1. (40 points) Refer to the graph below to answer the following questions. Home\
ID: 1107447 • Letter: 1
Question
1. (40 points) Refer to the graph below to answer the following questions. Home's Import-Competing Industry Note: All curves are linear Price Supply Po 100 Demand 800 1700 Quantity 1300 Home is a "small country" in this market. Po and Pw are prices domestically (that is, in autarky) and worldwide, respectively Given that the demand and supply curves are linear, what are the values of the price at the intercepts A and F? [Hint: There is enough information on this graph to figure these values out, and the values are important to do the calculations below. Once you figure these out it might not be a bad idea to write down the equations of the curves in slope intercept form. NOTE: F will be a negative number!!! It's weird, but don't worry about it. Proceed with the rest of the problem as usual.] With trade, what is the quantity of imports? What is the consumer surplus to H in autarky? What is CS with trade? What is the producer surplus to H in autarky? What is PS with trade? What are the gains from trade to H? a. b. c. d. e. Now suppose H imposes a tariff of 20% on imports of this good. f. g. h. i. What is the quantity demanded after the tariff? What is the Consumer Surplus? How much is domestically supplied after the tariff? What is the Producer Surplus? What is the tariff revenue? How large is the deadweight loss from the tariff?Explanation / Answer
(a)
(i) Equation of linear demand curve: P = a - bQ
When Q = 1300, P = 100
100 = a - 1300b......(1)
When Q = 1700, P = 50
50 = a - 1700b........(2)
(1) - (2) yields: 50 = 400b
b = 0.125
a = 500 + 1700b [From (2)] = 50 + (1700 x 0.125) = 50 + 212.5 = 262.5
Demand curve equation: P = 262.5 - 0.125Q
When Q = 0, P = 262.5 (Vertical intercept of demand curve, point A)
(ii) Equation of linear demand curve: P = c + dQ
When Q = 1300, P = 100
100 = c + 1300d......(1)
When Q = 800, P = 50
50 = c + 800d........(2)
(1) - (2) yields: 50 = 500d
d = 0.1
c = 50 - 800d [From (2)] = 50 - (800 x 0.1) = 50 - 80 = - 30
Supply curve equation: P = - 30 + 0.1Q
When Q = 0, P = - 30 (Vertical intercept of supply curve, point F)
(b) With trade, relevant price is Pw (= $50). At this price,
Quantity demanded = 1700
Quantity supplied = 800
Import = Quantity demanded - Quantity supplied = 1700 - 800 = 900
(c) Consumer surplus (CS) = Area between demand curve and market price
(i) In autarky,
CS = Area ABD = (1/2) x $(262.5 - 100) x 1300 = 650 x $162.5 = $105,625
(ii) With free trade,
CS = Area ACE = (1/2) x $(262.5 - 50) x 1700 = 850 x $212.5 = $180,625
(d) Producer surplus (PS) = Area between supply curve and market price
(i) In autarky,
PS = Area BDF = (1/2) x $(100 + 30) x 1300 = 650 x $130 = $84,500
(ii) With free trade,
PS = Area EFG = (1/2) x $(50 + 30) x 800 = 400 x $80 = $32,000
NOTE: First 4 parts are answered.
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