Consider the following dynamic supply-demand model:
Qd(t)=40-2p(t)-2p'(t)-p''(t)
Qs(t)=-4+2p(t)
In the above, p(t) denotes price in time t, Qd(t) and Qs(t) denote, respectively, quantity demand and quantity supplied in time t.
(a)Use the above system to derive a differential equation in p(t).
(b)Find the general solution for p(t).
(c)Does the limit of p(t) exist?
Consider the following dynamic supply-demand model: Qd(t)=40-2p(t)-2p'(t)-p''(t) Qs(t)=-4+2p(t) In the above, p(t) denotes price in time...
3. (An application to Economics: Demand, Supply and Price) Let Qd, Qs and P be the quantity demanded, quantity supplied and price, respectively, of a certain 1 commodity. We assume that: Qs = c1 + w1P + u1P' + v1P'' Qd = c2 + w2P + u2P'' + v2P'' where the primes denote derivatives with respect to t, time. Now let c = c1 − c2; u = u1 − u2; v = v1 − v2; w = w1 −...
Consider the following demand and supply curves: Qd = 200 – 2P and Qs = 20 + 4P. What are the equilibrium quantity and price? At that equilibrium what is the price elasticity of demand?
Consider a perfectly competitive market where Demand is described as Qd 100-2P. a. If the market price is 10, how many units are consumed in the market? What is the consumer surplus in the market? b. Suppose the market Supply is described as Qs 10 P. What is the equilibrium price in the market? Quantity? C. Suppose the market Supply is described as Qs 10+ P. What is the excess quantity supplied in the market at P demanded in the...
Deadweight Loss Given the following information: Qs = 2P P = Qs/2 QD= 180 - 4P P = (QD -180)/-4 AR = P = 45-.25Q TR = 45 - .25Q2 Hint: MC – supply curve MR = 45 - 5Q Qs = supply Qd = demand Using the above information, Graph and calculate the price-output solution under competitive market assumptions. How much is the consumer surplus producer surplus and total surplus? Calculate the price and the...
14. Let Qd, Qs and P be the quantity demanded, quantity supplied and price, respectively, of a certain 1 commodity. We assume that Qs =c1 +w1P +u1P′ +v1P′′ Qd =c2 +w2P +u2P′ +v2P′′ where the primes denote derivatives with respect to t, time. Now let c=c1−c2; u=u1−u2; v=v1−v2; w=w1−w2. (a) Using the typical Economics assumption that demand equals supply i.e. Qs = Qd, derive a non-homogenous O.D.E for P. (b) Given that w > 0 and c < 0, what...
Problem 1 Deadweight Loss Given the following information: Qs = 2P P = Qs/2 QD= 180 - 4P P = (QD -180)/-4 AR = P = 45-.25Q TR = 45 - .25Q2 MR = 45 - .5Q Hint: MC – supply curve MR = 45 - 5Q Qs = supply Qd = demand A) Using the above information, 1) Graph and calculate the price-output solution under competitive market assumptions. 2) How much is the consumer surplus producer surplus and...
The general demand and supply functions for good A are QD-2, 800-6P 0.5M-10PB Qs 40 4P - 8P1+6F where QD is the quantity demanded of good A, Qs is the quantity supplied of good A, P is the price of good A, M is the averaged income level of consumers, Pb is the price of a related good B, Pr is the price of an input, and F is the number of firms producing good A (a) Is good A...
16 . Demand and Supply curves can be represented by: Qd = 90-2P; and Qs = 3P. Calculate the equilibrium price and quantity: P = $18; and Q = 54 P = $90; and Q = 45 P = $30; and Q = 54 P = $30; and Q = 30
Suppose the demand equation can be represent as QD = 100 -2P and the Supply equation can be represented as QS = -10 + P. a. Find the equilibrium price and quantity. b. At a price ceiling of $20, what is the QD and QS. What is the deadweight loss, consumer surplus and producer surplus amount?
Use the following demand and supply functions to answer this question; Qd=100-2p; Qs=60+2p; The equilibrium quantity in this market is 60, 80, or 100?