Asked by Simon Kozloff on May 06, 2024
Verified
When peach canners process fresh peaches, they produce three products. The first, canned peaches, is sold in the marketplace. The others, liquid and solid wastes, are by-products that must be removed. The liquid is sometimes temporarily kept in holding ponds and later released into a nearby stream or sewer. Liquid dumped in the stream represents a negative externality to downstream users. In the peach growing region, the marginal external costs of the canning process have been estimated as:
MEC = 0.000043Q,
where Q represents output of canned peaches in cases per week. The marginal cost of canning peaches (ignoring MEC) is:
MC = 2.00 + 0.000157Q,
and the demand for canned peaches is:
P = 9.00 - 0.000243Q.
a. How many cases of peaches will be produced per week during the growing season, and what will the selling price per case be if producers ignore the costs imposed on others?
b. If producers are forced to incorporate the marginal external costs into their production decisions, what will the new production rate and selling price be?
c. In taking account of the external costs imposed on others (part b), what was the impact on the selling price and production rate of canned peaches? Explain the impact on market efficiency.
Marginal External Costs
The additional cost imposed on third parties not involved in a transaction or decision, for each additional unit produced or consumed.
Peach Canners
Peach canners are production facilities or workers involved in preserving peaches by canning them, which involves processing, sealing in an airtight container, and sterilizing to extend shelf life.
Market Efficiency
The extent to which market prices fully reflect all available information, making it impossible to consistently achieve higher returns.
- Investigate the impact of competitive markets on product pricing and availability, while considering external costs and benefits.
- Gain insight into how government policies contribute to achieving socially preferable results amidst external influences.
- Compute the optimal societal quantity and pricing for products in markets influenced by external costs.
Verified Answer
MC = demand
2.00 + 0.000157Q = 9.00 - 0.000243Q
Q = (9 - 2)/0.00040 = 17,500 case/week
The selling price is determined by demand.P = 9 - 0.000243(17,500) = 4.7475 = $4.75/case
b.The MPC and MEC must be added (vertically) to determine the marginal social cost of production (MSC). This expression is equated to demand to determine the production rate.MSC = MC + MEC
= 2 + 0.000157Q + 0.000043Q
= 2 + 0.0002Q
MSC = 2 + 0.0002Q = 9 - 0.000243Q = demand
Q = (9 - 2)/0.000443 = 15,801 case/week
The new selling price is:
P = 9 - 0.000243(15,801) = $5.16/case
c.As a result of internalizing the MEC, the canning industry produced fewer cases per week
(17,500 - 15,801 = 1,699)
Also, the selling price increased from $4.75/case to $5.16/case. Market efficiency was increased when the price increased by increasing price and reducing output. The market is efficient because MSC equals selling price.
Learning Objectives
- Investigate the impact of competitive markets on product pricing and availability, while considering external costs and benefits.
- Gain insight into how government policies contribute to achieving socially preferable results amidst external influences.
- Compute the optimal societal quantity and pricing for products in markets influenced by external costs.
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