A closed community with 15 houses wants to hire a security guard to take care of the community. Each household has a marginal demand curve for security equal to: p=20-q Where q is the hours devoted to security. Also, the wage of a security guard is 30 dollars per hour. Therefore, the marginal cost of supplying security is: p=30 or MC=30 What is the socially optimal quantity of security? This question is different from question 7 because this time you need to consider that you have 15 houses. Therefore, the demand curve needs to be multiplied by 15 to obtain the Marginal Benefit. As usual, the optimum result is when Marginal Benefit = Marginal Cost.

Question

Social Studies

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24 November, 21:30

A closed community with 15 houses wants to hire a security guard to take care of the community. Each household has a marginal demand curve for security equal to: p=20-q Where q is the hours devoted to security. Also, the wage of a security guard is 30 dollars per hour. Therefore, the marginal cost of supplying security is: p=30 or MC=30 What is the socially optimal quantity of security? This question is different from question 7 because this time you need to consider that you have 15 houses. Therefore, the demand curve needs to be multiplied by 15 to obtain the Marginal Benefit. As usual, the optimum result is when Marginal Benefit = Marginal Cost.

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Answers (1)

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Elliot Murillo · Answer 1

Socially optimal quantity of security is 18 hours.

Explanation:

Marginal Benefit & Marginal Cost are additional benefit, cost while producing / buying an additional unit of a commodity.

Social optimality is where Marginal Benefit = Marginal Cost

Marginal Demand/Benefit Curve (for 1 house) : p = 20 - q

Marginal Demand/Benefit Curve (15 houses) : 15 x Individual MR 15 [p = 20-q]. So, 15p = 300 - 15q

As Social optimality is at Marginal Benefit, Marginal Cost Equality.

MC = P = 30 {Given}

300 - 15q = 30

300 - 30 = 15q

270 = 15q

q = 270/15 = 18