Assignment
Answer all the questions below. You may work in groups of up to six students; please ensure that everyone in the group is credited. .
Please hand in one assignment per group. Please show all work for full credit.
1. A single firm produces widgets, with a cost function and inverse demand function as follows,
C(q) = 150 + 2q P (Qd) = 10 - 0.08Qd
(a) Calculate the monopolist's profit-maximizing price, quantity, and profit if he can charge a single price in the market (single price monopolist).
(b) Suppose the firm can sell units after your answer to (a) at a lower price (2nd-degree price dis- crimination). What quantity will be sold for what price in this second-tier market? Calculate the monopolist's profit.
(c) Suppose each new tier of pricing the monopolist introduces increases fixed costs by $2 (quantities can be irrational). What is the profit-maximizing quantity, number of prices, monopolist's profit, and deadweight loss?
(d) Suppose the firm can perfectly price discriminate with a 40% increase in marginal cost; calculate the profit-maximizing quantity, monopolist's profit, and deadweight loss?
(e) Between (c) and (d), which is socially preferred? Which would the monopolist choose to do?
2. The car manufacturer Edison is the sole producer of electric cars in the market, selling to two different types of customers. All else equal, travelers (type t) prefer batteries that go longer distances between charges and are willing to pay for this luxury. Urban drivers (type u) do not require as great a battery. Edison knows the willingness-to-pay of each type, and that there are q percent of type ts in the market. The willingness-to-pay for each type for different battery sizes are,
Vt(k = 100) = $160, 000, Vt(k = 60) = $80, 000,
Vu(k = 100) = $100, 000, Vu(k = 60) = $60, 000,
where k is the battery life in kilowatt hours (kWh). Producing 60 kWh battery costs $30,000, which is half the cost of a 100 kWh battery.
(a) Edison showroom salesmen believe they can perfectly identify which type of buyer walks through the door. Find the profit-maximizing prices (pi) and battery sizes (ki). What is the Edison's average profit per customer?
(b) It turns out Edison salesmen are not as smart as they think, and cannot identify any type of customer. If Edison offered the packages in (a), demonstrate who would buy which type?
(c) If Edison has no way of price discriminating, what should they do? Consider all possible options for different values of q.
(d) Sensing a better option, Edison hires some economists to help. Write out the participation/rationality constraints and the self-selection/incentive compatibility constraints. Which ones hold with equality?
(e) Determine the profit-maximizing pricing strategy for Edison for any distribution of buyers.
3. In a market with asymmetric information, a hiring manager is trying to hire high quality employees. The manager will pay hourly wages equal to the value of the marginal product of labor (VMPLi) for each type i. The manager will screen prospective employees based on the number of Linked-In connections they have, x, knowing that high type workers will have more connections. High types have a utility function, UH (w, x) = w - ½ x, with VMPLH = 10. Low types' utility function is, UL(w, x) = w - x, with V MPLL = 4. There are 50% of each type in the market, and if one doesn't work they receive a utility of zero.
(a) Find the wages and number of Linked-In connections if there is perfect information.
(b) Find the wages if the hiring manager can't observe types and cannot Linked-In information such that he breaks even on average.
(c) Design a pair of contracts, {wH , xH } and {wL, xL} where each type will reveal their type (select the contract designed for them).