Question

1. Say you have an “upstream” agent (the producer) who is producing charcoal.

(a). The firm-specific demand for grills in a week is given by the equation Q=200-2P. The firm’s marginal cost curve is Q= P - 40. Graph this market, labeling everything relevant. What are the equilibrium price and quantity? Show how to solve this algebraically. Assuming we have full cost pricing, how do you calculate CS, PS, and TS here? What are they in dollars?

(b). With production comes polluting. In this case chrome sludge is dumped in the river, and that pollution is damaging a downstream agent (the by-stander) who runs a lemonade stand using “spring-fed water” from the river. In particular, each grill has been estimated to cause a loss of $6 in revenue for Tricia, who runs the lemonade stand. In a new graph, add a social cost curve to the private market. Assuming the social cost is fully captured in the lost revenue to the resort (a heroic assumption, to be sure), how large is the social loss associated with weekly production? If that loss is added to CS and PS when calculating TS, what is the new TS?

(c). What are the social price and quantity? (Hint: Use algebra). What would CS, PS, the social loss (if any), and TS be at the social equilibrium? (Assume that the producer will pay Tricia $6 for each unit produced). Would society be better off if the social price replaced the private price in this market? Why or why not? (Hint: What has happened to Total Surplus)? Compared to the social equilibrium, is there too much or too little produced at the private equilibrium? Compared to the social equilibrium, is the private price too high or too low?    

Answer 1

The demand curve of the market is given by

Q= 200- 2P

2P= 200- Q

P= 100- Q/2

Thus the vertical intercept is 100

The marginal cost curve represents the supply curve of the market.

Thus, the supply equation is

Q= P- 40

P= Q +40

The vertical intercept is 40

The equilibrium quantity and price is determined by the equality of demand and supply equations

100- Q/2= Q+40

60= 3Q/2

3Q= 120

Q= 40

The corresponding price= Q+40= 40+40= 80

Thus the equilibrium price and quantity is 80 and 40 respectively. Diagramatically it can be shown as:

The consumer surplus is give by the are below the demand curve and above the pric line.

The triangular area is given by= 1/2*base*height

Base= 40, Height = (100-80)= 20

Thus the area= 1/2*40*20= 400

The consumer surplus is 400

The producer surplus s given by the are abpve the supply curve and beow the price line.

The triangular area is given by: 1/2* 40* (80-40) = 800

The producer surplus is 800

The total surplus= consumer surplus +producer surplus= 800+400= 1200.