The Role of Uncertainty in a Simple Temporary Equilibrium Model of International Trade with Quantity Rationing under Fixed Exchange Rates

Schittko, Ulrich K.; Eckwert, B. Article The Role of Uncertainty in a Simple Temporary Equilibrium Model of International Trade with Quantity Rationing under Fixed Exchange Rates Zeitschrift für Wirtschaftsund Sozialwissenschaften (ZWS) - Vierteljahresschrift der Gesellschaft für Wirtschaftsund Sozialwissenschaften, Verein für Socialpolitik Provided in Cooperation with: Duncker & Humblot, Berlin Suggested Citation: Schittko, Ulrich K.; Eckwert, B. (1983) : The Role of Uncertainty in a Simple Temporary Equilibrium Model of International Trade with Quantity Rationing under Fixed Exchange Rates, Zeitschrift für Wirtschaftsund Sozialwissenschaften (ZWS) - Vierteljahresschrift der Gesellschaft für Wirtschaftsund Sozialwissenschaften, Verein für Socialpolitik, ISSN 0342-1783, Duncker & Humblot, Berlin, Vol. 103, Iss. 5, pp. 461-483, https://doi.org/10.3790/schm.103.5.461 This Version is available at: https://hdl.handle.net/10419/291559 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ The Role of Uncertainty in a Simple Temporary Equilibrium Model of International Trade with Quantity Rationing under Fixed Exchange Rates* By Ulrich K. Schittko and B. Eckwert A two-period model of temporary equilibrium with rationing and international trade under fixed exchange rates is presented, emphasizing the importance of agent's expectations of future prices and constraints. It is shown that several traditional comparative statics results are only compatible with a specific expectational structure. Especially this is the case for the reaction of the trade balance to exogeneous parameter changes. 1. Introduction The failure of the price system to adjust immediately to its Walrasian equilibrium value gave rise to the formulation of temporary equilibrium models with quantity rationing, starting e.g. with J. P. Benassy (1975), E. Malinvaud (1977), W. and K. Hildenbrand (1978), and culminating in the work of V. Böhm (1980). If the planning horizon of the economic agents is not confined to one period, then the future overshadows the present in the sense that the agents have to decide now without knowing the prices and wages of tomorrow nor the quantity constraints they will have to face when the future unfolds. The following model of a small open economy tries to take this situation as a starting point in a formulation of a simple model with price expectations (depending on the current prices and wages) and uncertainty concerning future quantity constraints. Thereby we can complement A. Dixit's model (1978) in several respects. First our model contains an explicit intertemporal formulation of the consumers' and producers' optimizing behaviour, especially allowing inventory decisions. Secondly we examine the influence of a specified expectational pattern concerning future prices and wages as well as possible random * Financial support of the Deutsche Forschungsgemeinschaft is gratefully acknowledged. OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.103.5.461 | Generated on 2023-04-04 12:02:50 462 Ulrich K. Schittko and B. Eckwert restrictions in the labour market on the optimizing behaviour and the comparative statics properties of the whole model. The chosen formulation concerning price and quantity constraint expectations is sufficiently general to capture the main influences of these phenomena. Our results are quite robust against more sophisticated expectational formulations. With regard to price expectations we use a one-point-distribution, meaning that future prices are expected with probability one. Individuals have no rational expectation, so that expectional errors are possible. Quantity expectations are stochastic and modelled by a discrete probability distribution. A generalization of the assumed expectational pattern is not likely to alter our results in a central way. These enlargements produce several new insights concerning the influence of uncertainty on the properties of the possible short-run equilibria. Most of the individual decisions depend essentially on the expectational parameters. The entrepreneurial behaviour is dichotomized in the sense that the salesand inventory-decisions are sensitive with respect to expectations, while the productionsand labour demand decisions are not. This is not a consequence of our specific expectational pattern and will be interpreted economically. Our use of the small country assumption restricts as usual the power of the model, for it excludes some interesting disequilibrium situations, which show up in a two-country setting (compare Schittko and Eckwert (1981, 82, 83)). To study the intrinsic dynamics would be too lengthy and is left to a subsequent paper (1982). 