Suppose there are four people in the market, two people with u=X1X2 and two people with u=min{x1,x2}. Suppose everyone has the same income (m;=m), and p2-1. What is the demand curve of x1 for the market? Qd=m/p1 + 2m/(p1+1) Qd =4m/(p1+1) Qd=4m/2p1+2m/(p1+4) Qd=4m/(p1+1)
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![Suppose there are four people in the market, two people with u=X1X2 and two people with
u=min{x1,x2}. Suppose everyone has the same income (m;=m), and p2=1. What is the
demand curve of x1 for the market?
Qd=m/p1 + 2m/(p1+1)
Qd =4m/(p1+1)
Qd=4m/2p1+2m/(p1+4)
Qd=4m/(p1+1)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1542e5de-e392-4bdb-9d95-e5abdf8e6267%2F1c5a0fd5-867c-42c1-b08e-3bc4240c7b60%2Felonh3k_processed.jpeg&w=3840&q=75)
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- Your own a chocolate producing company which can advertise on both television (T) and internet(I). The effect of TV and online commercials on sales is again given byS(T,I) = 500 + 48T−6T2+ 112I−6I2+ 4TI. You have a budget of $25 that you can spend on T and I. The price of aTV commercial is $12per unit and the price of an online commercial is also $12 per unit. 1. Determine the optimal level of TV commercials T and online commercials I if you have to spend all of your budget. You should provide two methods to solve this, by direct substitution and by setting up the Lagrangian. Is the Lagrange multiplier positive or negative? Give an intuitive interpretation of why this is the case? 2. Now determine the optimal level of TV commercials T and online commercials I if you DO NOT have to spend all of your budget. Do you obtain the same answer as subquestion 5.1? What is the Lagrange multiplier equal to in this case? Discuss.Consider 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.The movie theater in Glendon has two types of customers: domestic students (group 1) and international students (group 2). At a price of p, cents, the number of movie tickets that domestic students are willing to buy per year is given by: q₁-170-0.7p₁. At a price of p₂ cents, the number of movie tickets that international students are willing to buy per year is given by: 92-87-0.3p2. The total costs for the movie theater depend on the total number of tickets sold, q₁+92, and are given by the following total cost function C(q₁+9₂2)=(91+9₂)². Suppose that the movie theater can identify which students are domestic and which students are international, and students are unable to resell movie tickets to each other. This enables the theater to charge different prices to domestic vs international students. If this is the case, then how much will the movie theater charge to domestic students (p.)? How much will the movie theater charge to international students (P₂)? Note: You should round all…
- The movie theater in Glendon has two types of customers: domestic students (group 1) and international students (group 2). At a price of p, cents, the number of movie tickets that domestic students are willing to buy per year is given by: q₁-170-0.7p₁. At a price of p₂ cents, the number of movie tickets that international students are willing to buy per year is given by: 92-87-0.3p₂. The total costs for the movie theater depend on the total number of tickets sold, q₁+92, and are given by the following total cost function C(q₁+92)=(91+9₂)². Suppose that the movie theater can identify which students are domestic and which students are international, and students are unable to resell movie tickets to each other. This enables the theater to charge different prices to domestic vs international students. How many movie tickets will domestic students buy (9₁)? How many movie tickets will international students buy (9₂)?The movie theater in Glendon has two types of customers: domestic students (group 1) and international students (group 2). At a price of p, cents, the number of movie tickets that domestic students are willing to buy per year is given by: q₁-170-0.7p₁. At a price of p2 cents, the number of movie tickets that international students are willing to buy per year is given by: 9₂-87-0.3p₂. The total costs for the movie theater depend on the total number of tickets sold, 9₁+92, and are given by the following total cost function C(q₁+92)=(9₁+9₂)². Suppose that the movie theater can identify which students are domestic and which students are international, and students are unable to resell movie tickets to each other. This enables the theater to charge different prices to domestic vs international students. The movie theater's management receives too many complaints from students about the fact that they charge different prices to domestic vs international students, so they are forced to charge…Finn is in charge of decorations for an upcoming festival, and he is planning to decorate withclovers (C) and flags (F). Suppose his preferences over decorations can be represented by theutility function U(C, F) = C^(3/4)F^(1/4) For this problem, assume C and F are infinitely divisible so you don’t need to worry aboutrestricting to whole-number answers.(a) Write Finn’s budget constraint as a function of the prices PC, PF , and his budget I.(b) Write Finn’s constrained optimization problem in Lagrangian form and derive the threefirst order conditions.(c) Use two of the first order conditions to show that Finn’s marginal rate of substitution(MRS) equals the marginal rate of transformation (MRT) at the optimum. (Note: Youdo not need to solve the constrained optimization any more than this.)
- 3. Maximize x1, x2 such that 232 u(x₁, x₂) = x³ x3 P1x1 + P2x2 = mViolet buys pies (x) and champagne (y) with her income of $400 and her utility function over pies (x) and champagne (y) (assumed to be divisible goods, where any real number unit pie or champagne is feasible) is Cobb-Douglas and given by u(x, y) = xy. The price of champagne is pY = $10 per bottle. (a) Pies cost pX = $10 per pie if she buys between zero and 20 pies; if she buys more than 20 pies, each additional pie is half-price, i.e., pX = $5. Draw her budget set, carefully labelling all relevant points. calculate the quantities of pies and champagne she will consume when she maximizes her preferences. (b) (HARDER! We haven’t covered this scenario in class) Pies cost pX = $10 per pie if she buys between zero and 20 pies; if she buys more than 20 pies, each pie purchased is half-price, i.e., pX = $5. The discount applies to all units purchased, not the additional ones! Draw her budget set, carefully labelling all relevant points. Calculate the quantities of pies and champagne she will…10
- Julia and Ralph need to decide which one of them will take time off from work to complete the rather urgent task of pruning their trees. Julia is pretty good with a pole saw; she can prune the trees in 1 hour. Ralph is somewhat slow; it takes him 6 hours to prune the trees. Julia earns $120 per hour as a business consultant, while Ralph earns $15 per hour as a lifeguard.Keeping in mind that either Julia or Ralph must take time off from work to prune the trees, who has the lowest opportunity cost of completing the task?Sam's extended family spends $3,200 per month on wine and beer. Their utility function is given by U = 200WB, where W represents the number of bottles of wine that they buy, and B represents the number of cases of beer that they buy. Wine costs $25 per bottle and beer costs $32 per case. Sam's family wants to maximize their utility. Calculate how many bottles of wine and how many cases of beer they should buy. Show your calculation(s).N=2 video broadcasting websites, You and Twi, must decide the number of minutes of ads to be displayed for every video that the user elects to watch. Let tY be the number of ad-minutes per video set by You, and tT the number of ad-minutes per video set by Twi. Streaming one video costs You cY=0.02, while it costs Twi cT=0.03. There are 100 million potential users, and each watches videos according to the following demand curves: qY((tY,tT) =10-2tY+tT=10-2tT+tY a- What is the cross-price elasticity between You and Twi? b- Suppose, for now, that You and Twi enter an (illegal) agreement by which they set tY=tT=t Derive the total number of users in the market as a function of t. Derive the profits for each website as a function of t. c- Now let the two platforms compete by each setting their number of ad-minutes: i. What is the best reply of You? What is the best reply of Twi? ii. Find the Nash Equilibrium of the game. iii. How many total users choose You and how many total users choose…