BPUB250_PROBLEM_SETS_2009 - Problem 1 Students at the...

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Problem 1 Students at the Wharton School love burritos. The market for burritos is perfectly competitive due to many substitute fast foods available on campus. Daily market demand is given by Q D as follows: Q D = 1000 – 100P The daily market supply curve of burritos is given by: P = 2 + 0.01Q S A national chain, Poblano’s Texas Grill, enters the Wharton School market for burritos. The market is still perfectly competitive but the additional daily market supply from Poblano’s burritos is given by Q POB as follows: Q POB = 100P – 300 (a) What is the initial market price and quantity traded (before Poblano enters the market)? (b) Obtain the new market supply curve after entry from Poblano’s Texas Grill. Is the new market supply curve linear over the entire relevant domain (Prices of $0 and greater)? Why or why not? (You may find a graph helpful in analyzing this problem, but it is not required for credit) (c) What is the market price and quantity traded after entry from Poblano’s Texas Grill? (d) Suppose that Poblano’s offers free burritos for a day. What is the number of burritos that will be consumed? Briefly, explain why not any more or any less?
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Solution: Problem 1 (Supply and Demand) (a) In a perfectly competitive market with no frictions (taxes, quotas, etc) the market clears at the point where the supply and demand schedules intersect. Start by rewriting: P = 2 + 0.01Q S => Q S = 100P – 200 Set Q S = Q D => 1000 – 100P = 100P – 200 => 1200 = 200P => 6 = P At P = 6, Q D = 1000 – 100(6) = 400 The initial market price is $6 and the quantity traded is 400 burritos. Note there are several ways of obtaining the answer. For example, one can substitute the supply curve directly for P in the demand function. However, we did it this way to simplify the next step. (b) We can analyze this by simply adding or subtracting from the supply or demand curve horizontally (using the quantity functions). In this case, we have an additional source of supply, so we will need to add the market supply curves. One challenge is that the resulting new supply or demand curve may not be linear – it may have a ‘kink’ in it. From (a), Q S = 100P – 200 and Q POB = 100P – 300 Horizontally sum the supply curves (add the Q’s): Q S(NEW) = Q S + Q POB => 100P – 200 + 100P – 300. Q S(NEW) = 200P – 500. Note that this supply curve is only valid for P of $3 and above, since Q POB is negative for P<$3. Therefore, the new market supply curve is nonlinear: Q=200P-500 for P $3 and Q=100P-200 for P<$3. (c) We may ignore nonlinearity in the market supply curve if the market-clearing price we solve for turns out to be greater than $3. Solve for the market clearing price just like in (a): Q D = Q S(NEW) => 1000 – 100P = 200P – 500 => 1500 = 300P => P = 5. At P = 5, Q
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This note was uploaded on 04/04/2012 for the course BPUB 250 taught by Professor Seim during the Spring '08 term at UPenn.

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BPUB250_PROBLEM_SETS_2009 - Problem 1 Students at the...

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