Lecture 9: Isoquant

x117x_1 \leq 17 is from 20.3

Two skills for isoquants - long run and short run and effects

q=K1/4L1/4q = K^{1/4}L^{1/4}, w=0.25w = 0.25, r=1r = 1, p=4p = 4, w=1w' = 1


a) μpLμpK=wr\frac{\mu p_L}{\mu p_K} = \frac{w}{r},0.251=KL=14\frac{0.25}{1} = \frac{K}{L} = \frac{1}{4} , q4=KL=4K2q^4 = KL = 4K^2, K=12q2K = \frac{1}{2}q^2 AND L=2q2L = 2q^2

TC=wL+rK=0.25(2q2)+1(12q2)=q2TC = wL + rK = 0.25(2q^2) + 1(\frac{1}{2}q^2) = q^2

μc=2q=p=4\mu c = 2q = p = 4, q0=2q_0 = 2, K0=2K_0 = 2, L0=8L_0 = 8, TC=q2=4=0.25L+KTC = q^2 = 4 = 0.25L + K


c) KL=1\frac{K}{L} = 1, K=LK = L, q4=K2q^4 = K^2, K=q2=LK = q^2 = L, TC=Lq2TC = Lq^2, μc=uq=p=u\mu c = uq = p = u, q2=1q_2 = 1

K=L=1K = L = 1, TC2=2=L+KTC_2 = 2 = L + K


b) {qB=qA=2=K1/4L1/4\left \{ q_B = q_A = 2 = K^{1/4}L^{1/4} \right., μRTS:K=L\mu RTS: K = L (from bundle c)

KL=16KL = 16, K=L=4K = L = 4, TC=K+L=8TC = K + L = 8



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