By Dr. Heinz H. Müller (auth.)
This paintings was once written in the course of my visits at middle (Belgium), on the school of Economics and Politics in Cambridge (England), and on the division of arithmetic on the ETH in ZUrich. I desire to thank J.H. Dr~ze (CORE) for many support ful feedback, and i'm indebted to H. BUhlmann (ETH) for his recommendation and for encouragement. The reviews by way of M. Granzio1, M. Janssen and through nameless referees have been very precious. even if, i suppose the accountability for ultimate mistakes. i'm thankful to R. Boller, I. Lather and M. Urfer for his or her cautious typing of the manuscript. aid by way of the SWiss nationwide technological know-how beginning is said. An past model of this paintings was once awarded on the eu assembly of the Econometric Society 1981 in Amsterdam. In 1981 it was once approved as a "Habi1itations schrift" in Mathematical Economics by way of the dep. of arithmetic on the ETH in ZUrich. CONTENTS advent 1 half I: the overall version eight 1.1. formula of the final version eight 1.1.1. basic homes eight 1.1.2. the shopper 10 1.1.3. The manufacturer 14 1.1.4. the general public quarter sixteen Equilibrium 1.2.
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2 (127) This leads to w=w i (1-~) Q q12 j o q12 ". 4 en[ (l-P)Q -2w-1 ] 1 -1 -1 w- + Q w +4) + (Q-1)Q -2 -1 w] (129) " -1 -1 ] := Ln[ (1-~) Q w := tn[4 (1-P) ] =w = O. 35 CftI au-j ()Q ~ aj3 Since -i ~ 9 - "8 CftI -k 9 ~ aQ "8 CM 1 30 15 -1 -2 0 0 1 (130) has no solution the first order conditions for a relative Pareto optimum are satisfied. But the equilibrium is obviously not an unconstrained Pareto optimum. The conflict of interests becomes obvious. Consumer i sumer prefers a decrease of j is in favour of an increase of interested in a decrease of and Q ~, ~,Q and j3, Q and w , whereas con- w.
14. 42 1) Locally the optimal production plan and the maximal profit are differentiable functions L(p,w), K(p,w), 7T(p,W). •• ,i o the optimal consumption plans and money holdings can be locally represented by functions i i i Q1 (fl,Q ,w) , Q2 (fl,Q ,w) , m (fl, Q,w) which are differentiable in i = 1, ... a,b and 1). ) a(fl,Q,w) Due to the fact that (62) holds with equality, government spending is locally a differentiable function g2(~,Q,w) . 1. c, 1), 2). ) Now we want to have a look at the employment level, Which is given by L(Q,w) • In order to do this we must analyse the optimal production plans.
3 Existence of Eguilibria In contrast to part I we do not need a strong assumption about em- bodied capital. This is due to the fact that the model considered here has much more structure. 37 Assumptions All) See above. AI2a) . l: 1El b) i 1 b (w 11 + ui i w21 ) i > 0 , . l: (w 12 + 1eI is continuous in (ql,q2,g) strictly increasing in A I 3) UO i w22 ) >0 • , quasi-concave in (Ql,q2) Q12,Q22 is continuous in all its arguments quasi-concave in Under 1 b 9 and strictly increasing in g . All, AI2, A I 3 the following propositions hold: Proposi tion 1': For fixed (Q , p) and !!
Fiscal Policies in a General Equilibrium Model with Persistent Unemployment by Dr. Heinz H. Müller (auth.)