Knowee
Questions
Features
Study Tools

Consider a competitive market in which the MPB = 138–4q and the MSC= 3q. In this market, however, there is a positive consumption externality of $74 per unit consumed. What is the DWL that results in the market equilibrium?[Round your answer to two decimal places when needed]

Question

Consider a competitive market in which the MPB = 138–4q and the MSC= 3q. In this market, however, there is a positive consumption externality of $74 per unit consumed. What is the DWL that results in the market equilibrium?[Round your answer to two decimal places when needed]

🧐 Not the exact question you are looking for?Go ask a question

Solution

To find the deadweight loss (DWL) in this market, we first need to find the market equilibrium, where the marginal private benefit (MPB) equals the marginal social cost (MSC).

  1. Set MPB = MSC to find the equilibrium quantity (q):

    138 - 4q = 3q

    Solving for q gives us q = 23.

  2. Substitute q = 23 into either the MPB or MSC equation to find the equilibrium price (p):

    p = 138 - 4*23 = 138 - 92 = 46

Now, we need to find the socially optimal quantity, where the marginal social benefit (MSB) equals the MSC. The MSB is the MPB plus the external benefit.

  1. Calculate MSB:

    MSB = MPB + external benefit = (138 - 4q) + 74

    Simplifying gives us MSB = 212 - 4q

  2. Set MSB = MSC to find the socially optimal quantity (q*):

    212 - 4q = 3q

    Solving for q gives us q* = 28.27 (rounded to two decimal places)

  3. Substitute q* = 28.27 into either the MSB or MSC equation to find the socially optimal price (p*):

    p* = 212 - 4*28.27 = 212 - 113.08 = 98.92 (rounded to two decimal places)

The DWL is the area of the triangle formed by the vertical distance between the MPB and MSC curves (which is the per unit external cost) and the horizontal distance between the market quantity and the socially optimal quantity.

  1. Calculate DWL:

    DWL = 0.5 * (p* - p) * (q* - q)

    DWL = 0.5 * (98.92 - 46) * (28.27 - 23)

    DWL = 0.5 * 52.92 * 5.27 = 139.32 (rounded to two decimal places)

So, the deadweight loss in this market is $139.32.

This problem has been solved

Similar Questions

Consider a competitive market in which the MPB = 129–3q and the MSC =3q. In this market, however, there is a positive consumption externality of $50 per unit consumed. What is the efficient level of output in this market?

Laura runs a nightclub, ‘Two Standard Drinks’. Given the popularity and cache of the club, she has a monopoly position in the market. The market demand curve is given by P = 176–q. Laura has a marginal cost per drink of MC = 4q and a fixed cost FC = $144. If Laura charges the same price to all customers, what is the resulting DWL? [Round your final answer to 2 decimal points when necessary]

Consider a market with a demand curve of P = 16–2q and a supply curve of P = 2q. If the government levies a tax on consumers of $4 per unit, what is the resulting DWL? [Round your answer to two decimal places when needed]

Consider the market for first-aid training class.Market demand is given by P=600-Q.Market supply is given by P=Q.Individuals who have received first-aid training are very helpful in some urgent situations.More specifically,first-aid training will generate a positive spillover equal to Q/3.What is the deadweight loss if the externality is not dealt with? DWL=3000 DML:6000 DWL:4500 DWL=1500

Consider a market where the demand is pD = 200 – 2Q while the supply is pS = 50 + Q (same as in the previous question). Calculate the deadweight-loss (DWL) if the government introduces a price cap at p = 80.

1/3

Upgrade your grade with Knowee

Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.