2. The basic model Our economy is a small country which produces its national product by means of the single nontradable factor labour, whose price is fixed in the short run. For the produced good the world product price is given for the small country, but there are no quantity constraints restricting the goods market decisions of the country. It can very well happen, that the domestic goods market is in disequilibrium, so that the foreign trade absorbs the excess supply or demand. We have then pt = n pt = 1,2, so that prices of the outputs are translated by means of the exchange rate from foreign currency to home currency units. We assume country specific outputs to be completely substitutable in consumption, so that we have in fact a single tradable good. Our model is a two-period one, OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.103.5.461 | Generated on 2023-04-04 12:02:50 Simple Temporary Equilibrium Model of International Trade 463 in which the economic agents base their behaviour in period t = 1 on the market dates of the present and on their subjectively certain point expectations concerning prices and wages in period t = 2 and their random expectations concerning the constraint levels on the labour market in the future. The use of a two period model does not mean that the economy ends after period 2 but rather, that the agents formulate plans only one period ahead into the future. The home country has its own money, which is the only asset serving as a store of value. Consumption and production decisions are described by means of representative decision units, the representative consumer and the representative producer. 2.1. Consumer behaviour Let us begin with the behaviour of the consumption side. The consumer decisions are the outcome of the maximization of a single, specified utility function which is defined on the present and future consumption possibilities comprising home and imported goods, i.e. (1) u (<cl9 Mlt c2, M2) = u (xly = xx-x2 , where xt: = ct + Mt, t = 1, 2, denotes the consumption of the produced good at time t, which consists of consumption of the home produced good ct and the imported good Mt. We could have chosen another utility function, say yj {u (xi, xg)) = = log xi + log X2, \p a strictly monotone transformation. This utility function has the special, but important property, that the marginal utility of consumption in period 2 becomes very large, when the amount of consumption becomes smaller and smaller. This utility function has an Arrow-Pratt-measure of risk-aversion of one, so that we have riskneutrality. Concerning the future market dates the consumer has the following point expectations { P2 = Wl (Pi) = flPl w2 = v>2 (wt) = bw1 , where pt is the price level and Wt the wage rate both in period f, t = 1, 2. The linear functions y>i, i = 1, 2, show the way price expectations are formed. If a> 1, then the price expectations of the consumer are called inflationary; if a — 1, then they are called static expectations, and if a < 1, then we have deflationary expectations. Depending on the OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.103.5.461 | Generated on 2023-04-04 12:02:50 464 Ulrich K. Schittko and B. Eckwert labour market situation in the present, the representative individual expects a rationing on the labour market in the future (period two) with different subjective probabilities. That amounts to that the representative consumer expects with a certain probability not be rationed, respectively to be rationed at a certain level h. It, t = 1,2, denotes the fixed labour supply of the consumer. The situation can be summarized in the following matrix, where R1 denotes a labour market rationing in period t and N* that the consumer is not rationed on the labour market in period t, t = 1,2. R2 JV2 m 