Example Economy with CRS, Perfect Competition, and Unilateral Tariffs

Transcription

1 Econ 425 Fall 2008 B. Lapham Eample Economy with CR, erfect Competition, and Unilateral Tariffs Case : MALL Country imposes a unilateral tariff This eample is based on Questions 3-4 from Assignment Two. Let be a MALL country. can trade with the rest of the world ROW at a fied price ratio of good X to good Y equal to W = 2/3. The technologies are the same in as in the ROW and are given by: X = min { LX 8, K } X 2 { LY Y = min 6, K } Y 4 All consumers in the world have the same utility function given by: UX, Y = X.75 Y.25. There is a single consumer in with the following factor supplies: L = 30 K = 0. Begin by calculating aggregate supply functions for each good in. Full Employment of factors is given by: 8X + 6Y = 30 2X + 4Y = 0. olving these gives X = 3 Y =. Net, we calculate aggregate demand functions for each good in : XD =.75I =.75p X + p y Y =.75 p p X + Y 2

2 Y D =.25I =.25p X + p y Y =.25 X + Y, 3 p y p y where we have used the fact that aggregate income equals GN I = p X and the notation of p p y. Now, calculate ecess demand functions for each good in : + p y Y E X = X D X =.75 X + Y Y X =.75.25X EY = YD Y =.25 X + Y Y =.25 X.75Y or, substituting in X = 3 and Y =, we have EX = = E Y = = Autarkic Equilibrium in. Impose closed economy market clearing for good X in to solve for the autarkic equilibrium price ratio in, A : XD = X EX = = 0 A or A =. 6 Note that this is the same answer as we calculated in Question 3.A. on Assignment Two. Free Trade Equilibrium. ince is small, the free trade equilibrium price ratio will be given by the price ratio in the rest of the world: = W = 2/3. Now note that the terms of trade for in the free trade equilibrium is the ratio of the price of its eport good good Y to the price of 2

3 its import good good X: T OT = py = p = 3/2. 7 The aggregate supply of each good in will be the same as in autarky because under Leontief production functions, supplies are independent of goods prices. The aggregate demand function for each good in will have the same form as derived above for autarky. ince the form of the aggregate supply function and the form of aggregate demand function are the same in autarky as in free trade, the ecess demand functions will have the same form in autarky as in free trade. o we can evaluate the ecess demand functions given in equations 4 and 5 at the free trade equilibrium price ratio, = 2/3 to determine eports and imports by in the free trade equilibrium: E X = = 2/3.75 = 3 8 = o since E X E Y = =.752/3.75 = 4 > 0, must be importing good X and since E Y = < 0, must be eporting good Y. This is the pattern of trade we epect since A = > 2/3 = W, implying that has a comparative advantage in good Y. Unilateral Tariff Equilibrium uppose the government in imposes a unilateral ad-valorem tariff at rate τ =. on its imports of good X. uppose the government distributes all of the tariff revenue back to the consumer in. We first note the following relationship between the prices of the goods in and in the ROW: p T = p W T + τp W T = + τp W T p T y = p W T y, 0 3

4 so T = + τ W T. Now, since is small, the tariff it imposes will have no effect on world prices so the price ratio at which trades with the ROW under the tariff will be the same as in free trade. ence, we have the following price ratios in the ROW and in in the tariff equilibrium: W T = = 2/3 T = + τ W T =.2/3 = /5. 2 o we see that T >, implying that the consumer in pays a relatively higher price for the import good under the tariff than in free trade. This also implies that the producers of good Y in that is, the producers in the import competing sector receive a relatively higher price for their good than in free trade. Of course, this is what we epect since the tariff is a ta on the import good. Furthermore, the TOT for in the tariff equilibrium is the ratio of the price of good Y to the price of good X using the prices at which trades with the ROW, that is, at the ROW prices not the prices in : T OT T = = 3/2. 3 W T Thus, as epected, the small country cannot affect its TOT by imposing the tariff so we have T OT T = T OT for a small country. Now we calculate eports and imports by in the tariff equilibrium. Under the tariff, aggregate income in equals the following: I = p X + p y Y + τp W E. Thus, the tariff modified ecess demand function for good X in is given by: E =.75 p p X + p y Y + τp W E X p =.75 y p Y + τ p W p E.25X. 4

5 Now substituting in the price relationships given in equation 0 and, we have E =.75 Rearranging this to solve for E X for : E = Y τ + τ + W T + τ +.25τ Now, we substitute τ =., W T = 2/3, X E.25X. 4 gives the tariff modified ecess demand function for good Y τx W T. 5 = 3, and Y to determine imports of good X by in the tariff equilibrium: E T == = into the above epression /3 It is easiest to calculate eports of good Y using the balanced trade condition given by: p W E + p W y E y = 0 E y = W E. or E T y = 2/3.293 = Comparing these to imports and eports by in free trade given by equations 8 and 9, we see that both are lower in the tariff equilibrium than in the free trade equilibrium. This is what we epect as trade barriers, here in the form of a unilateral import tariff, lead to less trade. Case 2: LARGE Country imposes a unilateral tariff uppose that is a large country trading with another large country called F. roducers in F have the same technologies as those in and there is a single consumer in F whose has the same utility function as the consumer in. The consumer in F owns 65 units of labour and 20 units of capital. 5

