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# a1-w13-de_ans.pdf

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School
Wilfrid Laurier University
Department
Economics
Course
EC238
Professor
Karen Huff
Semester
Winter

Description
Economics 238OC: Written Assignment #1 Due Friday January 25, 2013 Instructor: K. Hu▯ Written Assignment #1: Economic Tools This assignment covers two important skills: 1. Partial equilibrium analysis 2. Cost minimization 1. Suppose that the market for some private good involves external costs like pollution. The supply and demand are described by linear functions as follows: PC = 68 ▯ Q D (1) PP = 8 + 0:5QS (2) Where PC and PP are the prices paid by consumers and received by producers respectivelyD and QSare the quantities demanded and 1 supplied, respectively. There is \$24 worth of damage done every time a unit of the good is produced. [5] (a) Solve for the equilibrium price and quantity of this market if there is no tax or subsidy in place. P = P = P (3) C P M QS = Q D= Q M (4) Use equations 1 and 2 to get: 68 ▯ QM = 8 + 0:5Q M (5) 60 = 1:5Q M (6) Q M = 40 (7) 1These are sometimes called ‘inverse’ demand and supply functions because they relate price to quantity, rather than the other way around. 1 Plugging this into either equation 1 or 2 yields: P = \$28 (8) M [10] (b) Calculate the total social bene▯ts, total social costs and total net social bene▯ts associated with the market equilibrium. Show your calculations and explain the steps brie y in your own words. (A diagram may help.) P 68 S A 28 B C 8 D D Q 40 68 In terms of the diagram (which is not drawn to scale), we can ▯gure out the labelled areas as follows. 1 A = (68 ▯ 28)(40) = \$800 (9) 2 1 B = (28 ▯ 8)(40) = \$400 (10) 2 1 C = (28 ▯ 8)(40) = \$400 (11) 2 D = 8 ▯ 40 = \$320 (12) 2 Then TSB = A + B + C + D = \$1;920 (13) TPC = C + D = \$720 (14) TDC = \$24 ▯ 40 = \$960 (15) TSC = TPC + TDC = \$720 + \$960 = \$1;680 (16) TNSB = \$1;920 ▯ \$1;680 = \$240 (17) Note that total social cost is made up of total private costs of pro- duction TPC plus total damage costs (TDC). The damage costs are not shown on the diagram to make it less messy. [5] (c) Now suppose that the industry is taxed \$27 per unit of the good. Calculate the equilibrium quantity and prices, showing your work. PC = P P \$27 (18) t QD = Q =SQ (19) The superscript t stands for tax. Use equations 1 and 2 to get: 68 ▯ Q t = 8 + 0:5Q + 27 (20) t 33 = 1:5Q (21) Q t = 22 (22) Plugging this into equation 1 and 2 yields: t PC = 46 (23) P t = 19 (24) P [10] (d) Calculate the total social bene▯ts, total social costs and total net social bene▯ts associated with the tax equilibrium. Show your calculations and explain the steps brie y in your own words. (A diagram will help.) Very brie y explain in your own words. Note: Total Net Social Bene▯t can be positive or negative. 3 P 68 A 46 S B 19 C D 8 E D 22 68 Q The TSB is equal to the area under the MSB or demand curve which corresponds to the area of rectangle (B + C + D + E) and the area of triangle (A). B + C + D + E = 22 ▯ 46 = \$1;012 (25) 1 A = (68 ▯ 46) ▯ 22 = \$242 (26) 2 TSB = \$1;254 (27) The TPC is equal to the area under the MPC or supply curve which corresponds to (D) which is a triangle plus (E) which is a rectangle. The total damage cost (not shown on the diagram) will equal the marginal damages (\$24) times the output (22) which is \$528. 1 D = (19 ▯ 8) ▯ 22 = \$121 (28) 2 E = 8 ▯ 22 = \$176
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