1-Q2 q2 m 1-Ql Qi qi denotes the corresponding subjective probabilities. Let us start to derive the optimal consumption decisions. If the consumer is not rationed on the labour market in period one, the employment in period two, L2, is a discrete random variable whose probability distribution is given by with probability qt (3) I* = ' " { U wi _ k Wi with probability 1 — qt Let X21 denote the action of the consumer, if he is not rationed on the labour marked in period two, and the action he chooses, if he is rationed in that period. Then a random variable X2 can be defined as ^ __ L2 = I if L2 *22 > if L2 X2 is a discrete random variable with probability distribution qu (1 — qi). Let us now define a transformation by means of (5) X2 ; — X2~*21 *22 — x2l which posesses a binomial distribution according to (6) x'2 —• B (1, qfj) L2 = l2. From (5) we obtain , fO , if H..« (7) = X2 (X22 — ^l) + *21 OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.103.5.461 | Generated on 2023-04-04 12:02:50 Simple Temporary Equilibrium Model of International Trade 465 As X2 is a random variable, the expected value of the utility function (1) is a relevant optimality criterion, i.e. our consumer (in case of nonrationing in period one) has to maximize (8) max {xx • [x2l + (x^ - x21) Eq1 (X2)]} XV x2i' ^ s. t. (i) xt ¡> 0, x2i ^ 0, mi ¡> 0, i = l,2 (ii) Pi Xx -!- 77lj TTZ Q -jW^ (iii) P2 x2i = m1 + w212 (iv) p2x& = + w2'l2 . To find a solution of problem (8) we use a standard method of dynamic programming, i.e. we first maximize with respect to the second period's decision variables over the constraint set of period two (given an arbitrary but fixed decision in period one). So we have to solve the following maximization problem in case of non-rationing in period one (9) max E (u (xh X2)) = max E (u (xlt X2(x^ — x21) + x21) = X2V X22 x2i* X22 max u (xt, x2i + (x22 - x2i) Eqt (X2)) = X21,X22 max {x1 [x21 + {xm - x21) Eqt (X2)]} x2i,x22 s.t. (iii), (iv) and the non-negativity conditions for the decision variables. As a solution we find m1 + l2w2 (10) *21 = x22 = P2 m1 + ¿2 V2 As in our simplified set up the labour supply is fixed, the optimal solution (10) can be derived directly from (8) (iii) and (8) (iv).1 We have described the procedure of solving (8) in detail to prepare for the more complicated decision problem of the production sector. We recall, that given the (*i, mi)-decision x^i denotes the optimal decision in period two, if the consumer is not rationed in this period. Otherwise the optimal decision would be x^. If we substitute the 1 This was pointed out by the referee. OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.103.5.461 | Generated on 2023-04-04 12:02:50 466 Ulrich K. Schittko and B. Eckwert optimal solution for period two into (8), we obtain an indirect utility function. / mi -f bwt u \ (11) V (xh mlt plf wlf l2, ¿2, qlt a, b) = qt \xt — —j + / TTli + bWi U \ The indirect utility function (11) has now to be optimized with respect to xi, mi, subject to the following period-one restrictions (12) XX > 0, TTIi > 0 (13) m^ + w1li = p1x1 mi . We assume that mi > 0, which holds, if (14) q{ bw1l2 + (1 - gx) bw1 l2<mii + w1ll . By making this assumption, which says that the wealth of period one is greater than the expected labour income of period two, we exclude boundary solutions. For the optimal decisions we then obtain (15) 1 [7720 + wt lt 4- <?1 bwx l2 + (1 - <Zj) bwt y 2 Pl = [wio.+ Ii - Q± (bwt l2) - (1 - Qi) (bw^h*)] • The partial derivatives of the optimal decisions with respect to the exogeneous variables are 3 *J/3 \ = (1 - bi^/2 Pi > 0 , (16) 3 JCf /3 777o = 1/2 pj > 0 , bWi z Pi The last inequality e.g. shows, that the reaction of the optimal consumption decision in period one due to a change in the subjective probability to be fully employed in period two, is proportional to the expected unemployment in that period. Furthermore we deduce 3 xJ/3 a = 0 3 *J/3 b = —J— wt (q1 Iq + (1 - <?i)l2) > 0 A Pi OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.103.5.461 | Generated on 2023-04-04 12:02:50 Simple Temporary Equilibrium Model of International Trade 467 (17) 3xJ/3Pi = - (1/Pi)*|<0 q1 (Zi + bl2) + (1 - qt) (h + bl2) >0 . 