Question

1. Consider the perfectly competitive market for dogs. Suppose that the demand curve for dogs is given by MB_P = P = 200 - Q, and the supply curve for dogs is given by MC_P = P = 40 + Q.
   1. (6 points) How many dogs are bought and sold at equilibrium?
   2. (6 points) Suppose, to begin with, that dog buying and selling only affects parties that engage in it (i.e., buyers and sellers of dogs). How does the social marginal benefit MB_s compare with the private marginal benefit MB_P? And how does the social marginal cost MC_s compare with the private marginal cost MC_P?
   3. (6 points) Given the facts in (b), how does the equilibrium found in (a) compare with the socially optimal number of dogs?
   4. (6 points) Suppose now that dog buying and selling not only affects parties that engage in it (i.e., buyers and sellers of dogs), but also affects 3rd parties. Specifically, some people who don't own dogs are irritated by their yapping and defecating, and the cost to this irritated group is MC_E. Write down a general equation for social marginal cost (MC_S).
   5. (8 points) Suppose that we know that MC_E = 10 + Q. Finding a specific number, what is the socially optimal number of dogs?
   6. (8 points) If dog owners are granted a property right to let their dogs yap and defecate, how much do they gain (measured precisely, in dollars) by choosing the private optimum (compared to the social optimum) if they ignore the external cost to other citizens who object to yapping and defecating?
   7. (8 points) If dog owners are granted a property right to let their dogs yap and defecate and they ignore the external cost they impose (and choose the private optimum instead of the social optimum), how much additional external cost (measured precisely, in dollars) do they impose on other citizens who object to yapping and defecating?
   8. (8 points) Is it possible that a government policy that assigns the right to dog owners as described in parts (f) and (g) could result in society ending up at the social optimum?
   9. (4 points) Are there any practical issues that might make it difficult for this society to reach the social optimum after rights are assigned to dog owners as in part (f)?

Answer 1

A] Markets are at Equilibrium where,  Market demand = Market Supply. Analogously, where Marginal Private Benefit = Marginal Private Cost.

Given :- MBP (demand) : P = 200 - Q ; MCP (supply) : P = 40 + Q

Equilibrium : 200 - Q = 40 + Q

200 - 40 = Q + Q

160 = 2Q

Q = 160 / 2

Market Equilibrium Quantity [Q] = 80

Putting value of Q in demand, P = 200 - 80 = 120 [Market Equilibrium Price]

Putting value of Q in supply, P = 40 + 80 = 120  [Market Equilibrium Price]

B] If dogs sale & purchase effect only parties in transactions, no other third party. Then, social marginal benefit = private marginal benefit & social marginal cost = private marginal cost.

C] If there are no external (extra) social benefit or harm to third parties, social benefits & costs are same as private benefits & costs. So, socially optimal equilibrium is same as market equilibrium.

D] If dogs transactions effect the third un-involved parties in a negative way, they are like a negative externality & incur external (extra) marginal cost [MCE] to the ambient people. In such a case, marginal cost to society [MCS] includes both private marginal cost [MCP] & external marginal cost [MCE].

• Social Marginal Cost [MCS] = Private Marginal Cost [MCP] + External Marginal Cost [MCE]

E] If external marginal cost [MCE] is incurred ; Socially optimal dogs are where

Social Marginal Benefit [MBP] = Social Marginal Cost [MCS] = Private Marginal Cost [MCP] + External Marginal Cost [MCE]

200 - Q = (40 + Q) + (10 + Q)

200 - Q = 50 + 2Q

200 - 50 = 2Q + Q

150 = 3Q

Q = 150 / 3

Socially Optimal Quantity = 50