Question

Consider the perfectly competitive market for strawberries at the Davis farmers market.The market’s inverse demand curve isp= 600−20Q. Firms selling strawberries at thefarmers market have marginal cost curveM CP= 20Q. Also assume that, because there isa fixed amount of space at the farmers market, each strawberry sold at the farmers markethas negative social cost (less bread stands!), with a cost of space-taking ofM Cst= 12Q.However, because having stawberries around the farmers market puts buyers in a good mood,there is also a positive externality that strawberry firms receive equal toM Bgm= 2Q(MBis marginal benefit).

A. What are the perfectly competitive equilibrium price and quantity in thismarket?

B. What is the socially optimal equilibrium price and quantity in this market?8

C. Please draw this market, including the following curves—demand, privatemarginal cost, and social marginal cost. Also label the following points—theperfectly competitive equilibrium and the socially optimal equilibrium. Alsoplease label axes and where curves cross axes.

D. What is deadweight loss in this market?

Answer 1

a).

Consider the given problem here the market demand schedule is “P = 600 – 20*Q” and the marginal private cost of production is “PMC = 20*Q”, => at the equilibrium the “P” must be equal to PMC.

=> P = PMC, => 600 – 20*Q = 20*Q, => 40*Q = 600, => Q = 600/40 = 15, => Qp = 15.

The equilibrium market price is given by, => P = 600 – 20*Q = 600 – 20*15 = $300”. So, here the equilibrium market price and quantity are “P=$300” and “Qp=15”.

b).

Here the social marginal cost is the sum of PMC, MCst minus MBgm.

=> SMC = PMC + MCst - MBgm = 20*Q + 12*Q - 2*Q = 30*Q, => SMC = 30*Q. So, at the socially optimum equilibrium SMC must be equal to Price.

=> P = SMC, => 600 – 20*Q = 30*Q, => Q = 600/50 = 12, => Qs = 12. The corresponding market price is “P=600 – 20*Q = 600 – 20*12 = $360”, => P = $360.

c).

Consider the following fig.

Here “D” be the market demand schedule and PMC be the market supply, => the equilibrium under the perfectly competitive market is Ep, => the equilibrium price and quantity are “P1=300” and “Q=15”. Now, the social marginal cost is given by the curve SMC, => the socially optimum equilibrium is Es, => the socially optimum production is Qs=12.

d).

Here the producer are producing Qp=15 but the socially optimum level of production is Qs=12, => the producer is producing more than the socially optimum level, => associated dead weight loss is given by the area EsEpE3.

=> EsEpE3 = 0.5*(P3-P1)*(Qp-Qs) = 0.5*(450-300)*(15-12) = $225.