3 wt 2 Pi In (17) only the first partial derivative is surprising. Intertemporal substitution as a consequence of changes in price expectations does not occur because of our chosen utility function. The sign reaction of m\ can be deduced from the budget condition of period one, given the sign reactions of x\. In case of rationing in period one we calculate by a similar procedure the optimal decisions for period one as if a similar condition as before in (14) ensures the positivity of m\. The sign reaction to parameter changes can be inferred from (18) like before. It is evident, that the sign reactions are qualitatively similar to the previous ones in case of non-rationing in period one, because also in that case h is not a decision variable. Let us now describe the production decision of our economy. We assume that the profits of period t are taxed fully by the government. Therefore the representative firm has no initial money balances, but has an endowment a)o of the consumption good, which has been stored from the last period. The firm plans to sell yt units of the good and to buy zt units of labour (t = 1,2). With a production function f this input is transformed into output cot, t = 1,2, which is instantaneously available, i.e. (19) cot = f (zt) = hzQ ti 0 < q < 1, h > 0, t = 1,2 . The product is storable, and similar to the consumption sector the producers anticipate the future market dates by subjective expectations. Concerning future prices and wages we assume that their expectations are identical to those of the consumption side. If the producer is not rationed in period one on the labour market, he expects not to be rationed in period two with probability (so that his notional demand would be fulfilled) and to be rationed with probability (1 — qo) at the (18) x* = — [TOQ + w1l1 + q2 bw! u + (1 - q2) bwi U] ¿p ! - 1 m\ = [mo + Wi - qQ bwy l2 - (1 - q2) bw112) — , 2.2. Producer behaviour OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.103.5.461 | Generated on 2023-04-04 12:02:50 468 Ulrich K. Schittko and B. Eckwert full employment level. That means Z2 is a random variable with the following distribution: , w2) with prob. q3 ( z2 (P2» 1 (20) Z2 1 ' with prob. (1 — qf3) In case the producer is rationed in the first period, his expectation concerning the future labour market situation is given by { Zo (p9, w2) with prob. q4 l2 with prob. (1 — <?4) . The producer maximizes his expected profit over the planning horizon. To calculate the expected value of the profit function for the case of non-rationing in period one, we transform the random variables Z2 by means of z« - L (22) Z9: = 2 ' Z2 (p2, W2) - l2 which is distributed according to B {1, <?q), so that we have f 1 , if Z2 = z2 (p2, w2) (23) Z2 = \ [o , if Z2 = i2 . From (22) we obtain (24) Z2 = Z2 (z2 (p2, w2) - l2) + l2 . We know from the production function, that r co21 = hz% , if Z2 = z2 [œ22 = hlQ2t if Z2 = Z2, Q2 = hZ\=< so that Q2 is also random. As an accounting restriction we have to consider + — 2/1 = h (period one) (25) + h = (period two) , ii denoting the storage activity in period one. The future sales are also random, depending on Z2. This random variable Y2 can be transformed by Y2 - (hl% + i,) (26) ft2f-hzl OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.103.5.461 | Generated on 2023-04-04 12:02:50 Simple Temporary Equilibrium Model of International Trade 475 with Zi denoting the labour demand constraint. It is easy to show the existence and local stability of these two disequilibria. Let us now give an effective classification of the equilibria of the model in (pi, w{) — space. This classification is important, because it enables us to assign certain parameter constellations to the different types of disequilibria. Furthermore the classification increases our intuitive understanding of the model. We start to derive the slope of the labour market equilibrium curve in (pi, i^i) — space. An equilibrium in the labour market is described by (62) zA (plt wt) = I wi V " 1 \ PiQh ) The slope of this curve is given by 3 w< (63) 3 Pi Zi (plf wx) = Zi Pi Therefore we can illustrate the equilibrium locus as in fig. 1. The trade balance in case of unemployment (the effective trade balance) in period one is defined as Pi Pi - - (64) HB = y\ (Pi Jilt wly co0> a, b) xt (p? ny wv ttiq , <j2, b; lv U, l2) — 71 71 Pi Pi Pi (i - g) , , ( wi \(g"=r) , i 7t 9~ 7T [ 2 r(wt,b) +n[ Vloh ) +a>0~ 