Question

 Problem 18-5

 The figure below shows supply and demand for first-aid training, based on private costs and benefits.

 a. Suppose that the external benefit from first-aid training is worth $6. Graph the social benefit curve for first-aid training that accounts for the external benefit.

 Instructions: Use the tool provided (MBsociall and plot only the two endpoints across the entire range of output (0 - 30).

 b. Ignoring the social benefits of training, _______  hours of first-aid training will occur.

 c. The socially optimal quantity of first-aid training is _______ 

 d. Graph the deadweight loss that occurs when consumers are unable to capture the $6 external benefit they provide from first-aid training.

 Instructions: Use the tool provided (DWL) to draw the deadweight loss.

 The deadweight loss to society when consumers are unable to capture the $6 external benefit they provide from first-aid training is _______ 

Answer 1

Solution:

An external benefit of first-aid training is like a positive externality. With an external benefit of $6, the private marginal benefit curve will make an upward parallel shift of equal amount. This is like with training, price incurred is worth $6 less than that under no external benefit. Or, for same number of training hours, price paid is $6 less than that under private.

So, if denoting hours of training by H and price/costs by P, using the equation of line form:

It is like P(social) = P(private) - 6, along the marginal benefit curve

Marginal private benefit curve has slope = -1, and vertical intercept 24, so MB private: P = 24 - H

That is, H = 24 - P ... (1)

For marginal benefit social, this equation becomes: H = 24 - (P - 6), indicating that now for same number of hours of training, now price/cost incurred will be $6 less than that incurred under private. So such external benefit will give reduced private costs, as part of them are covered socially. So, equation: H = (24+6) - P

H = 30 - P ... (2)

or P = 30 - H (so, new intercept is now 30)

Private/Social cost curve (with same equation of straight line analysis) is: Vertical intercept = 9, slope = +(1/2)

P = 9 + (1/2)*H

2P = 18 + H

H = 2P - 18 ... (3)

So, solving (1) and (3) gives optimum number of hours, ignoring benefits of training: 10 hours (as you've answered)

And solving (2) and (3) gives optimum number of hours, with benefits of training: 14 hours (as you've answered)

So, marginal social benefit curve can be shown as such shift in the graph:

Dead weight loss is shown as the central grey triangle. When such benefit isn't captured, there is under supply of first-aid training. That is, only 10 hours of training is provided, when still an additional surplus can be generated by increasing the number of hours to social optimum.