Hal's utility function is U (x, y) = 2x + 5y. The price of x is $4, and the price of y is $15. Hal has $200 a week to spend on x and y. Hal is offered a chance to join a club of consumers of good y. If he joins, he can get y at a price of $8. What is the most that Hal would be willing to pay to join
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- abby is a single mom with a weekly budget of $100. She can spend her weeklyincome on food and diapers for her son. Price of food is $1 and price of a diaperis 50 cents. Her son needs at least 5 diapers a day, therefore she must purchaseat least 35 diapers weekly. Jennifer’s utility function is U (f, d) = f 0.9d0.1,where f and d represent quantity of food and diapers, respectively.Question 1 Part aFind abbys optimal consumption bundle. Make sure to draw her budgetconstraint and indifference curves and clearly demonstrate your solution.Question 10 Which of the following startements about network externalities is CORRECT? Air pollution is an example of a network externality. For a good with network externalities, the number of people who are willing to buy a unit of the good is uniquely determined by the price. Network externalities are always positive. The manufacturer of a new good with network externalities might give away a free version of the good. For a good with network externalities, one person's valuation of the good is always increasing in the number of other people using the good.Consider the market for a single network good and suppose thatconsumers differ in their valuation of both the stand-alone and thenetwork benefits (it can indeed be argued that it is more plausiblethat a user who has a higher value for the stand-alone component of atechnology also assigns more importance to the size of its network.) Tocapture this idea, write the consumer’s utility function for joining thenetwork as U(θ) = θ(a + νne), where a is the stand-alone benefit, ν > 0measures the network effect, neis the expected number of users joiningthe network, and is uniformly distributed on the unit interval.a. What happens if p > a + νne? (Hint: Identify all consumer who buythe good for at price p and a given expected network size ne).b. What is the consumer’s willingness to pay for the nth unit of thegood when ne units are expected to be sold? Is the demand downwardsloping? Does the demand increase with the expected network size?c. Express the fulfilled-expectations demand curve…
- 1) Alex spends all his income on blueberries and strawberries. His Marginal Utility of blueberries is MUB=100-B. His total utility of strawberries is Us=900+150S-S². Find Alex's income if the price of blueberries is PB=$8/kg, the price of strawberries is Ps=$10/kg, and Alex consumes 30kg of blueberries. 2) A profit-maximizing monopoly faces a demand curve D(P)=1000-P, has variable costs VC(Q)=Q², and fixed costs equal to $30,000. Find this monopoly's profit.Suppose the price of Xylophones is $3 and the price of Yoyos is $7. Robin's marginal utility of Xylophones is 15 and the marginal utility of Yoyos is 21. In order to maximize utility, Robin should O Buy fewer Xylophones and fewer Yoyos O Buy fewer Xylophones and more Yoyos Buy fewer Yoyos and more Xylophones Continue to buy the same number of Xylophones and Yoyos.maddy is a single mom with a weekly budget of $100. She can spend her weeklyincome on food and diapers for her son. Price of food is $1 and price of a diaperis 50 cents. Her son needs at least 5 diapers a day, therefore she must purchaseat least 35 diapers weekly. maddy utility function is U (f, d) = f 0.9d0.1,where f and d represent quantity of food and diapers, respectively.Part aFind Jennifer’s optimal consumption bundle. Make sure to draw her budgetconstraint and indifference curves and clearly demonstrate your solution.Part bmaddy uncle Sam, who is aware of her financial troubles, offers to help herout. Specifically, he offers to pay half of her weekly diaper expenses. Howmany diapers maddy would buy now? Again, demonstrate your solution bothgraphically and analytically.
- When consumers have a budget, their utility is maximized by buying a combination of goods such that the marginal utility per dollar is the same for all of these goods. This is because if this were not the case, it would mean that the consumer hadn't used up their entire budget. of their insatiability. if a consumer could get higher marginal utility from one good than from others, they would want to buy more of that good, and less of others. if a consumer could get higher marginal utility from one good than from others, they would want to buy less of that good, and more of others. it guarantees them some variety.Guerdon always puts half a sliced banana, q, , on his bowl of cereal, q, The two 14 goods are perfect complements. What is his utility function? Derive his demand curve for bananas graphically and mathematically. 12- 10- e, Guerdon's utility function (as a function of q, and q2) is 6- VA U= min/2q1.92} 4- O B. U=q, +92- 2- 0+ OC. U=29, + q92- 10 12 14 16 18 20 6 22 Bananas O D. U=0.5q1 + q2- OE. U=q, xq2- 5.00- 4.50- Guerdon's demand function for bananas (as a function of the price of bananas, P1. the price of a bowl of cereal, p2, and income, Y) is 4,00- 3.50- 91 = (p1 + 2p2) (Properly format your expression using the tools in the E 3.00 palette. Hover over tools to see keyboard shortcuts. E.g., a subscript can be created with the_ character.) 2.50- * 2.00- P. 1.50- 1.00- 0.50- 0.00+ 10 12 14 Bananas tv 80 DI DD F1 F3 F4 F5 F6 F7 F8 F10 @ %23 $ & 1 3 4 7 Q W E Y U S F H. J く C V M option command command optic ーの * CO Cereal (bowls) p. S per banana B * * N ASuppose 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 = $
- Enrique is a movie buff. He likes to watch on demand movies from his cable company, which cost $5 each, and so likes to go to the local movie house, which charges $15 a ticket. Suppose that given his budget and his tentative spending plans, the marginal utility from a cable movie is 15 utils and the marginal utility of a movie at the local cinema is 45 utils. Assuming he is spending his entire budget, Enrique is currently maximizing his utility Enrique can increase his utility by buying more cable movies and watching fewer cinema movies Enrique can increase his utility by buying more cinema movies and fewer cable movies27. Mike spends all his income on films (F) and concerts (C). Films cost $10 and concertscost $30. Mike’s preferences can be described by the utility function: U = F C and hence themarginal utility of films is C and the marginal utility of concerts is F. Which of the followingbundle will Mike purchase? (Hint: You do not need to know income in $ amount. Answerthe question using the tangency condition.)(a) Mike purchases 30 concerts and 10 films a month.(b) Mike purchases 10 concerts and 30 films a month.(c) Mike purchases 20 concerts and 20 films a month.(d) Mike purchases 5 concerts and 10 films a month.Suppose we have a market with 200 individuals with preferences over two goods, and y. 3. Suppose now that we know m = 135, P = 3, 4. What is the market demand for x? and Py This should be a number. 4. Consider now that 100 individuals (type A) have the utility function U = x²/³y¹/³ and the other 100 (type B) have the utility function U = x¹/3y2/3. Each individual still has the same 'y income and is subject to the same prices. Calculate the market demand for x as a function of income and prices. 5. Suppose now that we know m = 250, P = 5, and Py 3. What is the market demand for x? This should be a number. F =