# Equilibrium wage and rental rate in an competitive economy

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## Equilibrium wage and rental rate in an competitive economy

 Consider an economy producing a single good by a production function Y= min(L,K) where Y is the output of the final good. K and L are input use of capital and labour respectively. Suppose this economy is endowed with 100 units of capital and labour supply s L is given by the function L(supply)=50*w, where w is the wage rate. Assuming that all markets are competitive find the equilibrium wage and rental rate. Firstly, efficient productions are K=L, hence L quantity is produced with L units of labour and capital. Compeitive good market requires 0 profit==> p=w(L) plus w(K) Consumer expenditure on good equals their earnings from labour == p*L=w(L)*L == w(K)=0 Demand equals supply in capital market== D(capital)=100 Demand equals supply in labour market== 50*w(l)=D(labour)=D(capital)=100 So w(l)=2 But the answer says w(l)=1 and w(k)=0!? How come?
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## Re: Equilibrium wage and rental rate in an competitive economy

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## Re: Equilibrium wage and rental rate in an competitive economy

 Sir, why are we assuming the price to be 1, or how is it justifiable? I solved the problem and concluded p=2.
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## Re: Equilibrium wage and rental rate in an competitive economy

 In reply to this post by Amit Goyal We could just as easily choose p=3, and then the w plus l would equal 3, so the labour demand always less than labour supply will not hold.