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- 2. A small college is trying to predict enrolment for the next academic year. Thevice president for business states that enrolment has tended to follow apattern described by E = 18,000 – 0.5P, where E denotes total enrolment andP is yearly tuition.a) If the school sets tuition at €20,000, how many students can it expect to enrol?b) If the school wants to maximize total tuition revenue, what tuition should itcharge?c) As the vice president for business, what tuition would you recommend? Explainbriefly.d) Due to a strong post-COVID-19 recovery, the income conditions in the regionimprove substantially. Explain in one sentence how this could affect the college’senrolment pattern and the enrolment level maximizing its tuition revenue.4GE 10:01 ITEMS INFO 8. 2 attempts remaining. TAMU_QID: BM_00048 Consumers will demand 1070 items at a price of $2.75 per item. When the price per item increases to $5, the number of items demanded will decrease by 45. Write the linear demand function, p(x), for this item. Enter your answer in slope-intercept form, using exact numbers. p(x) = Submit answerLet say you have 3 products: cake, candy, and bread. The revenue per cake is $8. The revenue per candy is $4. The revenue per bread is $5. Define the number of cake, candy, and bread you are about to produce per day as x, y, and z respectively. The manager wants that the number of candy is at least equal to the total number of cake and bread. What is the correct linear constraint to show this? Group of answer choices z – x – y ≥ 0 x – 2y – z ≥ 0 y – x – z ≥ 0 x – y – z ≥ 0
- A TV channel has estimated the demand for its service to be givenby the following function: Q=9.83p-1.2A2.5Y1.6P0-1.4whereQ = monthly sales in unitsP = price of the service in $A = promotional expenditure in $’000Y = average income of the market in $’000P0 = price of ‘home movies’ in $ The current price of the TV channel is $60, promotional expenditure is$120,000, average income is $28,000, and the price of ‘homemovies’ is$45.Indicate whether the following statements are true or false, givingyour reasons and making the necessary corrections h. Current sales are over a million units a month. i. The demand curve for the channel is given by:Q=9.83p-1.2j. The channel’s sales are more affected by the price of ‘home movies’ than by the price of its own service.k. If the channel increases its price this will reduce its profit.Let say you have 3 products: cake, candy, and bread. The revenue per cake is $8. The revenue per candy is $4. The revenue per bread is $5. Define the number of cake, candy, and bread you are about to produce per day as x, y, and z respectively. The manager wants that the number of cake accounts for at least 30% of the total production per day. What is the correct linear constraint to show this? Group of answer choices 0.3x – 0.7y – 0.7z ≥ 0 0.7x – 0.3y – 0.3z ≥ 0 0.7x – 0.3y – 0.7z ≥ 0 0.3x – 0.7y – 0.3z ≥ 02. Supose that a consumer has utility function U with U (₁,22) = x1426, where ₁ and ₂ are demand of commodity 1 and 2. Suppose that the price of commodity 1 and 2 is $3 and $5, respectively. This consumer has money m = 12 to spend and wants to maximize utility with constraint the money. (a) Write the Lagrangian function. (b) Find the critical point using first order condition. (c) Find the Hessian matrix to check whether the critical point is maximiser or minimiser. (d) Find the maximum utility.
- 1. A standard model of choice under risk is Expected Utility Theory (EUT) in which preferences over lotteries that pay monetary prizes (x₁, x2, ..., xs) with probabilities (P1, P2, ..., Ps) with Eps = 1 are represented by the function L S (a) What does it mean to say that a function represents the consumer's prefer- ences? Σpsu(xs) Choice 1 8=1 (b) State and briefly comment on the axioms required for the EUT representation. (c) Consider the following experiment of decision making under risk in which sub- jects are asked which lottery they prefer in each of the following two choices: Lottery B 0 with prob. 0.01 10 with prob. 0.89 50 with prob. 0.10 Lottery D Choice 2 Lottery A 0 with prob. 0 10 with prob. 1 50 with prob. 0 Lottery C 0 with prob. 0.90 10 with prob. 0 50 with prob. 0.10 Suppose that the modal responses are Lottery A in Choice 1 and Lottery D in Choice 2. Assume that utility of zero is equal to zero and illustrate why it is not possible to reconcile these experimental…A stadium can seat 60,000 people. Assume 35% of seats are not occupied (not for sale) because of Covid-19 and social distancing requirements. You are told that the current price of tickets is $70 and that the demand is linear and that the demand function (Qd) = 60,000 - 250P. examine the market for tickets for games at the stadium during these Covid times. You should Illustrate themarket for tickets using a demand and supply diagram. Show all your calculations and properly label the diagram. At $70 a ticket the cap on the number of seats available (because of Covid restrictions) is creating a shortage. How many people miss out on tickets when they are priced at $70 per ticket?A food truck vendor averages 150 tacos sold when the price per taco is $4. A study shows that the average number of tacos sold will increase by 25 facos for every $1 that the price per taco is lowered. Which equation models the food truck's average sales in dollars, s, in terms of the price per taco, x ? A 325x + 250 3 = - 25x + 250 3 = 25x + 250x 3 = - 25x + 250x P Type here to search 315 P 1/28/20 Esc Delete CD & 2 8 Backspace Num Lock R T. Y P Home D K L Enter Z. B Shift End Alt Pgup Alt Ctrl Home PgDn End deapad S rivacy Shutter on Webcam Delivery
- If the supply and demand functions for a commodity are 100 + 2(4+ Pa = - (Q.) P₁ = (Q + 2)² E plot each function on the same graph Estimate the quarum price and quarty aigebraicaty and graphicaly w▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪ ‒‒‒‒‒‒‒‒‒‒‒‒wwwwwwwwwSuppose the average age of Stanford Alumni increased at the same time the smaller stadium was built and the income elasticity of ticket sales is .5 Group of answer choices Tickets are an inferior good. If income increases with age, it is more likely the smaller stadium will increase total revenue because any increase in ticket revenue from the increase in prices will be reinforced by an increase in ticket sales from the higher income of Stanford Alumni. If income increases with age, it is less likely the smaller stadium will increase total revenue because any increase in ticket revenue from the increase in prices will be offset by a decrease in ticket sales from the higher income of Stanford Alumni.Scenario The government of the island nation of Autarka has become increasingly concerned about the health and wellbeing of low-income households. Medical experts stress the importance of a healthy diet in this regard. They have determined that, ideally, a household would consume at least 10kg of fresh fruit and vegetables each week. The government has proposed implementing a new voucher scheme to ensure that the 10kg per week consumption target is met. Under the government’s proposal, the vouchers would be redeemable for fresh fruit and vegetables, but could not be used for other types of food, or for non-food consumption. Moreover, to limit the cost of the voucher scheme, the value of the vouchers sent to a household would be linked to the household’s income. Community groups in Autarka have expressed concern that a voucher scheme is unnecessarily paternalistic; depriving low-income households of the choice of how to spend their income. These groups argue that the government’s…