2Pl w ( 1 ) • [77-io + ^ j 9 +q>2 (^1 bl2) + (1 - q2.) (1^1 bi2)] - g . From (64) we calculate 30* OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.103.5.461 | Generated on 2023-04-04 12:02:50 476 Ulrich K. Schittko and B. Eckwert (65) and (66) 3 HB 3 Pi Pi (1 - a) ( W1 \(rH)( h(o2) V + \ Pl e h ) \ 2 (<? - 1) ) r (wlt b) (+) 3 r 3 HB 3 w, (Pi)2 (1 - a) ^ (2 r {wv b))2 (—) b (<£> h + (1 - + Pi£ 2 - e \ h I \2Pl(Q-l) ) 2 Pi q2) k). (+) The first term in (65) and (66) represents the storage effects of the parameter variation, while the second term in (65), respectively, the second and third term in (66) represent the effects on the excess goods supply in our economy. ^ ^ (1_a) (p^U-a)-^- Notice first, that the storage effects?^ - and — ^ 6 r(wlfb) (2 r(wltb))2 of (65) and (66) are always of opposite signs. The slope of the HB = 0curve in (w\, pi)-space, given by dwi dp! HB = 0 3 HB/3 Pj 3 HB/3 w. , is therefore positive, if we either assume both storage effects to be dominant or weak. So we can specify (67) 3 Pi 3 w1 U HB = 0 >0 in the unemployment region normally. Note that for special values of the expectational parameters the slope of the HB = 0-curve in the unemployment region could also be negative. This can be summarized in the following picture (fig. 2). fig. 2 OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.103.5.461 | Generated on 2023-04-04 12:02:50 Simple Temporary Equilibrium Model of International Trade 477 When the economy faces overemployment the trade balance is given by Pi Pi (68) HB (2/1 (Pi ft, wlt <o0, a, b; IJ) -xt (pj n, wh rn^, qv b\ L2, Z2) 71 El 71 + (1 - qt) (bwt l2)) - g For the partial derivatives we derive (69) (70) 3 HB 3 Pi 3 HB 3 w1 1 71 EL 71 2 Pi (-) (+) P! (1 — a) 3 r/3 2(r(u71>b))2 (+) - (Zi + Qi bl2 + (1 - Qi) bZ2) If we assume the storage effects in (69) and (70) both to be either dominant or nondominant, we get opposite signs for (69) and for (70). We can conclude, that (71) 3 w1 3 Pi 3 HB/3 pi >0 , HB = 0 3 HB/3 wt which is illustrated in fig. 3. Note that for special values of the expectational parameters the slope of the trade balance equilibrium curve in the region of overemployment can be negative as illustrated by the broken line in fig. 3. fig. 3 OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.103.5.461 | Generated on 2023-04-04 12:02:50 478 Ulrich K. Schittko and B. Eckwert 4. Comparative Statics 4.1. Unemployment equilibrium First we study the influence of parameter changes on the endogeneous variables Zi and HB, when the economy is not fully employed. The equation system is given by (72) Ki : = L z1 (71 V1 , U>l) = 0 K2 : = V*[y\ (p*n, VJ1, a> k) - xl wl> fe b'y h> h> h) - -g] -HB = 0 The implicit function theorem gives us the effects of a parameter change on the endogeneous variables h, HB in a neighbourhood of the equilibrium solution. // denotes a special parameter of interest: (73) dlt 3 11 dHB whereby D : 3 Ki 3 K« 3 K< 3 K2 • = - 1 < 0 dlt dHB dHB dlt For a change in government expenditures we derive by means of (73) (74) 3^/30 = 0; dHBJdg = -pj<0 . In a system of fixed exchange rates a change of government expenditures has no influence on the employment level. Since the goods market is always equilibrated, there exists no transmission mechanism from the goods market to the labour market. The negative reaction of the trade balance to an increase of g is obvious. Wage rate policy results in (75) and (76) 3 HB/3 wt = 3 3 w-^ — 3 z^J3 i^! •< 0 3 xt 3 zj P* I 3 2/j 3 xx 3Zi 3 w1 3 z j + 71 \ 2 Pi 3 w1 (-) 71 3 w1 3 yt ( dVt 3*i \ \ 3 wt 3 wt J (+) 3 w1 3 xt (+) OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.103.5.461 | Generated on 2023-04-04 12:02:50 Simple Temporary Equilibrium Model of International Trade 479 In (76) we have 3 yi/d w\ < 0 for high price expectations. If the goods market effects are dominant, we end up with a negative sign. A variation of the fixed labour supply leads to The employment level Zi is independent of the aggregate labour supply Zi. Since unemployment can be measured by we can derive the effect of labour supply variations on the excess labour supply as dU/dh = 1. As is intuitively clear, a reduction of the aggregate labour supply causes a reduction of unemployment. The trade balance reaction is at first sight surprising, since the employment level in period one is determined by the demand side. But note that a reduction of the labour supply reduces the expected income of period two, because the consumer expects with probability q<% not to be rationed in that period. So the expected loss of income in the future has a consumption demand effect in period one. We further deduce the effects of an exchange rate policy (79) 3 yd = 3 ztJ3 n > 0 . A devaluation has positive labour market effects. The trade balance reaction depends on two real and a kind of monetary effect. 