Consider a competitive market for some commodity x in which some firms are polluters. Firm A: C(xA ) = 25xA and the environmental cost to society is E(xA ) = 15xA. Firm B: C(xB) = (1/10)x (xB x xB ) and the environmental cost to society is E(xB ) = 0. Assume initially that the market operates without any recognition of environmental costs. Both firms are price-takers. Determine for what prices Firm A will provide the good? Does it matter to firm A what quantity is supplied? Find the supply function for Firm B. Assume the market demand for the commodity is given by x(p)=40000/p 3. Find the competitive market equilibrium price and quantity using your answers in 1) and 2) when the firm supplies reflect their ability to compete at a given price. 4. Suppose a planner uses the representative consumer’s utility function, to find the socially optimal allocation of resources to the two firms. Choose (xA, xB, Y) to solve max U(x, y) = (40000)ln(X) + Y Subject to x= xA + xB, xA ≥ 0 xB ≥ 0 and C(xA) + C(xB) + E(xA) + Y= 100,000 5. What will be the aggregate production level, and how much will each firm supply? 6. Use a pair of sketches of the market and planner allocations (using the market demand/marginal benefit curve and cost curves of the firms) to compare the net benefit to society from the outcomes in 3) and 4)
Consider a competitive market for some commodity x in which some firms are polluters.
Firm A: C(xA ) = 25xA and the environmental cost to society is E(xA ) = 15xA.
Firm B: C(xB) = (1/10)x (xB x xB ) and the environmental cost to society is E(xB ) = 0.
Assume initially that the market operates without any recognition of environmental costs. Both firms are price-takers.
- Determine for what prices Firm A will provide the good? Does it matter to firm A what quantity is supplied?
- Find the supply function for Firm B.
Assume the market demand for the commodity is given by x(p)=40000/p
3. Find the competitive
4. Suppose a planner uses the representative consumer’s utility function, to find the socially optimal allocation of resources to the two firms. Choose (xA, xB, Y) to solve
max U(x, y) = (40000)ln(X) + Y
Subject to x= xA + xB, xA ≥ 0 xB ≥ 0 and C(xA) + C(xB) + E(xA) + Y= 100,000
5. What will be the aggregate production level, and how much will each firm supply?
6. Use a pair of sketches of the market and planner allocations (using the market demand/marginal benefit curve and cost curves of the firms) to compare the net benefit to society from the outcomes in 3) and 4).
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