This question asks you to find the socially optimal outcome. Suppose a social planner takes the demand function and cost functions as given, and can choose (i) the market price, (ii) the number of firms, and (iii) the quantity produced by each firm [the planner is free to choose any quantity, even if the firms would lose money]. The social planner’sgoal is to maximize the sum of consumer surplus and firms’ profits. To do this, the planner will take into account the two economic principles of efficiency we discussed in class, (i) Allocative efficiency which implies price=mc. (2) Efficiency in production, which means that the cost of production of the total market quantity should be minimized. Suppose the demand function is Q(p) = 40 – 5p. For each of the followingcost functions, what market price, number of firms and quantity for each firm will the social planner choose?a)C(q) = 20 + 4qb) C(q) = 3 + q^2/3 + 3q.

Microeconomic Theory
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ISBN:9781337517942
Author:NICHOLSON
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Chapter19: Externalities And Public Goods
Section: Chapter Questions
Problem 19.7P
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This question asks you to find the socially optimal outcome. Suppose a social planner takes the demand function and cost functions as given, and can choose (i) the market price, (ii) the number of firms, and (iii) the quantity produced by each firm [the planner is free to choose any quantity, even if the firms would lose money]. The social planner’s
goal is to maximize the sum of consumer surplus and firms’ profits. To do this, the planner will take into account the two economic principles of efficiency we discussed in class, (i) Allocative efficiency which implies price=mc. (2) Efficiency in production, which means that the cost of production of the total market quantity should be minimized. Suppose the demand function is Q(p) = 40 – 5p. For each of the following
cost functions, what market price, number of firms and quantity for each firm will the social planner choose?

a)C(q) = 20 + 4q
b) C(q) = 3 + q^2/3 + 3q.

Expert Solution
Step 1

Social planner wants to maximize sum of consumer surplus and firms' profits. Firm's profit is nothing but producer surplus.  The social planner is trying to increase Total surplus which is  Consumer Surplus + Producer surplus.

When this total surplus gets maximized, it fuels economic effieciency. Total surplus is maximized when  a perfectly competitive market produces market equilibrium quantity.

Step 2

Equilibrium price and quantity corresponding to cost functions C1 and C2 have been calculated.

 

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