Find the consumer and producer surpluses (in dollars) by using the demand and supply functions, where p is the price (in Supply Function Demand Function p = 700 x p = 0.008x² + 260.8 consumer surplus $ producer surplus $
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- 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.Suppose the demand function for a product is given by the function: D(q) = -0.014g + 54.6 Find the Consumer's Surplus corresponding to q = 1,400 units. (Do no rounding of results until the very end of your calculations. At that point, round to the nearest tenth, if necessary. It may help you to sketch the demand curve, which crosses the horizontal at q = 3,900.) Answer: dollarsSuppose the demand function for a product is given by the function: D(q) = -0.018q+50.4 Find the Consumer's Surplus corresponding to q = 1,550 units. (Do no rounding of results until the very end of your calculations. At that point, round to the nearest tenth, if necessary. It may help you to sketch the demand curve, which crosses the horizontal at q = 2,800.) dollars Answer:
- The demand for a particular item is given by the function D(x) = 1, 500 – 3x² . Find the consumer's surplus if %3D the equilibrium price of a unit $300. The consumer's surplus is $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.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 certain product is? = 86 − ?2and the supply function is? = ?2 + 6? + 30where p is in millions of dollars and x is the number of thousands of units. Find the equilibriumpoint (x, p), then find the consumer’s surplus and producer’s surplus. Round your answer to thenearest unit (the nearest million dollars).During the 1950s the wholesale price for chicken for a country fell from 25c per pound to 14c per pound, while per capita chicken consumption rose from 21.5 pounds per year to 27 pounds per year. Assume that the demand for chicken depended linearly on the price. (a) Construct a linear demand function q(p), where p is in cents (e.g., use 14c, not $0.14). Then, find the revenue function. R(p). R(p) = (b) What wholesale price for chicken would have maximized revenues for poultry farmers? ¢ per pound Second derivative test: Your answer above is a critical point for the revenue function. To show it is a maximum, calculate the second derivative of the revenue function. R"(p)=Find the consumer and producer surpluses by using the demand and supply functions, where p is the price (in dollars) and x is the number of units (in millions). Demand Function: p = 360 - x Supply Function: p = 160 + x
- Consider the following example of a supply function, Qsx = -875 + 1250Px – 25C where Qsx refers to the quantity supplied of product X, Px is the price of product X, and C represents the cost of production (in hundreds). How much will be the quantity supplied of product X assuming X is sold for P5 and the cost of production is P1,500.Given: (x is number of items) Demand function: d(x) = 300 – 0.4x Supply function: s(x) = 0.4x %3D Find the equilibrium quantity: Find the consumers surplus at the equilibrium quantity:Suppose the demand function is linear. At p = 8, quantity demanded is Q = 16. At p = 15, quantity demanded is Q = 10. For the price increase from 8 to 15, the loss in consumer surplus due to fewer goods being purchased is -- surplus due to a higher price on the goods still purchased is and the loss in consumer