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201Spring2011HW1SOLUTIONS

201Spring2011HW1SOLUTIONS - Solutions to Problem Set 1...

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Solutions to Problem Set 1. Microeconomic Theory 201, Spring 2011, University of Waterloo Questions marked with THINK are the most challenging. Question 1. 11 for 1 DVD 21 for 2 DVDs 30 for 3 DVDs 38 for 4 DVDs 45 for 5 DVDs 49 for 6 DVDs 49 for 7 DVDs a) How many DVDs will Henry buy if the price of each DVD at Movie Max is \$5 ? 11 for 1st DVD 21-11=10 for 2nd DVD 30-21=9 for 3rd DVD 38-30=8 for 4th DVD 45-38=7 for 5th DVD 49-45=4 for 6th DVD 49-49=0 for 7th DVD Because the marginal bene±t from the 5th DVD exceeds the marginal cost (7 > 5) but the marginal bene±t from the sixth DVD is below the marginal cost (4 < 7) Henry buys 5 DVDs. b) THINK How many DVDs will Henry buy if Movie Max only sells DVDs in pairs and the price of each bundle of two DVDs at Movie Max is \$10 ? 21 for 1 pair of DVDs (equals total willingness to pay for 2 DVDs) 38 for 2 pairs of DVDs (equals total willingness to pay for 4 DVDs) 49 for 3 pairs of DVDs (equals total willingness to pay for 6 DVDs) 1

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49 for 4 pairs of DVDs (equals total willingess to pay for 8 DVDs) 21 for 1st pair 38-21=17 for 2nd pair 49-38=11 for 3rd pair 49-49=0 for 4th pair Because the marginal bene±t from the 3rd pair of DVDs exceeds the marginal cost (11 > 10) but the marginal bene±t from the 4th pair of DVDs is below the marginal cost (0 < 10) Henry buys 3 pairs of DVDs. Question 2. Assume that the demand curve for candy bars is D ( p ) = 100 3 p , where p is the price of a candy bar Candy bars are produced and sold by a monopolist with the cost curve C ( Q ) = 2 Q; where Q is the quantity of candy bars produced. TR = pQ; where Q is quantity. We then substitute the D ( p ) = 100 3 p for Q to get TR = p (100 3 p ) ( p p ) (100 3 ( p p )) p (100 3) = p (100 3 ( p p p (100 3 ( p p )) p (100 3) = p (100 3 p p p (100 3 p p ) p (100 3) = p p p (100 3 p p ) p (100 6 p p ) p : p (100 3 p p ) p = (100 6 p p ) 2
Setting p = 0 MR = 100 6 p The total costs are 2 Q; where Q is the quantity sold. We then substitute the demand curve D ( p ) = 100 3 p for Q in total costs 2 Q to get Total costs = 2 (100 3 p ) : The change in total costs when price increases from p to p p is thus 2 (100 3 ( p p )) 2 (100 3 p ) = p The rate of change in total costs

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201Spring2011HW1SOLUTIONS - Solutions to Problem Set 1...

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