eek. We carns $1,000 each week and earns a real interest rate of p = 0.01 on any money ved today. He also needs to pay the same interest rate if he borrows money today and pays it next week. If his utility function is U (C₁, C₂) = c₂, where c₁ is units of consumption day and c₂ is units of consumption next week, how many units will he consume this week?
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![4. Mateo is deciding how many dollars to consume today and how many to consume next
week. We earns $1,000 each week and earns a real interest rate of p = 0.01 on any money
saved today. He also needs to pay the same interest rate if he borrows money today and
repays it next week. If his utility function is U (C₁, C₂) = cc₂, where c₁ is units of consumption
today and c₂ is units of consumption next week, how many units will he consume this week?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd87dc6da-d993-4c29-b5ce-5755787d1d8a%2Fd87ab536-eebb-4f43-8a05-bc7d92081867%2Fvcwunyf_processed.png&w=3840&q=75)
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- 1. Complete the following table and answer the questions below: Units consumed Total utility Marginal utility 1 10 10 2 8. 25 4 30 5 6. 34 2. Columns 1 through 4 in the table below show the marginal utility, measured in utils, that Ricardo would get by purchasing various amounts of products A, B, C, and D. Column 5 shows the marginal utility Ricardo gets from saving. Assume that the prices of A, B, C, and D are P18, 6, 4, and 24, respectively, and that Ricardo has an income of 106. Column 1 Column 2 Column 3 Column 4 Column 5 Unit Unit Unit Unit No. of MU MU MU MU P saved MU of A of B of C of D || || || || | 1 72 1 24 1 15 1 36 1 2 54 2 15 12 2 30 2 3 45 3 12 8 3 24 3 36 4 18 2 27 5 7 5 13 5 1 18 6. 7 6. 1/2 7 15 7 7 3.5 7 4 7 1/4 8 12 8. 1 8 2 8. 1/8 a. What quantities of A, B, C, and D will Ricardo purchase in maximizing his utility? b. How many pesos will Ricardo choose to save?Also calculate monthly budget. Thanks!Suppose you expect to earn $10 this year and $10 next year. Each dollar you earn this year can be either spent, or saved at an interest rate of 10%. If you want to spend more than $10 this year, you can borrow money at 10% interest and repay it next year. Next year, you plan to pay oyour debts (if any), then spend all your earnings and all your savings (if any). Draw your budget line between “dollars spent this year" and “dollars spent next year". Suppose the government imposes a 50% income tax on all your earnings this year and next year (not including your interest earnings). Draw your new budget line. Suppose the government imposes a 50% sales tax on everything you buy this year and next year. Draw your new budget line. Suppose the government imposes a 50% income tax on all your earnings this year and next year, including your interest earnings. Draw your new budget line. True or False: If interest earnings are not subject to income tax, then an income tax and a sales tax…
- Explain how does adecrease in the current income y affect the consumer’s consumption-saving decision. In particular,explain: 1) How will current consumption c, future consumption c′, and savings s change; 2) Arethere any substitution effect or income effect. Make sure you draw two figures, one for the borrowersand one for the lenders1. How many hours will a person allocate to leisure activities if her indifference curves between consumption and leisure activities are concave (NOT convex) to the origin? 2. Tom earns $15 per hour for up to 40 hours of work each week. He is paid $30 per hour for every hour in excess of 40. Tom faces a 20 percent tax rate and pays $4 per hour in child care expenses for each hour he works. Tom receives $80 in child support payments each week. There are 110 (non-sleeping) hours in the week. Graph Tom's weekly budget line. 3. John's utility function is U(C, L) = C²/² L?/2. The most leisure time he can consume is 110 hours. His wage rate is $10. Find John's optimal amount of consumption and hours for leisure and work. 4. Suppose the wage rate increased (e.g. from $10 to $20), how many hours would a worker take for work and leisure activities? Assume that the income effect dominates the substitution effect, draw a graph and explain in detail. 5. Cindy gains utility from consumption C and…3. Consider a home energy storage (battery) system that can store up to 2 units of energy. At every time step, there is a demand for energy in the home which is drawn from 0,1,2 units with equal probability independent of the demands in the previous time steps. At every point in time, you have to satisfy the demand either by discharging the needed energy from the battery or purchasing power from the grid (or a combination of the two). You could also choose to purchase power from the grid to charge your battery. The grid energy price is either H(igh) or L(ow) according to a Markov chain (Price moves from H to L with probability p, and from L to H with probability q). (a) Model the decision making as an infinite horizon MDP where the objective is to minimize the discounted cost of energy purchased over an infinite horizon. (b) Write down a policy a of your choosing. Perform two steps of the operator T, for your policy, followed by one step of T..
- 106. For your birthday, you receive a hamper from your friend, which contains food and drink. They have chosen to buy you 8 packs of hot chocolate and 10 packs of luxury biscuits. Unfortunately, the hot chocolate is not milk chocolate and the biscuits are chocolate chip and not your favourite ginger biscuits! They haven't provided the receipt, but you return to the shop where the hamper was bought and ask to exchange the items. Each pack of hot chocolate was priced at £5 and each pack of biscuits was priced at £6. You face a utility function of U (Hċ, B) = H²B. When you return to the shop, you see that all of the biscuits are now half price, but all of the types of hot chocolate haven't changed in price. You are able to exchange your biscuits and hot chocolate, but can only receive a refund based on the current marked price of the products in the shop. Given this information and assuming hot chocolate is on the horizontal axis and your aim to maximise utility, what should you do? (a) You…1-3
- Explain how does adecrease in the current income y affect the consumer’s consumption-saving decision. In particular,explain: 1) How will current consumption c, future consumption c', and savings s change; 2) Arethere any substitution effect or income effect. Make sure you draw two figures, one for the borrowersand one for the lenders.4. Peter's utility function is equal to: U (L, C) = LVC where L is hours of leisure time per day and C is daily consumption, denoted in €. When he is looking for a job as a consultant he finds the following possibilities: i) Working for "ABC of M", where he may get 100€ per day and 2h of leisure time per day ii) Working for "101 of M", where he may get 25€ per day and 4h of leisure per day iii) Working for "M for Dummies", where he may get 50€ per day and 3h of leisure per day Each day, apart from sleeping and other basic necessities, Peter has 15 hours of available time. He may tutor during as many hours as he desires, receiving 20€ per each hour of work. Assume Peter cannot save and consumes all he receives. a. How many hours does Peter decide to rest? 9h 10h 11h 15h 13.5hColumns 1 through 4 of the accompanying table show the marginal utility, measured in utils, that Ricardo would get by purchasing various amounts of products A, B, C, and D. Column 5 shows the marginal utility Ricardo gets from saving. Assume that the prices of A, B, C, and D are $18, $6, $4, and $24, respectively, and that Ricardo has an income of $105. Column 1 Column 2 Column 3 Column 4 Units Units Units Units of A MU of B MU of C MU of D MU 1 72 1 24 1 15 1 36 54 15 12 2 30 3 45 3 12 3 8. 3 24 4 36 4 7 4 18 27 7 5 5 13 6 18 6 5 6 4 6 7 7 15 7 2 7 3.5 7 8 12 8 1 8 3 8 2 а. What quantities of A, B, C, and D will Ricardo purchase in maximizing his utility? b. How many dollars will Ricardo choose to save? c. Check your answers by substituting them into the algebraic statement of the utility-maximizing rule. In other words, show it works when using this rule.