ronsumer's demand xy for two different to maximize the goods are lefility function chosen x and y $3 and $4, are The per unit of respectively, and the Consumer's in come is $ © tell rite out the fagrangean for the Constrained maximization problem Find the utility maximi zing demands for both goods and He Larange multiplier, 2 o What is the change in consumer's utility if income changes from $72 to $75
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- goods, XandY per of good X is N$4 and the price of good Vis No10 Harrys unlity funchon is UCX,)==XY. Harry consumes 2 and he spend's Npbo month The price Find The values of gocal X and Y maximizes Harcys unly illustruate Hary's utlty maximizing.combinason clearly labelled on a graph. Suppose llustrate Harrys price & spod X increased to Ngb effects income and substitution ef the anel laballed graph.Mylie’s total utility from singing the same song over andover is 50 utils after one repetition, 90 utils after tworepetitions, 70 utils after three repetitions, 20 utils afterfour repetitions, 250 utils after five repetitions, and 2200utils after six repetitions. Write down her marginal utilityfor each repetition. Once Mylie’s total utility beginsto decrease, does each additional singing of the songhurt more than the previous one or less than the previousone?ilable Paragraph H AaBbCсD AabbCcDc AaBbC, AaBbCcE Normal 1 No Spac... Heading 1 Heading 2 Consider a consumer with the following utility function: U(x1, x2)=(x1+4) (x2 + 6) for x1, x2 20 with the accompanying budget constraint: p1x1 +p2x2=Y where p1, p2, Y>0 Styles b) c) For Replace Select- Editing a) Show that the utility function is strictly increasing in x1 and x2. For a given level of utility U, derive the marginal rate of substitution between good 1 and good 2. Find the optimal choice of x1 and x2 when the consumer maximizes his/her utility. Create and Share Request Adobe PDF Signatures Adobe Acrobat A ENG Add-ins Add-i 9:56 PM 12/15/2023 1009
- I like drinking Smirnoff and Stoli Vodka, but I really only careabout the total amount of alcohol I get out of it. They areperfect substitutes. Smirnoff is sold in liter bottles that are100 proof (that’s 50% alcohol). Stoli is sold in liter bottlesthat are 80 proof (40% alcohol). What is my utility functionfor bundles of these two vodkas? What do my indifferencecurves look like?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…a. A consumer is willing to trade 3 units of x for 1 unitof y when she has 6 units of x and 5 units of y. She isalso willing to trade in 6 units of x for 2 units of y whenshe has 12 units of x and 3 units of y. She is indifferentbetween bundle (6, 5) and bundle (12, 3). What is theutility function for goods x and y? Hint: What is theshape of the indifference curve?b. A consumer is willing to trade 4 units of x for 1 unitof y when she is consuming bundle (8, 1). She is alsowilling to trade in 1 unit of x for 2 units of y when sheis consuming bundle (4, 4). She is indifferent betweenthese two bundles. Assuming that the utility function isCobb–Douglas of the form U (x, y) = xα y β, where α andβ are positive constants, what is the utility function forthis consumer?c. Was there a redundancy of information in part (b)? Ifyes, how much is the minimum amount of informationrequired in that question to derive the utility function?
- ceriuppose that Isaiah has a weekly fixed budget and spends it all on haircuts and ice cream. At his current combination arof consumption, the marginal utility of the last dollar spent on haircuts is greater than the marginal utility of the last dollar spent on ice cream. Has Isaiah maximized his utility? A C E Yes, because changing his current consumption combination will reduce his total utility B No, because he can increase his total utility by purchasing more haircuts and D fewer ice creams Yes, because he has purchased 2 goods in proportion so that he can get- the maximum utility from each Yes, because he purchased the maximum possible with a limited budget No, because he can increase his total utility by purchasing fewer haircuts and more ice creamsConsider a town with a single street of 1 km long with 3,000 people spread uniformly along it. Two stores, 1 and 2, are located at the opposite ends of the street and sell the same product (store 1 is locatedattheleftend).Thecostofwalkingist1 =$6perkmtostore1andt2 =$9perkmtostore2for each consumer. The net utility of a consumer located at point x from buying a product at store 1 is U1(x) = 100 – p1 – t1x, where pi is a price of the product at store i = 1,2. The net utility from buying at store 2 is U2(x) = 100 – p2 – t2(1 – x). The average cost of the product for each store is c = 4. (a) Assume that all consumers buy product from the sellers. Find the demand functions Di(p1,p2) and the profit functions πi(p1,p2) for each store i = 1,2 as functions of prices p1,p2.(b) Find the equilibrium prices.ayesha derives utility from travelling and outdoor dinning o weekends as given utility function U(t,d)=TD.the price of a day spent travelling is $160{Pt=160} and price of dining outdoor $200{Pd=200}.ayesha annual budget for this is $8000. find ayesha's utility maximizing choice of days travelling and dining outside. and alsoo find uutility level from consuming that bundles .show findings graphically
- Figure 4.2 P3 P2 P1 A C Q Q2 Q3 Q4 Qs Qs Q7 Refer to Figure 4.2. The demand curve A indicates that O the smallcst price change will cause consumcrs to change their consumption by a large amount, O therc is no change in quantity demandcd as the price changes. consumcrs can purchase any quantity they want regardless of the price, Oithc smalcst price incrcasc wil.causc.consuners to switch to the producer with thc lowestMike has a decreasing marginal uity of income We know that Mike's income in greater than S10, but we de not know his exact inome Adam offers Mika the folloeing bet Adam wil throw a fair coin (that is, heads and tals have equal probatilty) a heada. Mke pays Adam $10. ta Adam pays Mke S10 What can we conclude from this infonmation? O Mike will reject the bet only it his income is high emought Ob. Mike will reject the bet, independently of how high his income is Oc Mke wil accept the bet independently of how high his income is Od Mke will accept the bet only if his income is high enought O Mka will always be indiferent between accepting and rejecting the betO let y= F(,k) = 2Č K be a pretustion funtion e ue told daivanve, to deniue, TRS this praquition fumition duplay mmu kinMartin a prequct in ? Hene about in k?