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HW3 Answers - Econ 1: Tang Fall Quarter 2007 Homework 3:...

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Econ 1: Tang Fall Quarter 2007 Due Wednesday November 7, at the beginning of class. Please write your name, PID, and section number/TA name on your homework. 1. The table gives the demand and supply schedules for spring water. Price (dollars per bottle) Quantity demanded (bottles per day) Quantity supplied (bottles per day) 0 80 0 0.50 70 10 1.00 60 20 1.50 50 30 2.00 40 40 2.50 30 50 3.00 20 60 3.50 10 70 4.00 0 80 a. What is the maximum price that consumers are willing to pay for the 30th bottle? 2.50 b. What is the minimum price that producers are willing to accept for the 30th bottle? 1.50 c. Are 30 bottles a day less than or greater than the efficient quantity? less d. What is the consumer surplus if the efficient quantity of spring water is produced? CS=$40 e. What is the producer surplus if the efficient quantity is of spring water is produced? PS=$40 f. What is the deadweight loss if 30 bottles are produced? Dwl=$5
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Econ 1: Tang Fall Quarter 2007 2. Suppose that the supply curve for wheat is given by Q S =10P-10 and suppose that the demand curve for wheat is given by Q D =200-20P . a. Find the equilibrium price and quantity of wheat. b. Sketch a picture of the supply curve and the demand curve. Be sure to label i) both axes, ii) the y-intercept both curves, iii) the slope of both curves, and iv) the equilibrium price and quantity. c. Concerned about rising food prices, suppose that the government introduces a price ceiling of $5. What will be the new equilibrium quantity of wheat bought and sold on the market? d. Is this new quantity economically efficient? Explain. e. On the graph you drew in part c, label producer and consumer surplus after the introduction of the price ceiling. Answer: For this question we should first notice that the equations presented are expressed in terms of Q. Since we are going to want to graph these equations with P on the vertical axis and Q on the horizontal axis, we must first re-express the equations to get P on the left hand side. Supply: P = (1/10)Q S + 1 Demand: P = -(1/20)Q D + 10 a. To obtain the equilibrium price and quantity we can combine the two equations, by noting that P = P, to solve for Q* = Q D = Q S . (1/10)Q + 1 = -(1/20)Q + 10 (1/10)Q + (1/20)Q = 10 – 1 (3/20)Q = 9 Q* = 60 Now we can plug this Q back into either equation to obtain P*: P* = (1/10)Q* + 1 P* = (1/10)(60) + 1 P* = 6 + 1 P* = 7. b. Before we sketch the graph, we note that our supply curve intersects the P- axis at (Q, P) = (0, 1). Our demand curve intersects the P-axis at (Q, P) = (0, 10). And we have our equilibrium point (Q*, P*) = (60, 7). This is enough to construct our graph. But we can also note that the demand curve also intersects the Q-axis at Q = 200. (To obtain our Q-intercept for the demand curve, we take the demand equation, set P = 0, and solve for Q: 0 = -(1/20)Q + 10 (1/20)Q = 10 Q = 200.)
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Econ 1: Tang Fall Quarter 2007 So in the graphs above I’ve answered parts c., d. and e. of this question also.
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HW3 Answers - Econ 1: Tang Fall Quarter 2007 Homework 3:...

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