1. The real consumption demand increases (labour market effect). 2. The real goods supply increases. 3. The consumption demand in foreign currency decreases nominally. The trade balance reacts positively if the labour market induced consumption effect is dominated by the two remaining effects. Depending on the price expectations an opposite sign specification of (80) could be reasonable. Finally we examine the influence of changes of the expectational parameters a, bf on the unemployment equilibrium of our model. (81) 3 yd a = 0 , 3 yd b = 0 , 3 yd q2 = 3 yd q3 = 0 (77) 3 lt/d li = 0 , 3 HB Id h= - —< 0 . (78) U: = h-h , (80) (82) OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.103.5.461 | Generated on 2023-04-04 12:02:50 480 Ulrich K. Schittko and B. Eckwert 3 HB pi 3 ¡/i 1 (83) = V^b 2V lq*wi ^ + (1 ~ ^ h) __ 1 pt2 (l - a) 3 r/3 b _ ~ ~~ 2 n r2 (+) ^— (Q2 w2 h + tt -<?2) ^ 0 (-) (81) tells us that expectational variations do not affect the employment level of our economy. In our regarded disequilibrium the employment level is according to (72) demand determined. The labour demand however does not depend on expectations. Increases in price expectations lower current sales plans und worsen thereby the trade balance (compare (82). Higher wage expectations increase storage costs and thereby current sales plans as well as total current consumption. If the positive storage effect is dominated by the consumption effect, then we have a negative sign in (83). (84) 3 HB/3 q<> = - —— bwt (Zg - Zg) < 0 , 3 HB/3qf3 = 0 . 2 71 The expectational parameters have no influence on the entrepreneurial labour demand decisions, so that the level of employment does not vary when expectations change. This is due to the fact that in our model production does not take time. The trade balance however depends sensitively on the price-, wage-, and constraint expectations. 4.2. Overemployment equilibrium In this type of equilibrium which is described by (85) the employment level is given by the fixed labour supply l\. (85) K,: = - lt + lt = 0 K4: =p* [y1 (p* n, wlt o)0, a, b; lt) - xt (pf n, wl9 m<,, qv b\ llt l2, l2) - - g] - HB = 0 . As endogeneous variables we have Zi and HB. The comparative statics properties can be obtained like before and are summarized as follows. OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.103.5.461 | Generated on 2023-04-04 12:02:50 Simple Temporary Equilibrium Model of International Trade 481 For a change in government demand we have (86) 3 zi/3 Q = 0 , 3 HB/3 g = - p* < 0 . Wage rate policy results in 3 Zj/3 w1 =0 (87) 3 HB/3 wt = - + + W " «1) Pi 2 (1 - a) 3 r/3 ^ /I - \ ^ - 1 — W1 + 91W2 + a2 7*2 (+) (-) du^ \ KPiQh ) np*Qh(o - 1) Dl denoting excess labour demand. dDL / wt \\Q - (88) —?- = [ — <0, H \ a Pi&h ) These multipliers lend themselves to a completely analogous interpretation as the preceeding ones. A change in Zi gives 3 V\ (89) 3 Z^ h = l ; 3 HB/3 Zx = p* dlt 1 2 71 [w± (1 + qt bwt)] ^ o . An exogenous increase in the labour supply stimulates sales plans as well as consumption demand. The net effect depends on the relative strength as shown in (89). Exchange rate policy leads to 3 V\ pi (90) 3 Z^S ¡7T = 0 ; 3 HB/3 n = pj ^ + ^ 0 where the sign of the trade balance reaction depends on the price expectation. The higher the price expectation, the more likely a negative trade balance reaction will follow. This atypical result underlines the importance of expectations. OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.103.5.461 | Generated on 2023-04-04 12:02:50 482 (91) Ulrich K. Schittko and B. Eckwert 1 3 DL! 3 n : 3 n aplçh Q - 1 - h >0 . For the influence of a change in the expectational parameters we calculate (92) (93) (94) (95) 3 ltJ3 a = 3 lt/d b = 3 lt/d qt = 0 3 HB/3 a = pj ^ < 0 