d the consumers' surplus if the demand function for a particular beverage is given by D(q) = 2000 (2q+9)² and if the supply and demand are in equilibrium at q = 9.
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- The demand function for a certain kind of laptop is given by -0.04x p = 600e where p is the unit price in dollars and x (in units of a hundred) is the quantity demanded each month. (a) Find the number of laptops demanded per month of the unit price is set at $500 per laptop. (b) Use the results of part (a) to find the consumers' surplus if the selling price is set at $500 per laptop.The demand and supply functions for a particular commodity are D(x) = 80e-0.001x and S(x)= 30e0.001r , where x is the number of units of the product, D(x) is the price that results in a consumer demand of x units and S(x) is the price that results in a producer supply of x units. a. Find the equilibrium point using your calculator and identify the equilibrium units and price. Give your answers to the nearest whole unit and nearest dollar. The value of x at equilibrium is units. The value of p at equilibrium is b. Determine the consumers' surplus.Demand and Supply functions are P=-2Qd+50 and P=0.5Qs+25, the equilibrium output is: 9 11 12 8 10
- a) The demand function for a product is p = 60 3-9/15) where q is the number of units and p is the price of one unit. At what price will the demand be 15 units? How many units will be demanded if the price is $41.60?For the supply function, s (x) = 100 – 100e 0.02 and the demand function, d (x) = 300e-0.01r %3D a) Find the market demand (the positive value of x at which the demand function intersects the supply function using your calculator). Round your answer to 2 decimal places. b) Find the consumers' surplus at the market demand found in part a). Round your answer to 2 decimal places. c) Find the producers' surplus at the market demand found in part a). Round your answer to 2 decimal places.The quantity demanded each month of Russo Espresso Makers is 250 when the unit price is $140. The quantity demanded each month is 1000 when the unit price is $110. The suppliers will market 750 espresso makers when the unit price is $76 or higher. At a unit price of $96, they are willing to market 2250 units. Both the supply and demand equations are known to be linear. (a) Find the demand equation. P = (b) Find the supply equation. p= (c) Find the equilibrium quantity and the equilibrium price. units $
- The quantity demanded x each month of Russo Espresso Makers is 250 when the unit price p is $150; the quantity demanded each month is 1000 when the unit price is $120. The suppliers will market 750 espresso makers if the unit price is $50. At a unit price of $80, they are willing to market 3000 units. Both the demand and supply equations are known to be linear. (a) Find the demand equation.p = (b) Find the supply equation.p = (c) Find the equilibrium quantity and the equilibrium price. equilibrium quantity units equilibrium price $There 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 movie theater has been charging $ 10.00 per person and selling about500 tickets on Saturday and Sunday nights. After surveyingtheir customers, theater owners estimate that for every 50 cents theylower the price, the number of attendees will increase by 50 per night.Find the demand function and calculate the consumption surplus whentickets are sold for $ 8.00.
- The demand function for a certain brand of DVD is given by p = = -0.001x? – 0.2x + 8 where p is the unit price in dollars and x is the quantity demanded each week, measured in units of a thousand. Determine the consumers' surplus if the mar- ket price is set at $18 per disc.Consumers' Surplus The demand function for a certain brand of mattress is given by P = 300e where p is the unit price in dollars and x (in units of a hundred) is the quantity demanded per month. (a) Find the number of mattresses demanded per month if the unit price is set at $200/mattress. (Round your answer to the nearest integer.) 1352 mattresses -0.03x (b) Use the results of part (a) to find the consumers' surplus if the selling price is set at $200 per mattress. (Round your answer to the nearest dollar.) $The demand function for a manufacturer's product is p= f(q) = – 0.16q + 432, where p is the price (in dollars) per unit when q units are demanded (per day). Find the level of production that maximizes the manufacturer's total revenue and determine this revenue. What quantity will maximize the revenue? q = units