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

Product Curves

﻿$y = f(x_1 , x_2)$﻿﻿$,$﻿ ﻿$TP_1 = f(x, \bar{x_2})$﻿ in short run﻿$,$﻿ ﻿$AP =\frac{TP}{x_1}$﻿

﻿$\mu P_1 = \frac {\delta \ T P_1}{\delta x_1}$﻿

If ﻿$y=x^2, \ x_2 \ ^2, \ \bar{x} =2$﻿ so ﻿$TP_1 = 4x_1 \ ^2$﻿

﻿$\mu P_1 = 8x_1$﻿ ﻿$AP_1 = 4x_1$﻿

ISO Profit Analysis

Short run theory of ﻿$L$﻿ and ﻿$q/ \bar{K}$﻿

﻿$q = k^{1/2} L^{1/2}$﻿﻿$,$﻿ ﻿$\bar{K} = 4$﻿ and ﻿$TP_L = 2L ^{1/2}$﻿

﻿$\mu P_L = \frac{\delta \ T P_2}{\delta L}$﻿ and ﻿$TP_L = 2L ^{1/2}$﻿ and ﻿$\mu P_L = L ^{-1/2}$﻿

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

﻿$g_1 = pq - wL -rK$﻿

﻿$pq = g_1 -rK -wL$﻿

﻿$rK=16$﻿ ﻿$g_1 = 8 \times 16 - 1 \times 64 - \gamma \times \gamma = \gamma 8$﻿

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

What if ﻿$w \uparrow$﻿? ﻿$L \downarrow$﻿ ﻿$q \downarrow$﻿ ﻿$g_1 \downarrow$﻿ 3 Predictions

What is ﻿$P \downarrow$﻿? ﻿$L \downarrow q \downarrow G_1 \downarrow$﻿ 3 Predictions

Cubic Example from Worksheet

How much output/Labour/Profit?

Cost Curve Analysis

To derive cost curve:

1) Get ﻿$L_{SR}$﻿ ﻿$L_SR$﻿ from ﻿$T_P$﻿ curve

﻿$q=K^{1/2}L^{1/2}$﻿ ﻿$K=4$﻿

﻿$q=2L^{1/2}$﻿ ﻿$L_{SR} = \frac{1}{2} q^2$﻿

2) ﻿$SVC = wL_{SR}$﻿ ﻿$SA﻿

﻿$SFC = r \bar{R}$﻿

﻿$SC = w_L{SR} + r \bar{K}$﻿

﻿$S \mu C = \frac{\delta SC}{\delta q}$﻿ ﻿$SAC = \frac{SC}{q}$﻿

3) ﻿$q^*$﻿ from ﻿$P = \mu c$﻿

﻿$G^* = (P-SAC)q^*$﻿

﻿$L^* = L_{SR}$﻿

Shutdown if ﻿$P﻿

Because if ﻿$q=0$﻿