BPUB250_PROBLEM_SETS_2010

# BPUB250_PROBLEM_SETS_2010 - Managerial Economics BPUB250...

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Managerial Economics BPUB250 Spring 2010 Problem Set 1 Due Wednesday/Thursday, January 28-29 in Class (or Friday, January 30 in Recitation). Question 1 The market for used college books is very competitive. Students search for used college books online and at local bookstores. There are many bookstores competing against each other trying to obtain profits. The demand for used college books (Q D ) depends only on the book’s price (P) and can be written as: Q D = 250,000 – 2,700 P The supply of used college books (Q S ) is given by: Q S = – 50,000 + 2,300 P (a) What is market price (P*) and the number of books traded (Q*)? Draw a graph showing the price and quantity in equilibrium. Because of government incentives, more students are attending college this year. This new group of students will also demand used books. The supply of books does not change. Their demand for used books (Q’ D ) is given by: Q’ D = 29,994 – 238 P (b) Given this new piece of information, what is the new estimated price (P*) and the new equilibrium quantity (Q*) in the market for used books (including the additional students receiving the government incentives)? Will the price of used books go up or down as a consequence of this policy? Draw a graph showing the new price and quantity in equilibrium . Suppose that, aware of the possible consequences of its policy, the government decides to give financial incentives to all bookstores across the country. This incentive shifts the supply of used books to the right. The new market supply function is: Q S = – 29,048 + 2,300 P (c) What is the new market equilibrium (P* and Q*) when the government gives incentives to students and to bookstores? Draw a graph showing the new price and quantity in equilibrium .

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Managerial Economics BPUB250 Spring 2010 Problem Set 1 Due Wednesday/Thursday, January 28-29 in Class (or Friday, January 30 in Recitation). Question 2 Monica has 24 hours to spend on doing MGEC problems (M hours), socializing (S hours), or napping (N hours). Her objective is to have the product of all three activities, i.e., Z = MSN be as large as possible. Formally (mathematically) state Monica’s optimization problem. How many hours should she spend on each activity? Show by using first order conditions. What is the highest product (Z = MSN) she can attain.
Managerial Economics BPUB250 Spring 2010 Problem Set 1 - Solutions Due Wednesday/Thursday, January 28-29 in Class (or Friday, January 30 in Recitation). Question 1 (a) In a perfectly competitive market, the market clears at the point where supply and demand are equal to each other. Q D = 250,000 – 2,700 P = – 50,000 + 2,300 P = Q S Hence, 250,000 – 2,700 P = – 50,000 + 2,300 P 300,000 = 5,000 P P* = 60 Substitute P* back in Q D or Q S to find Q* = 88,000 . To draw the graphs, we need to write the supply and demand in terms of Q. Rewriting each equation we obtain: P = 2,500/27 – Q D / 2,700 , which is equal to P = 92.6 – 0.00037 Q D .

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BPUB250_PROBLEM_SETS_2010 - Managerial Economics BPUB250...

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