6 Free Trade Equilibrium. The aggregate supply of each good in will be the same as in autarky because under Leontief production functions, supplies are independent of goods prices. The aggregate demand function for each good in will have the same form as derived above for autarky. ince the form of the aggregate supply function and the form of aggregate demand function are the same in autarky as in free trade, the ecess demand functions will have the same form in autarky as in free trade and recall are given by: E X = E Y = We now determine ecess demand functions for F. Full employment in F is given by: 8X + 6Y = 65 2X + 4Y = 20. olving these gives X F = 7 Y F =.5 20 Aggregate demand functions in F will have the same form as in so we have the following ecess demand functions in F: EX F =.75 X F + Y F Y X F F =.75.25X F E F Y =.25 X F + Y F Y F =.25 X F.75Y F or, substituting in X F = 7 and Y F =.5, we have E F X = = E F Y = =

7 We now impose world market clearing on good X to determine the free trade equilibrium price ratio: E + E F = = 0 olving this gives = 3/4 = Furthermore, the TOT for in the free trade equilibrium are given by: T OT T = = 4 3 = We can calculate eports and imports by each country in the free trade equilibrium using the ecess demand functions above: E = E F = = /4 E y = E F y =.753/4.75 = Note the following relationship between factor demand ratios for the two goods: K L = 4 < 2 3 = K y L y, so good X is relatively labour intensive and good Y is relatively capital intensive. Also note the following relationship between factor supply ratios for the two countries: K L = 3 > = K F L F. Thus, the O Theorem tells us that will eport the good that uses capital relatively intensively, good Y and import good X which is what we see in equations 25 and 26. Unilateral Tariff Equilibrium uppose the government in imposes a unilateral ad-valorem tariff at rate τ =. on 7

8 its imports of good X. uppose the government distributes all of the tariff revenue back to the consumer in. We first note the following relationship between the prices of the goods in and in F : p T = p F T + τp F T = + τp F T p T y = p F T y, 27 so T = + τ F T. 28 Now, since is large, the tariff it imposes WILL affect the price ratio at which it trades with F. To find the tariff equilibrium price ratio at which these countries trade, we first derive the tariff modified ecess demand function for good X for each country. Under the tariff, aggregate income in equals the following: I = p X + p y Y + τp F E. Thus, the tariff modified ecess demand function for good X in is given by: E =.75 p p X + p y Y + τp F E X p =.75 y p Y + τ p F p E.25X. Now substituting in the price relationships given in equation 27 and 28, we have E =.75 Rearranging this to solve for E X for : E = Y τ + τ + F T + τ +.25τ E.25X. gives the tariff modified ecess demand function for good Y τx F T. 8

9 Now, we can substitute τ =., X E = = 3, and Y = into the above epression to derive F T or E = F T Because F is not imposing a tariff, the form of its ecess demand function for good X is unchanged so is still given by 30: EX F = F T We now impose world market clearing on good X to determine the tariff equilibrium price ratio: E + E F = F T.75 = 0 F T olving this gives F T The price ratio in in the tariff equilibrium is then given by T = + τ F T =..727 = Finally, the TOT for in the tariff equilibrium is given by T OT T = F T =.727 = Comparing the price ratios in the tariff equilibrium to those in free trade, we see the following: F T < < T, 9

10 and T OT T > T OT, so eperiences a TOT improvement when it imposes the tariff. These results are consistent with our intuition as follows. When the large country imposes the unilateral tariff, this initially raises the price of its import good, good X, and the consumer in demands less of the good. This decreases world demand for the good and puts downward pressure on the relative price of good X in the foreign country so falls to F T to clear the market. ince the relative price at which buys goods from F to the price at which sells goods to F i.e. F T falls when imposes the tariff, has an improvement in its TOT. Finally, since the import good is taed through the tariff, the consumer in pays a higher relative price for the good than in free trade which is why we have T >. We can calculate eports and imports under the tariff by evaluating the ecess demand function for good X for at F T =.727: E T.75 = E F T = =.202. Using balanced trade, we have E T y = E F T y = F T E T = =.47. Comparing these to the imports and eports in free trade given by equations 25 and 26, we see that both are lower in the tariff equilibrium than in the free trade equilibrium. This is what we epect as trade barriers, here in the form of a unilateral import tariff, lead to less trade. 0