Sarah Industries and Alexis, Inc Sell a Homogenous Product - Washington Metropolitan Area Transit Authority - Economics Assignment Help

Assignment Task:

SECTION I:

True/False and explain. When answering you must explain why the statement is true or false. Illustrations can count as explanations.  An answer of true or false alone will be considered wrong. Each question is worth 4 points. Partial credit can be earned. 
1. The utility functions, U(X, Y) and V(X, Y) = F(U(X, Y)) where F is strictly increasing function, have the same MRS. 
2. Coach Jackson says that between any two players, he prefers the one who is taller AND faster. This means Coach Jackson’s preference over players can be expressed by a utility function. 
3. The production function is to producer theory what the budget constraint is to consumer theory. 
4. If criminals are risk-neutral, then an increase in the probability of getting caught will not affect their behavior. 
5. A profit-maximizing firm always sets P=MC. 

SECTION II:

Full Answer, In the following problems, please answer 4 of the following 6 questions in the space provided.  Circle the number of the question that you would like for me to grade.  The number of points in indicated by each number. 
 
1. There are 200 price taking pharmaceutical firms selling a "miracle pill" that is supposed to make people more attractive. The cost function for each firm is C(q) = q2 + 20q + 100. The market demand is QD = 5000 - 40p.

a. Derive the market supply function QS(p). 

b. What would be the short-run equilibrium price and quantity?

c. What would be the long-run equilibrium price and quantity? How many firms will operate on the market?

d. Suppose now that the "Miracle pill" company obtains an exclusive patent on producing and selling "miracle pill".  How much will the monopolist produce and charge for each pill? 

2. There is only one firm that produces test solutions, Answer-All.  Answer-All faces a linear demand function given by P=320-4Q and has an MC=40.

a. How many test solutions and what price will Answer –All charge for them? (5 points)

b. Teachers seeing the profit that Answer-All is making decisions to form a company called Teach-Cheat.  Teach-Cheat and Answer-All now are the only companies that provide test solutions.  The market demand is (P=320-4(QAA +QTC)). Answer-All still has MC=40, however, Teach-Cheat has a cost advantage with MC=0 (Teachers make the test so they have the answers!). Graph Answer-All and Teach-Cheat reaction  (best response) functions. Show output levels for Counrot, Monopoly, and Perfect Competition for each firm. (Hint:  The reaction curves are not symmetric.)

c. Competing in Cournot duopoly fashion, which firm will make the most profit?  Explain why?  (Hint: You do not have to solve for the profit to answer this question.)

 
3. Suppose that there are two firms, Sarah Industries and Alexis, Inc.,  and they sell a homogenous product, and each have a constant marginal cost of 10.  Consider the possibility that the two firms will coordinate their activities in order to increase their profits.  The cartel agreement would have each firm restrict its output so that the market price will be high.  However, each firm might consider raising its output beyond the cartel quota (cheating on the agreement).  Thus, for each firm the two possible strategies are to comply and to cheat.  Assume that both firms have the same cost curves so when they agree to produce the same output.  Together they will produce the monopoly output for the industry because that maximizes their combined profits, and with both producing the same amount each will receive half the monopoly profit.  Their payoffs are as follows:

i. If both cheat, they will earn profits of 10.

ii. If they both comply, they will earn profits of 20. iii. If one firm cheats and the other does not the firm who cheats will earn profits of 25; the firm who doesn’t cheat will earn profit of 5.

a. Draw this normal form game. 

b. Do either of the firm have a dominant strategy?  Is there a Nash Equilibrium of this game?  If so, what is it? (2 points)

c. Suppose cartel agreements are contractible and contracts are enforceable by law.  Would Sarah Industries and Alexis, Inc. want to sign a legal contract?  If so, how would the outcome change from part b? 

d. Suppose instead of competing in the game described above, these two firms were to compete in a Bertrand fashion.  That is, the firms would simultaneously set their own price at any level.  All of the demand for the good would go to the lower-priced firm.  Does either of the firms have a dominant strategy in this case?  What is the Nash Equilibrium of this game?

4. Rice, important agricultural product for both the US and other countries, has different demand and supply curves in different regions of the world thanks to the difference in technology, geography, climate, etc. Now suppose that the supply and demand curves in the US rice industry are as follows: Supply of Rice in the US: Qs = 0.3 * P Demand of Rice in the US: Qd = 2 - 0.5P

a. Draw the supply and demand curve in the US domestic rice market, and find the equilibrium price and quantity.

b.  In 2014, the price of the world rice market was $1.5. Assuming that there is no tariff, show the equilibrium of the rice market in the US. Calculate the consumer surplus and producer surplus in the market. (5 points)

c.  In Jan. 2015,  the US government got through a federal law issuing a tariff of rice of $0.5/pound. Now, draw the new supply and demand curve in the graph you have drawn above, and recalculate the consumer surplus (CS) and producer surplus (PS). (5 points)

d. Compare the sum of CS and PS from part d with that in part b, and explain why there is some difference between them if any. 

6. The Washington Metropolitan Area Transit Authority (WMATA) is considering raising fares.  You are the Chief Economist for WMATA and they want your opinion on some issues.  Please answer each of the following questions.

a. WMATA has done some research and determined that if the price goes from $3.00 to $5.00, then ridership will fall from 20,000 to 18,000 hourly.  What is the price elasticity of demand for metro riding on an hourly basis?

b. Is it elastic or inelastic?  

c. Would the total spending on the metro increase or decrease due to the change in price?  Explain.   

d. WMATA thinks that metro trips are a normal good.  During the economic downturn, which saw average income go from $50,000 to $40,000, metro ridership was unchanged at 20,000 hourly.  Is WMATA correct that metro trips are a normal good?  Explain.  

e. WMATA outsourced some research to a consulting firm.  The consulting firm reported, “The cross-price elasticity between gasoline and metro trips is negative if a person lives in DC, while zero if they live in the suburbs.”  Are these results reasonable? Explain. 
 

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