Question

Problem Setup

Analyze each of 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 = 50 – 3Q. The supplier(s) in that market have a market (aggregate) marginal cost curve of MC = 10 + 2Q.

Efficient Outcome

● Use the marginal benefit and marginal cost equations given above to determine the efficient quantity

Equilibrium with Marginal Cost Pricing (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.

Equilibrium with Nonmarginal Pricing (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 choose to set the price at P = 14. Thus, their supply curve is a horizontal line at that value.

● Find the market 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.

For each of the two pricing scenarios (A and B), find the equilibrium outcome predicted by the model, and answer the following questions about that outcome.

Find the equilibrium (both scenarios):

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

● What will be the market price in equilibrium (P)?

Only for the nonmarginal pricing scenario (B), answer these questions:

● What is the marginal cost of the equilibrium quantity [MC(Q)]?

● What is the quantity at which marginal cost equals price (MC = P)?

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

● What is the consumer surplus (CS) in equilibrium?

● What is the producer surplus (PS) in equilibrium?

● What is the joint surplus (JS) in equilibrium?

● What is the deadweight loss (DWL)?

Answers You can write your answers in the following table. You should keep this table (and your notes and calculations) for discussing the problem in class. Efficient Outcome Marginal Cost Pricing Scenario A Nonmarginal Pricing Scenario B Efficient quantity (Q*) NIA NIA Equilibrium quantity (Q) NIA Equilibrium price (P) NIA Marginal cost [MC(Q)] Quantity where MC- P Consumer surplus (CS) Producer surplus (PS) Joint surplus (JS* or JS) NIA NIA NIA N/A NIA N/A Deadweight loss (DWL) NIA

Answer 1

1) EFFICIENT QUANTITIY : This is at the point where MB curve and MC curve intersect

So, 50 - 3Q = 10 +2 Q

or, 50-10 = 2Q +3Q

or, 5Q = 40

or, Q* = 8 Efficient quantity is 8

2) SCENARIO A

This scenario is exactly the same as above. So, Q*=8. Thus P = 50 - 3(Q) = 50 - 3(8) = 26 or, P* =26

MARKET EQM SCENARIOS ARE THEREFORE : P*=26 , Q*=8

Consumer surplus/welfare is defined as the difference between the amount that a consumer is willing to pay and the amount he is actually pays. Geometrically, it is the area under the MB curve and above the price line.

Producer surplus/welfare is defined as the difference between the amount that a producer is willing to accept and the amount he is actually receives. Geometrically, it is the area above the MC curve and below the price line.

3) SCENARIO B

DD curve (same) : 50 - 3Q , P = 14 (set by producers)

So, Q* = (50-14)/3 = 12 or, Q*=12

MARKET EQM SCENARIOS ARE THEREFORE : P*=14 , Q*=12

DWL IN THE ABOVE FIGURE (SCENARIO B) IS THE SMALL TRIANGLE BESIDE AREA D :

(1/2) * (50/3) * 14 = 350/3 = 116.67

4) BOTH SCENARIO

	EFFICIENT OUTCOME	SCENARIO A	SCENARIO B
Q*	8	N/A	N/A
Q	N/A	8	12
P	N/A	26	14
MC	N/A	N/A	14
Q WHERE P=MC	N/A	N/A	12
CS	N/A	96	216
PS	N/A	64	168
JS	(64+96)=160	(64+96)=160	216+168=384
DWL	N/A	0	116.67