1. Suppose your firm is told that the demand curve it faces from its market is given by
Q = 8 − 0.5p
Its cost per unit is constant and equal to $1.5. Assume that it produces integer number of units (i.e. Q = 0,1,2, 3…and so on).
(a) Construct a table showing the Price, Demand, Marginal Revenue and Marginal Cost schedule for the firm.
(b) Using Marginal Analysis, obtain the profit-maximizing linear price for the firm and calculate its profit level.
(c) Calculate the level of consumer surplus retained by consumers at this price.
(d) Now, imagine you are planning on introducing a two-part tariff that includes an upfront fixed payment F and a per-unit price p. Suppose you choose p to be equal to the price you obtained in (b) above. How would you describe the consumer surplus retained by consumers from purchasing under this two-part tariff?
(e) Suppose you know that consumers would buy the product so long as their consumer surplus after purchasing the product and paying the two-part tariff is at least zero. What should be the optimal value of the fixed payment F in the two-part tariff?
(f) Calculate the profit level from this two-part tariff. Explain the difference in profit level earned from the two-part tariff compared to that earned from the linear price in (b).
(g) Show that the firm’s profit can be even higher if the per-unit price is chosen to be lower, say $2.