3) The marketing research department of a large manufacturing company has determined that the demand equations for two major items it produces are given by p = 2,000 - 5x + 8y and q = 4,000 +9x-7y where p is the price of item A, q is the price of item B, x is the monthly demand for item A, andy is the monthly demand for item B. Find the total monthly revenue from items A and B whenx=15 and y - 5.
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- Suppose a firm has estimated the function of its demand (Qv) as follows: Qv = 400000-10Pv+10Pc+0.5I+0.5A where, Qv = quantity demand of good V Pv = price of Qv (own price) = 10 000 Pc=price of the competitor's product = 8 000 I = average income of consumers = 10 000 A = average advertising expenditure= 30 000 1.Calculate the total amount of vehicles that wouldbe sold given the equation and values of the variables? 2.Calculate price income and advertisement elasticity?2. Suppose your marketing research department estimates the demand for your company’s product as Qx= 500-11Px+0.5Y, where Qx is the quantity demanded per week, Px is the price of product X, and Y is the average household income per week in the city. R2=0.87, the standard error of the coefficients of the price (Px) and household weekly income (Y) are 2 and 0.1, respectively. a. Are the coefficients of Px and Y statistically significant? b. Given the initial values Px=$10 and Y=$1000, find price elasticity (Ep) and income elasticity(EY), respectively. Is the demand for the company’s product price and income elastic, or inelastic? c. What action should the manager take to increase the company’s operating revenue? d. Is the company’s product a normal good? How do you know? e. Interpret what R2=0.87 means. Assume equations 1 and 2 below were estimated from the data gathered that will represent the demand and supply functions respectively of an individual buyer and seller respectively for product X. Qd, 65,000 – 11.25Px + 15Py – 3.751 + 7.5A Qsx = 7,500 + 14.25Px – 15P, – 3.75C Eq. 1 Eq. 2. where Px price of product X; Py - price of product Y; I - average consumer's income; A – advertising expenditure; Pz - price of product Z; and C - cost of production. — = If the new supply equation will be Qs'x = 26,250 + 712.50PX; 0. What would be the new equilibrium price (round-up to two decimals)? P. How many of this product will be bought and sold at this new market price? Round-up to two decimals. Q. What is the specific reason for this change in supply?
- Johnson's Household Products has a division that produces two types of toothpaste: a regular toothpaste and a whitening tooth paste. The demand equations that relate the prices, p and q (in dollars per thousand units), to the quantities demanded weekly, x and y (in units of a thousand), of the regular toothpaste and the whitening toothpaste are given by p=3000-20 x-10 yp=3000−20x−10y and q=4000-10 x-30 yq=4000−10x−30y respectively. The fixed cost attributed to the division is $20,000/week, and the cost for producing 1000 tubes of regular and 1000 tubes of whitening toothpaste is$400 and $500, respectively. a. What is the weekly total revenue function R(x, y)? b. What is the weekly total cost function C(x, y)? c. What is the weekly profit function P(x, y)? d. How many tubes of regular and whitening toothpaste should be produced weekly to maximize the division's profit? What is the maximum weekly profit?The market research conducted by a firm in the drinking water industry shows that the demand for water has a constant elasticity equal to − 1/? where ? is 9 a) Express the demand function in the form of a differential equation b, Find the general solution for the differential equation by expressing Q (the quantity demanded) as a function of P (the product price). c, ) Suppose that the demand for bananas has a constant elasticity equal to – 9. Explain in words (without providing any calculation) how decreasing the price would affect a banana seller’s total revenue and profits. Please help me. Thank you so much.6) a. Given that f is a differentiable function of x, show that the following notation of elasticity of a function El(f) = d(ln(f))/dx / d(In x)/dx corresponds with the definition of elasticity of a function f.b. Given that f and g are differentiable functions of x, prove that the elasticity of the product,Elx(f/g) = Elx(f) − Elx(g)c. Using part (b) above or otherwise calculate the following elasticity with respect to x, Elx (x−1/x5+1)
- Using a linear specification, you estimate your demand curve to equal Q=10-5P+20C+2A, where • Q = the quantity demanded of your product • P = the price of your product • C = college-ratio, which is the percentage of the local population that attends college. For instance, C=0.10 would indicate 10% of the local population attends a college. • A = digital advertising spend (in thousands of dollars) What is your demand elasticity with respect to the college-ratio when your price is $5, your digital advertising spend is $100,000 (i.e. A=100), and the college-ratio equals 0.25? a. εQ,C=0.0013 b. εQ,C=0.0263 c. εQ,C=20 d. εQ,C=15200The price p (in dollars) and the quantity x sold of a certain product obey the demand equationp = (-1/6) x + 100(a) Find a model that expresses the revenue R as a function of x. (Remember, R = xp.)(b) What is the domain of R?(c) What is the revenue if 200 units are sold?(d) What quantity x maximizes revenue? What is the maximum revenue?(e) What price should the company charge to maximize revenue?Consider the demand function d(p)=300e^−0.01p^2 items purchased when charging p dollars per item. Currently the price is 9 dollars per item. Use marginal analysis to estimate the decrease in demand when the price increases by 0.3 dollars per item. Demand would decrease by approximately _____ items. Round your answer to three decimal places.
- Suppose the demand (in thousands) for a toaster is given by 100p-2, where p is the price in dollars charged for the toaster.a. If the variable cost of producing a toaster is $10,what price maximizes profit? b. The elasticity of demand is defined as the percentage change in demand created by a 1% change in price. Using a data table, show that the demand for toasters has constant elasticity, that is, the elasticity doesn’t depend on the price. Would this be true if the demand for toasters were linear in price?Suppose that the management of Sun City resort is trying to understand the income elasticity of their resort. As an advisor, they provide you with the following figures;If the average income of visitors is R3 000 (which is the current income), then 45 000 visitors visit Sun City resort each year and if the average income increases to R5 000, then 60 000 visitors visit Sun City resort each year. 1. Calculate the income elasticity of demand using the arc method. (5) 2. Based on your answer above (1), explain what type of a product (service) the resort is.An economic consultant for Gumbcorp. recently provided the firm’s marketing manager with this estimate of the demand function for the firm’s product: Qxd=12,000 -3Px + 4Py - 1M + 2Ax where Qxd represents the amount consumed of good X, Px is the price of good X, is the price of good Y, M is income, and Ax represents the amount of advertising spent on good X. Suppose good X sells for $200 per unit, good Y sells for $15 per unit, the company utilizes 2,000 units of advertising, and consumer income is $10,000. How much of good X do consumers purchase? Are goods X and Y substitutes or complements? Is good X a normal or an inferior good