given the following solution (see attached), how would you calculate the average price paid by demander B? Inverse demand functions are $ PA = 10 - QA $ and $ PB = 5 - 0.5QB $. Under a two-part tariff, the fixed fee is the consumer surplus of smaller demand, which is $ PB $. Hence the profit is given by\[\text{Profit function} = 2 \times F + (P - MC) \times (QA + QB)\]\[= 2 \times 0.5 \times (5 - P) \times (10 - 2P) + (P - 2) \times (20 - 3P)\]\[= 50 + 2P^2 - 20P + 20P - 40 - 3P^2 + 6P \]\[= 10 - P^2 + 6P\]Profit is maximum when\[2P = 6\]\[P^* = 3\]Hence the price per unit is 3 and is the same for A and B. The fees amount is \[F = 0.5 \times (5 - 3) \times (10 - 2 \times 3) = \$4\]Profit:\[= 4 \times 2 + (3 - 2) \times (20 - 3 \times 3) = \$19\]

Given information Pa=10-Qa Pb=5-0.5Qb

Inverse demand functions are PA = 10 - QA and PB = 5 - 0.5QB. Under a two part tariff, fixed fee consumer surplus of smaller demand which is PB. Hence the profit is given by Profit function = 2 x F + (P-MC)*(QA + QB) = 2 x 0.5*(5 - P)*(10 - 2P) + (P - 2)*(20 - 3P) = 50 + 2P^2 - 20P + 20P - 40 - 3P^2 + 6P

Inverse demand functions are PA = 10 - QA and PB = 5 - 0.5QB. Under a two part tariff, fixed fee consumer surplus of smaller demand which is PB. Hence the profit is given by Profit function = 2 x F + (P-MC)(QA + QB) = 2 x 0.5(5 - P)(10 - 2P) + (P - 2)(20 - 3P) = 50 + 2P^2 - 20P + 20P - 40 - 3P^2 + 6P

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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