Question

Analyze the following three scenarios (Efficient, A, and B) describing the market for widgets.

● Consider the market for widgets, consumers have a market (aggregate) marginal benefit curve of MB = 90 – 2Q. The supplier(s) in that market have a market (aggregate) marginal cost curve of MC = 4Q.

Efficient Outcome

● Use the marginal benefit and marginal cost equations given above to determine the efficient quantity (Q*) and the joint surplus (JS*) based on that quantity.

Equilibrium with No Regulation (Scenario A)

● Assume that consumers are rational utility-maximizers and price-takers. Thus, their demand curve is based on (i.e., the same as) the marginal benefit equation above.

● Assume that producers are rational profit-maximizers and price-takers. Thus, their supply curve is based on (i.e., the same as) the marginal cost equation above.

● Find the market equilibrium for this scenario and calculate the associated measures of consumer and producer welfare.

● Note: This scenario is the same as the basic model.

Outcome with Price Ceiling (Scenario B)

● Assume that consumers are rational utility-maximizers and price-takers. Thus, their demand curve is based on (i.e., the same as) the marginal benefit equation above.

● Assume that producers are rational profit-maximizers and price-takers. However, they are constrained by regulation not to sell their products for a price higher than P = 40.

● Find the market outcome (not really an equilibrium) for this scenario and calculate the associated measures of consumer and producer welfare.

Questions

Find the quantity (Q*) that represents the efficient outcome and also the joint surplus (JS*) that results from that quantity.

Only for the price ceiling scenario (B), answer these questions:

● What quantity is demanded (QD) at the ceiling price?

● What quantity is supplied (QS) at the ceiling price?

● What is the consumers’ marginal benefit at the quantity supplied [MC(QS)]? You do not need to record this answer in the table, but it will help you calculate consumer surplus.

For each of the two scenarios (A and B), find the outcome predicted by the model, and answer the following questions about that outcome. Note that the outcome in scenario A is an equilibrium, but not the outcome in scenario B.

Find the market outcome:

● What market quantity (Q) will be produced and consumed?

● What will be the market price (P)?

Find the consumer and producer welfare measures (both scenarios):

● What is the consumer surplus (CS) of the market outcome?

● What is the producer surplus (PS) of the market outcome?

● What is the joint surplus (JS) of the market outcome?

● What is the deadweight loss (DWL)?

Answer 1

1). MB = 90 - 2Q MC = 4Q  

Same as equilibrium output, efficient output is produced by market when MB = MC.

90 - 2Q = 4Q => 4Q + 2Q = 90 => 6Q = 90 => Q* = 90/6 = 15 units   

iJoint surplus is the sum of consumer and producer welfare.

In this question few things students need to keep in mind, so that they doesn't get confused. Efficient output or price is same as equillirbrium output or price in case of rational market behavior and no constraints. Consumer/producer surplus is same as consumer/producer welfare in case of applied welfare economics. Also many questions are repeated as the last few questions in last part where output , price consumer and producer welfare and joint surplus is repeated.

The market equilibrium scenario A, is shown in the image below.

So the joint surplus in part 1 (efficient outcome) is

JS* = Consumer surplus + producer surplus = 225 + 450 = 675

And efficient output Q* = 15

Now scenario B

Consumer surplus = Area of ( a+b+c)= 250 units

Producer Surplus = Area below ceiling price level and above supply curve = area of triangle ( F) = 200 units

Joint surplus in scenario B= CS + PS = 250 + 200 = 450 units

Deadweight loss (DWL) = 150 units.

In scenario B, quantity supplied is 10 units, while quantity demanded is 25 units.

Consumer marginal benefit also called marginal willingness to pay is price for that particular unit. So here the consumer marginal benefit for the quantity supplied under price ceiling is 70 units.