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Question 1 - A theater on Broadway recently increased the price of a ticket for a popular play by 8%. The attendance went down by 3%. What is the price elasticity of demand for tickets for this play? What factors, besides the increase in the price of the ticket, could have contributed to the reduction in attendance? Should the theater further increase or instead decrease the price of the ticket? What would be the optimal price of a ticket?
Solution - Price elasticity of demand = %change in demand/%change in price=-3/8=-0.375
Maybe the competitor doesnot increase the price due to which consumer might have shifted.
Some consumer might be left the market as price increases.
To maximized total revenue,price should be increased, but to maximise profit, we can't say anything because it depends on the marginal cost curve.
Pricing should be based on this formula=P-MC/p=1/Ed
Question 2 - Auto Parts, Inc. is a medium-sized company that manufactures auto parts in Buffalo, New York. The company currently loses $30,000 per month. The owner of the company is evaluating whether she should shut down the factory. She thinks that the factory should continue to operate until the economic environment improves, and buyer for the factory can be identified. The logic of the owner is that her company has already invested millions of dollars in the factory over the years. The monthly fixed costs for the factory are $40,000. The CEO of Auto Parts, Inc., thinks the factory should be shut down because most the monthly fixed costs ($40,000/month) are sunk costs. Evaluate the arguments of the owner and CEO. Provide a recommendation as to whether Auto Parts, Inc. should shut down its factory in Buffalo.
Solution - The assessment of CEO is wrong. The company should shut down if it is unable to cover the minimum of average variable costs. That is upto a point where the firm can cover all its variable to the firm should continue operating. No matter what amount of fixed costs, if the firm is covering variable costs, it should keep itself in operations. The point when the price of the product falls below the minimum of AVC, it should shut down. The losses are 30000, and the fixed costs are 40000, this means that the firm can cover some of its fixed costs also, other than covering variable costs. Thus the firm should continue operating.
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Question 3 - Digital Books, LLC is a company that sells e-books related to career advising and professional development. Digital Books, LLC earns a yearly positive economic profit of $25,000 if it can sell 10,000 e-books. Each time, a customer buys an e-book, it incurs a cost of $0.50 (cost of downloading each e-book). Digital Books, LLC spends each year $100,000 developing new e-books (new topics and new editions). What is Digital Books, LLC's profit-maximizing price?
Solution - Profit = (P-MC)Q =
Or, 25000 = (P-0.5)10,000
Or, P = $3
Thus profit maximising price is $3
In the long run, profits will fall to zero and the profit maximising price will fall to be equal to MC of $0.50. This is because in the long run because of entry-exit of new firms, LLC firm will experience fall in profits till they reach 0.
Question 4 - Assume you are the owner of a concert hall with 6,000 seats. The demand function for seat tickets is Q = 10,000 - 200P, where Q is the quantity demanded and P, is the price for a seat ticket. You are charging $30 per ticket and selling tickets to 4,000 consumers. Further, assume that you incurred only fixed costs. Is charging $30 the optimal pricing policy? What other pricing policy might you use to increase your profits? Could you increase profits through price discrimination? If so, what type of price discrimination should you use?
Q = 10,000 - 200P
200P = 10,000 - Q
P = 50 - 0.005Q
Since only fixed costs are incurred, Marginal cost (MC) is zero.
(a) Profit is maximized by equating Marginal revenue (MR) with MC.
Total revenue (TR) = P x Q = 50Q - 0.005Q2
MR = dTR/dQ = 50 - 0.01Q
Equating with MC,
50 - 0.01Q = 0
0.01Q = 50
Q = 5,000
P = 50 - (0.005 x 5,000) = 50 - 25 = $25 (Optimal price)
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(b) I could increase profit by using price discrimination, by charging a different price to different groups of consumers for the same concert. I could maximize profit by charging a higher price to consumers with more inelastic demand, and lower price to consumers with more elastic demand.
(c) Perfect price discrimination would result in maximum profit where the price per seat (P) equals MC, but a fixed entry fee is charged that equals the entire consumer surplus (CS). The entire amount of CS would be my profit.
Question 5 - Assume you run a company that offers a product for which all consumers have an identical demand curve. Each consumer's demand curve is P = 20 - 4Q. The marginal cost of production is $4. Devise an optimal two-part tariff pricing policy.
Solution - For two-part tariff
Per unit fee or usage, fee is always equal to marginal cost. So per unit fee=4
And fixed fee used to be in such a way that it takes all consumer surplus. Thus when P=4,Q=4 and consumer surplus =1/2*16*4=32
Thus lumpsum or fixed fee=32 and per unit fee=4
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Question 6 - Jennifer Shapiro is a worker for XYZ Company. She has an effort cost function of C = 2e2 and a monthly reservation wage of $2,500. Her wage function is W = 2,500 + 0.4Q. If the incentive coefficient is equal to 0.4, then Q = 300e. Q is Jennifer's output. Assume that the incentive coefficient decreases from 0.4 to 0.3 and Jennifer's base salary increases from $2,500 to $2,700. What will happen to her level of effort? How will this change XYZ Company's profits?
Solution - Benefit = wages - cost
=2500 + 0.4Q - 2e^2
When Q = 300e
Benefit = 2500 + 0.4(300e) - 2e^2
B = 2500 + 1200e-2e^2
Db/De = 0 =120-4e = 0
E = 30
When Income changes,
Benefit = 2700 + 0.3Q -2e^2
=2700 + 0.3(300e) -2e^2
= 2700-90e - 2e^2
Db/De = 0 = 90-4e
E = 22.5
Level of effort will decrease because marginal benefit from effort decreases.
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Question 7 - Motorcycles USA is a company that manufactures and sells motorcycles in North America. It has the following demand function for its motorcycles: P = 30,000 - 100Q. Motorcycles USA has a marginal cost (MC) that is constant and equal to $4,000.
What will Motorcycles USA's price be if it decides to sell the motorcycles by itself? What will the price be if it sells them though MC Dealership, LLC an independent distributor?
Consider that when Motorcycles USA contracts with MC Dealership, LLC, it takes into account that MC Dealership, LLC faces the same demand curve. Assume that (MC) is constant and equal to $4,000.
What is the impact of distributing the motorcycles through MC Dealership, LLC on the price of the motorcycles?
P = 30000 - 100Q
TR = 30000Q - 100Q^2
MR = 30000 - 200Q
MC = 4000
If Motorcycle USA sells it off, the profit is maximized when MR=MC
30000 - 200Q = 4000
Q = 130
Profit = 30000- 100(130) = 17000
Profit USA = (17000 - 4000 ) x 13
=13000 x 13
When Dealership LLC, sells the motorcycle then
(i) Either he will sell it at P = 17000 & gives USA motorcycle less than 17000
(ii) If USA motorcycle sells LLC at P = 17000, then for LLC will charge
MR = MC
30000 - 200Q = 17000
Q = 65
P = 30000- 100(65) = 23500
LLC will charge 23500
Thus USA automobile should sell them in order to maximise profit.
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