3HB 3 b Pi \db db) = PÎ — n pi (1 — a) 3 r/3 b 3 ^ 3b~ 2r2 3 HB dqt 2 ZZ7| b (¿2 - Z2) < 0 . We recognize that the reaction of the trade balance essentially depends on the expectational parameters, while the labour market situation is not influenced by expectations. In a model with an explicit temporal production structure, which we will present in the future, of course, this conclusion does not hold. 5. Concluding Remarks Though our model has a dramatically simplified structure, it became evident that expectations play a significant role in classifying the effective equilibria and for the results of comparative statics. As a consequence of our specification of the production process mainly price expectations are responsible for the qualitatively different results. Since the production and labour demand decisions do not depend on expectational parameters in our model, the influence of these parameters shows up in the trade balance only via the goods demand decisions. Even very traditional results concerning the effectiveness of a devaluation can be upset by our simple expectational structure. Wage expectations would become more decisive, if the production process is specified differently. We saw that contrary to Dixits* results even in the case of fixed exchange rates the trade balance shows different reactions depending on the kind of expectations. The expectations concerning the labour market constraints would also play a more distinctive role, if we would admit goods market rationing. On this question work is in progress. OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.103.5.461 | Generated on 2023-04-04 12:02:50 Simple Temporary Equilibrium Model of International Trade 483 Summary In a two period model of temporary equilibrium with quantity rationing and international trade under fixed exchange rates expectations concerning future prices and constraints play a significant role in classifying the effective equilibria and for the results of comparative statics. If the production sector can hold inventories (as in our model), the expectational structure influences significantly the sales but not the production and labor demand decisions. This surprising result depends on the way the production process is modelled, revealing the role of an atemporally formulated production structure. Zusammenfassung In einem temporären Gleichgewichtsmodell einer offenen Volkswirtschaft mit Mengenrationierung (bei festen Wechselkursen) spielen Erwartungen bezüglich zukünftiger Preise und Mengenschranken bei der Effektivklassifikation der Gleichgewichte und für die Resultate der komparativen Statik eine wichtige Rolle. Wenn für den Produktionssektor Lagerhaltung zugelassen wird (wie in unserem Modell), beeinflußt die Erwartungsstruktur signifikant die Verkaufsaber nicht die Produktionsund Arbeitsnachfrageentscheidung. Dieses überraschende Resultat hängt von der Art der Modellierung des Produktionsprozesses ab und offenbart die Rolle einer atemporal formulierten Produktionsstruktur. References Benassy, J. P. (1975), Neo-Keynesian Disequilibrium Theory in a Monetary Economy. Review of Economic Studies 42, 503 - 523. Böhm, V. (1980), Preise, Löhne und Beschäftigung. Tübingen. Dixit, A. (1978), The Balance of Trade in a Model of Temporary Equilibrium with Rationing. Review of Economic Studies 45, 393 - 404. Hildenbrand, K. and W. Hildenbrand (1978), On Keynesian Equilibria with Unemployment and Quantity Rationing. Journal of Economic Theory 18, 255 - 277. Malinvaud, E. (1977), The Theory of Unemployment Reconsidered, Oxford. Schittko, U. K. (1981), Zur mikroökonomischen Fundierung der makroökonomischen Theorie — ein temporäres Außenhandelsgleichgewichtsmodell mit Mengenrationierung. Jahrbuch für Sozialwissenschaften 32, 241 - 278. — and B. Eckwert (1981), A Two-Country Temporary Equilibrium Model with Quantity Rationing. Diskussionspapier 50, Universität Augsburg. —/— (1982), Dynamic Aspects in a Temporary Equilibrium Model of International Trade with Quantity Rationing. Diskussionspapier 53, Universität Augsburg. —/— (1983 b), Local Stability and Dynamic Aspects in a Two-Country Model with Fixed and Flexible Exchange Rates. Diskussionspapier, Universität Augsburg. OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.103.5.461 | Generated on 2023-04-04 12:02:50