Question

Create an example of positive externality for a single producer whose production benefits a neighbor. In your example, make sure you do the following: • The MC function must be a linear function of Q (MC increasing as Q increases) • The total revenues are a linear function • Assume the externality to be a fixed amount per unit produced • Compare outcomes without internalization of the externality and with the internalization • Graph MC, MR, and MSB with the internalization of the externality (Marginal Social Benefit, MSB), as well as the area of profit pre- and post-internalization • Discuss how internalization of the externality could be achieved • The numbers are simple enough and the answer should not unnecessarily complicated. Make sure you address the following in Parts 1 and 2: o Linear MC function o Correctly identify the MR function o In your graph, correct labeling of MC, MR, MSB with internalization (Marginal Social Benefit, MSB) and outcomes Part 3

Answer 1

A producer's honey production increases the local bee population, creating a positive externality for neighboring farms through improved pollination. Initially producing 5 units with no internalization, internalization leads to an increase in production to 6.5 units. A subsidy of $3 per unit can internalize the externality, increasing profit and the social benefit.

Step-by-step explanation:

Consider a scenario where a producer makes honey and the production process increases the population of bees in the area. These bees pollinate the flowers in the neighboring farms, which is a positive externality for the neighboring farmers. Let's assume the marginal cost (MC) for producing honey is a linear function of quantity (Q), where MC = 2Q. Total revenues (TR) are also linear, and can be defined by the price per unit times quantity, TR = P*Q. Let's assume the price remains constant at $10 per unit, making the marginal revenue (MR) constant at $10 as well. The positive externality is worth $3 for every unit produced.

Without internalization, the producer will produce where MR = MC; thus, 10 = 2Q, Q = 5 units. With internalization, the marginal social benefit (MSB) is MR plus the externality: MSB = MR + 3 = 13. The producer would produce where MSB = MC; thus, 13 = 2Q, Q = 6.5 units.

Profit maximization pre-internalization occurs at Q = 5 with an area under the MR up to 5 units subtracted by the area under the MC up to 5 units. Post-internalization, this area increases because MR is effectively higher when considering the MSB. Internalization of the externality could be achieved by offering the producer a subsidy of $3 per unit.

On a graph, the MC function has a positive slope, MR is a horizontal line at $10, and MSB with internalization is a horizontal line at $13. Q = 5 and Q = 6.5 are marked on the quantity axis to show the quantity produced pre- and post-internalization. The areas of profit are shown between MR and MC, illustrating an increase in profit post-internalization.