with one consumption good q1 and one type of leisure q2
c) Show mathematically and diagrammatically the decomposition of total
effect.
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- The Fly-by-Night finance company advertises a "bargain 6% plan" for financing the purchase of automobiles. To the amount of the loan being financed, 6% is added for each year money is owed. This total is then divided by the number of months over which the payments are to be made, and the result is the amount of the monthly payments. For example, a woman purchases a $10,000 automobile under this plan and makes an initial cash payment of $2,500. She wishes to pay the $7,500 balance in 24 monthly payments: Find the IRR and Effective Annual Interest rate. Purchase price -Initial payment = Balance due, (Po) +6% finance charge = 0.06 × 2 years × $7,500 = Total to be paid .. Monthly payments (A) = $8,400/24 = $10,000 2,500 7,500 900 8,400 $350Cindy is considering going to law school. If she does, she will spend $70,000 on tuition and books to get a college education (during the first time period), $140,000 on tuition and books to get a law degree (during the second time period), and her law degree will earn her $700,000 during the remainder of her work-life (during the third time period). Cindy's time preference for money is associated with a per-period interest rate of 10 percent. Approximately what is Cindy's present value of obtaining a law degree?Which of the following is correct? For every additional dollar in Lifetime_value, Incore is expected to increase by $0.042 For every additional dollar in Lifetime_value, Income is expected to decrease by $0.042 For every additional dollar in Income, Lifetime_value is expected to decrease by $0.042 For every additional dollar in Income, Lifetime_value ($) is expected to increase by $0.042
- Every week I spend a total of £400 buying two goods, luxuries (L) and necessities (N). I obtain utility (U) from these goods according to the rule U(L, N) = 10 + L + 20N−2N2. Suppose that I pay £10 for each unit of L and £20 for each unit of N and that I am a utility-maximiser. MUL=1 and MUN=20-4N. Define the Marginal Rate of Substitution (MRS) as MRS ≡ MUL/MUN). Calculate its value at the bundle (L = 0 and N = 4) and at (L = 1 and N = 4). By referring to a graphic illustration of the above calculations or otherwise, argue that an increase in my budget will have no effect on my consumption of N if I am already consuming 2.5 units of N. Calculate my optimum choice of L and N if instead I have £40 to spend. Fully explain your answer.Draw the cash flow diagram with your solution.In a certain department store, the monthly salary of a saleslady is partly constant and partly varies with her sales for the month. When the value of her sales for the month is P10,000, her salary for the month is P900. When her salary for the month goes up to P12,000, her monthly salary becomes P1,000. What must be the value of her sales for the month so that her salary for the month will be P2,000?The vending machine in Katherine's office building offers cans of pop and candies. Katherine's utility function is U = 3PC, where P is the amount of pop consumed per %3D week and C is the amount of candy consumed per week. Pop costs $1 and candy costs $0.5 per bag. If Katherine has $10 to spend, she will consume A bags of candy.
- For a certain Utility function, which is a simple sifted parabolic equation, the maximum utility is 10 for n=5. Determine the mathematical expression of this Utility function. Hint: look up (h,k) values for a parabola. Multiple Choice 10n + 5 10n + 5n - 2n2 +10n + 5 - (n-5)2+10When Amanda wakes up in the morning, she will either purchase Timbits (T) or a bagel (B). This is represented by the utility function U(T, B) = 15T + 10B. %3D In addition, the price of a bagel is $2 and the price of Timbits is $0.50 apiece. Amanda has a daily budget of $5 to spend on breakfast. She is planning to purchase 1 Bagel (B) and 6 Timbits (T). Is this allocation of goods utility-maximizing? a) Yes, since MUt/Pt = MUb/Pb b) No, Amanda should only consume Timbits c) Yes, since this bundle lies on Amanda's budget line d) No, Amanda should only consume bagelsA consum sumer of two goods has indirect utility v(p, w) = √w -1/2 P₁ + P₂ (a) Find the indirect money-metric utility e(p, v(p, w)). (b) Calculate the compensating variation associated with the change from (p, w) = ((4,4), 2) to (p', w')= ((1,9), 5). can you explain the notation please break it down each part of it, please teach How do you know where to place the values? The indirect money-metric utility e(p, v(p, w)) can be calculated as follows: e(p, v(p, w)) = v(p, w) - ((p1* w1) + (p2 * w2)) plugging in the values from the problem, we get: e(p, v(p, w)) = (sqrt(w))/p1^-0.5+p2^-0.5- ((44) + (9 * 5)) e(p, v(p, w)) = 2 - 41 CV = 2 e(p, v(p, w)) = -39 The compensating variation associated with the change from (p, w) = ((4,4), 2) to (p', w')= ((1,9), 5) can be calculated as follows: CV = e(p', w')- e(p, w) plugging in the values from the problem, we get: CV-39 (-41) This means that the consu would be willing to pay up to $2 in order to maintain their original level of utility.
- You have k20per week to spend and two possible uses for this money,:telephoning friends back home and drinking coffee. Each hour of phoning costs k2 and each cup of coffee costs k1. Your utility functions U(X,Y)=XY,where X is the hours of phoning you do and Y the number of cups of coffee you drink. How much income per week will enable you to achieve the same quantities at the new process the ones you chose before? What income will enable you to attain the same utility as you did before.? Comment on your answer in the context of equivalent variation and compensation variation3) Marco has $100 worth of grain in period 1 but gets no grain in period 2. Marco has two choices. He can store the grain that he does not consume in period 1. This results in a loss of 20% of the grain due to pests. Assume that with this option he will choose to consume 68 units of grain in period 1 and 26 units in period 2. Instead, Marco can sell the grain he does not consume in period 1 and lend the money from that sale to someone today at an interest rate of 10%. He can then use the repayment of that loan to buy gain in period 2. a) Based on this information, draw a diagram that outlines Marco's choices. Is he definitely better off once the opportunity to lend is available to him? b) Relative to his initial equilibrium point, does he unambiguously consume more in both periods once he can lend out the excess he does not consume in period 1? c) Now assume that Marco can sell any excess grain he doesn't consume in period 1 and invest the money he gets in a new type of risky activity.…5.3 (0) Ambrose, the nut and berry consumer, has a utility function U(21,x2) = 4/T +x2, where ¤; is his consumption of nuts and r2 is his consumption of berries. %3D (a) The commodity bundle (25,0) gives Ambrose a utility of 20. Other points that give him the same utility are (16, 4), (9, ), (4, - ), (1, –), and (0, ). Plot these points on the axes below and draw a red indifference curve through them. (b) Suppose that the price of a unit of nuts is 1, the price of a unit of berries is 2, and Ambrose's income is 24. Draw Ambrose's budget line with blue ink. How many units of nuts does he choose to buy? (c) How many units of berries? (d) Find some points on the indifference curve that gives him a utility of 25 and sketch this indifference curve (in red). (e) Now suppose that the prices are as before, but Ambrose's income is 34. Draw his new budget line (with pencil). How many units of nuts will he choose? How many units of berries?