If club members charge $9 admission to a classic car show, 1,000 people will attend, and for each $1 increase in price, 100 fewer people will attend. Let x represent the amount of increase in price (in dollars). Find R(x), the total revenue function (in dollars). R(x) = Find R'(x). R'(x) = What price will give the maximum revenue for the show? per ticket Find the maximum revenue.
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- The inverse demand function of a group of consumers for a given type of widgets is given by the following expression: π=−10q+2000 $ ( I ) where q is the demand and π is the unit price for this product. A. Determine the maximum consumption of these consumers. B. Determine the price that no consumer is prepared to pay for this product. C. Determine the maximum net consumers’ surplus. Explain why the consumers will not be able to realize this surplus. D. For a price π of 1000 $/unit, calculate the consumption, the consumers’ gross surplus, the revenue collected by the producers, and the consumers’ net surplus. E. If the price π increases by 20% (The new price π=1200), calculate the change in consumption and the change in the revenue collected by the producers. F. What is the price elasticity of demand for this product and this group of consumers when the price π is 1000 $/unit. G. Derive an expression for the gross consumers’ surplus. H. The supply function for the widget…The weekly demand function for a particular product is q=f(p)=2400-15p. Where q is stated in units and p is stated in dollars. Determine the quadratic total revenue function, where R is the function of p. What is the concavity of the function? What is q intercept? What does total revenue equal at a price of 60 dollars.The market research department of the Better Baby Buggy Co. predicts that the demand equation for its buggies is given by q = −2.5p + 500 where q is the number of buggies it can sell in a month if the price is $p per buggy. At what price (in dollars) should it sell the buggies to get the largest revenue? p = $
- 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 demand function for a truckload of firewood for college students in a small town is Qc = 400-p. It is sometimes convenient to rewrite a demand function with price on the left side. We refer to such a relationship as the inverse demand function. Therefore, the inverse dimand function for college student is p = 400 - Qc. The demand function for other town residents is Qr = 400 -2p. What is the inverse demand function for other town residents? At a price of $300,. will college students buy any firewood? What about town residents? At what price is the quantity demanded by other town residents zero? Draw the total demand curve, which sums the demand curves for college students and other residents?The marketing department of a business has determined that the demand for a product can be modeled by p=2000−10x, where p is the price per unit (in dollars) and x is the number of units. The cost (in dollars) of a producing x units is given by C=2000+500x. What price will yield a maximum profit?
- In a small town in North India where winter temperatures are very low, the demand function for a truckload of firewood for college students in a small town is Qc = 400 - p. It is sometimes convenient to rewrite a demand function with price on the left side. We refer to such a relationship as the inverse demand function. Therefore, the inverse demand function for college students is p = 400 - Qc. The demand function for other town residents is Qr = 400 - 2p. Solve the following & Show all your calculations. [1 + 2 + 2 = 5] (a) What is the inverse demand function for other town residents? (b) At a price of Rs.300, will college students buy any firewood? What about other town residents? At what price is the quantity demanded by other town residents zero? (c) Draw the total demand curve, which sums the demand curves for college students and other residents. Clearly label X-axis and Y-axis. Draw the curve for at least five pointThere is no demand for a certain make of one-time use camera when the unit price is $ 12. However, when the unit price is $ 8, the quantity demanded is 8000/week. The supplier will not market any cameras if the unit price is $ 2 or lower. At $ 4/camera, however, the manufacturer will make available 5000 cameras/week. Given that both the supply and demand equations are linear: Determine the associated linear demand function Determine the linear supply function. At what price should the camera be sold so that there is neither a surplus nor a shortage?A toy company is trying to determine the optimal price for their weekly supply to meet the demand for a toy they are about to release. They estimate that the supply function follows p= 0.006q^2 + 0.14q+ 8.62 and the demand function follows p= -1.25q+ 65 , where p is the price of the toy (in dollars) and q is the weekly quantity of the toy (in hundreds). If the company tries to sell the toy for $24, will there be a shortage or surplus of toys each week?