Lecture 7: Product Curves, Isoprofit Analysis & Cost Curve Analysis

Product Curves

y=f(x1,x2)y = f(x_1 , x_2),, TP1=f(x,x2¯)TP_1 = f(x, \bar{x_2}) in short run,, AP=TPx1AP =\frac{TP}{x_1}

μP1=δ TP1δx1\mu P_1 = \frac {\delta \ T P_1}{\delta x_1}

If y=x2, x2 2, x¯=2y=x^2, \ x_2 \ ^2, \ \bar{x} =2 so TP1=4x1 2TP_1 = 4x_1 \ ^2 

μP1=8x1\mu P_1 = 8x_1 AP1=4x1AP_1 = 4x_1

ISO Profit Analysis

Short run theory of LL and q/K¯q/ \bar{K}

q=k1/2L1/2q = k^{1/2} L^{1/2},, K¯=4\bar{K} = 4 and TPL=2L1/2TP_L = 2L ^{1/2}

μPL=δ TP2δL\mu P_L = \frac{\delta \ T P_2}{\delta L} and TPL=2L1/2TP_L = 2L ^{1/2} and μPL=L1/2\mu P_L = L ^{-1/2}

TAN: L1/2=18L^{-1/2} = \frac{1}{8} \Rightarrow L=64L=64


g1=pqwLrKg_1 = pq - wL -rK

pq=g1rKwLpq = g_1 -rK -wL

rK=16rK=16 g1=8×161×64γ×γ=γ8g_1 = 8 \times 16 - 1 \times 64 - \gamma \times \gamma = \gamma 8

488+168=8\frac{48}{8} + \frac{16}{8} = 8  (intercept) WP=1\frac{W}{P} =1 (slope)



What if ww \uparrow? LL \downarrow qq \downarrow g1g_1 \downarrow 3 Predictions

What is PP \downarrow? LqG1L \downarrow q \downarrow G_1 \downarrow 3 Predictions

Cubic Example from Worksheet

How much output/Labour/Profit?


Cost Curve Analysis

To derive cost curve:

1) Get LSRL_{SR} LSRL_SR from TPT_P curve

q=K1/2L1/2q=K^{1/2}L^{1/2} K=4K=4

q=2L1/2q=2L^{1/2} LSR=12q2L_{SR} = \frac{1}{2} q^2

2) SVC=wLSRSVC = wL_{SR} SA<C=SVCqSA<C= \frac{SVC}{q}

SFC=rR¯SFC = r \bar{R}

SC=wLSR+rK¯SC = w_L{SR} + r \bar{K}

SμC=δSCδqS \mu C = \frac{\delta SC}{\delta q} SAC=SCqSAC = \frac{SC}{q}

3) qq^* from P=μcP = \mu c

G=(PSAC)qG^* = (P-SAC)q^*

L=LSRL^* = L_{SR}

Shutdown if P<SAVCP<SAVC

Because if q=0q=0


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