Problem 1 Modelling the Market (10 points)

Suppose the estimated market demand and supply (bottles/month) for a new product call hydro water are given by:

Qd = -50P + 1000

Qs = 100P - 500

whereQdis the market demand,Qsis the quantity supplied andPis price of a 1 liter of bottled hydro water. The market is assumed to be competitive.

1. Write the inverse demand function and supply function (2 points)
2. Calculate the equilibrium price and quantity (1 points)
3. Sketch the demand and supply curves (2 points)
4. Is this equilibrium level of output efficient? Explain using the concepts of marginal benefit and marginal cost. (2 points)
5. Illustrate the Consumer Surplus (CS) and Producer Surplus (PS) on the diagram from part (c) and calculate the value of these at the market equilibrium. What is the total value of social welfare? (3 points)

Problem 2 Modelling Externalities and the Coase Theorem (10 points)

A chemical pesticide producer releases wastes into a nearby river. The negative effects of this waste are not captured by the private market. As a result, there is a market failure, illustrated by the following functions for the inverse demand curve (or Marginal Social Benefit MSB) and inverse supply curve (or Marginal Private Cost MPC) and the marginal external cost (MEC):

P(Qd) (or MSB) = 60 - 0.3Q

P(Qs) (MPC) = 30 + 0.2Q

MEC = 0.1Q

1. Find the competitive market equilibrium assuming the market supply is described by theP(Qs). (2 point)
2. Find the efficient equilibrium. (2 points)
3. Sketch the curves for these functions and illustrate the competitive equilibrium and labelPCandQCand efficient equilibrium (labelingPEandQE). (2points)
4. On the diagram from part c, illustrate the areas corresponding to the loss in profit for the firm, the total gain to society and the net gain to society when comparing the competitive equilibrium to the efficient equilibrium. (2 points)
5. In one sentence, state the Coase Theorem. Based on this theorem, in the example above, who should be given the property rights over river pollution (or no pollution). (2 points)