What are the optimal prices that the firm should set

Reference no: EM132239695

Question 1 - Double Marginalization

Your company Must-Stash is the sole producer of the popular "I am awake and this is interesting" expression mask. The mask is a highly useful product for students everywhere.

(a) You are currently selling your product via a distributor. Your cost of production is TC(x) = 20x and the demand for the masks is given by D(P) = 50(30 - P), where P is the price to consumers. Assume the distributor's costs are zero and you are charging your distributor a single price W per mask. What is the price W you charge your distributor? What price P do they charge the consumers and what is the quantity of masks produced and sold? What are your profits? Explain your calculations.

(b) You decide to open an online store to sell your masks in addition to using your distributor. You have reached an arrangement with the distributor that whatever price P they charge consumers for your masks, you will charge the same price P in your online store. From the knowledge of the industry, you and the distributor know that once you open the online store, you will get 40% of the buyers of masks buying from you directly instead of buying from the distributor. Hence for every price P that the distributor selects, your online store will sell 20(30 - P) masks and the distributor will sell 30(30 - P) masks. What is the price W you should charge your distributor? What price P will they choose to charge the consumers (this will also be the price in your online store) and what is the quantity of masks produced and sold? What are your profits? (Notice, the price in your online store is determined by the distributor according to the optimal price they charge when facing the demand D(P) = 30(30 - P).)

Question 2 - Breaking up a monopolist

The firm Software Monopolist sells two software products. The two products are called Editor and Spreadsheet. The software is already written and hence MC is zero, so that profits are just revenue. Customers view those products as complementary: the products are especially valuable when used together with each other, and so when the price of one of them increases, the demand for both decreases.

Specifically, the demand functions for the two products are:

D_E(p_E, p_S) = 300 - 2p_E - p_S

D_S(p_E, p_S) = 300 - 2p_S - p_E

a) What are the optimal prices that the firm should set for the two products?

Hint: write the profit directly as a function of prices (instead of quantities).

b) The antitrust authorities did not like the Software Monopolist's monopoly and decided to split it into two firms, Editor Software and Spreadsheet Software, each independently selling the corresponding product. The demand functions for the products are not affected by this change. Suppose that Editor Software keeps price p_E at the same level as your answer in part (a). What is the best response of Spreadsheet Software? (That is, given the value of pE that you computed in part (a), what price p_S should Spreadsheet Software set to maximize its profit from the sales of Spreadsheet?)

c) Find a Nash equilibrium of this game. That is, find prices p_E and p_S such that each firm plays a best response given the price of the other firm. Are customers better or worse off after the breakup?

Hint: Express p_E as a function of p_S (p_E has to be optimal given p_S), express p_S as a function of p_E(p_S has to be optimal given p_E), and solve the system of two equations with two unknowns.

Question 3 - Stable Matching

There are four men (Andy, Bob, Charlie, and Dennis) and four women (Ann, Beth, Cathy, and Dianne), whom you need to match. The preferences of men and women over those of the opposite gender are given below (from most preferred to least preferred):

Andy: Beth, Dianne, Ann, Cathy

Bob: Dianne, Beth, Ann, Cathy

Charlie: Beth, Cathy, Ann, Dianne

Dennis: Dianne, Cathy, Beth, Ann

Ann: Charlie, Bob, Dennis, Andy

Beth: Dennis, Charlie, Bob, Andy

Cathy: Andy, Dennis, Bob, Charlie

Dianne: Charlie, Andy, Bob, Dennis

(a) Find a matching that is NOT stable, and point out which (man, woman) pair blocks this matching. It is sufficient to give just one unstable matching, and to give just one pair that blocks this matching (and explain why that pair blocks that matching).

(b) Find a stable matching.

Note: Don't forget that a matching is a set of pairs, not just one pair.

Note - It will also use excel/solver.

Reference no: EM132239695

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