Three residents of a community are deciding the size of their police force. Each policeman costs $24,000. The marginal benefit of an additional policeman for each individual at a given number of existing policemen is as follows. The socially optimal number of policemen (policeman's salary = $24,000). Number of policemen (z) 1 2 3 4 5 6 7 Marginal benefit for consumer A $19,000 $17,000 $15,000 $13,000 $11,000 $9,000 $7,000 Marginal benefit for consumer B $16,000 $14,000 $12,000 $10,000 $8,000 $6,000 $4,000 Marginal benefit for consumer C $13,000 $11,000 $9,000 $7,000 $5,000 $3,000 $1,000 Marginal social benefit $48,000 $42,000 $36,000 $30,000 $24,000 $18,000 $12,000 (a) Draw the invidual marginal benefit curves separately for A, B, and C. Draw the social marginal benefit curve. (b) What is the socially optimal number of policemen? (c) If the number of policemen is decided by majority voting, who is the medium voter? (d) If each consumer is subject to a head tax, how many policemen will be hired?