Given the demand function d(q) = -0.8q+150 and the supply function s(q) = 5.2q, find the equilibrium quantity and price and use integral calculus to find the consumer and producer surplus at equilibrium %3D
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Q: The demand and supply functions of two related goods are given by Qd1 = 300 – 50P1 + 20P2 Qs1 = -200…
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- Given the following Market Model: nP = m-X (Demand Function for commodity X')wP = e+ X (Supply Function for commodity 'X)(Where n,m,e, w > 0)Find out changes in equilibrium price when intercept of demand function and slope of supply functionchange. Draw suitable diagrams?Consider a market characterized by the following inverse demand and supply functions: PX = 10 - 2QX and PX = 2 + 2QX. Compute the number of units exchanged and the price at which those units will be exchanged when there is an $8 per unit price floor.Q3Use a matrix method to find the equilibrium prices and quantities where the supply and demand functionsfor Good 1, Good 2 and Good 3 are asQd1 = 50 − 2P1 + 5P2 − 3P3, Qs1 = 8P1 − 5Qd2 = 22 + 7P1 − 2P2 + 5P3, Qs2 = 12P2 − 5Qd3 = 17 + P1 + 5P2 − 3P3, Qs3 = 4P3 − 1
- 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 isQr = 400 − 2p. 1. What is the inverse demand function for other town residents? 2. At a price of $300, will college students buy firewood? What about other town residents? At what price is the quantity demanded by other town residents zero? 3. Draw the total demand curve, which sums the demand curves for college students and other residents.Suppose the demand and supply function of the item x and y are associated with each other. If qx and qy are the units produced and sold of x and y, respectively, and px and py are the corresponding prices, the demand functions are qx=7-px+py and qy=24+px-py and the supply functions are qx=-3+4px-2py and qy=-5-2px+4py. What is the equilibrium prices?You are given following demand function: Demand function: P=300e−0.2QP=300e^−0.2QGiven equilibrium price and quantity P=119.6 and Q=4.6 respectively, the consumer surplus at the equilibrium is: Select one: 352 902 550 378 1380 Clear my choice
- For the demand function (image 1) and supply function (image 2) a) the equilibrium price is: b)the consumers surplus under marker equilibrium, rounded to the nearest integer is: c) the producers surplus under marker equilibrium, rounded to the nearest integer is:Suppose that we can represent Joyce's preferences for cans of pop (the x-good) and pizza slices (y-good) with the utility function min[4x,5y]. a) Find her Marshallian Demand Functions. b) Find her Hicksian Demand FunctionsSuppose the quantity of good X demanded by individual 1 is given by X1 = 10 − 2PX + 0.01I1 + 0.4PY and the quantity of X demanded by individual 2 is X2 = 5 − PX + 0.02I2 + 0.2PY a) What is the market demand function for total X (= X1+X2) as a function of PX, I1, I2, and PY . b) Graph the two individual demand curves (with X on the horizontal axis, PX on the vertical axis) for the case I1 = 1000, I2 = 1000, and PY = 10. c) Using these individual demand curves, construct the market demand curve for total X. What is the algebraic equation for this curve?
- The estimated monthly U.S. demand function for avocados isQ = 144 − 40p + 20pt where p is the price of avocados and pt is the price of tomatoes, a substitute for avocados. The estmated supply function is Q = 58 + 15p − 20pf where the price of fertilizer, pf , is $0.40, so the supply function can be written asQ = 50 + 15p. The initial price of tomatoes is $0.80 per lb. Using algebra, determine the initial equilibrium price and quantity of avocados, and then determine how price and quantity change if the price of tomatoes increases by $0.55 to $1.35Find the consumer and producer surpluses (in dollars) by using the demand and supply functions, where p is the price (in dollars) and x is the number of units (in millions). See Example 5. Demand Function Supply Function p = 200 − 0.2x p = 100 + 1.8xThe 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…
