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# hw1a - In the past they found that when they priced at \$450...

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ISyE 4803B – Supply Chain Economics HW1 1. The total potential market for an item is 20,000. In addition the willingness to pay (wtp) is distributed uniformly between \$0 and \$10. Do the following: a. Write the wtp distribution. b. Derive the corresponding price-response curve and draw a sketch of it. c. Find the unit elastic point for this price-response. 2. Answer the following: a. Derive the elasticity and wtp distribution for the logit model we discussed in class. b. Suppose market price is \$13000, C=13000, and elasticity at that price is 6.5. Find the parameters (a and b) for the logit model. c. Sketch the logit model and wtp distribution. 3. Show the following relation is true: c p p p - = * * *) ( ε 4. A firm is currently pricing an item at \$400 with a unit cost of \$180.
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Unformatted text preview: In the past, they found that when they priced at \$450 the demand was 250 and when they priced at \$350 the demand was 500. Do you think \$400 is a good price? Why or why not? If not, what price would you recommend? 5. An auto manufacturer can manufacture compact cars for an incremental cost of \$50000 each. She faces a logit price-response function for sales in the next month where market saturation is 40,000 cars, b=0.0005, and market price is \$12000. What price will maximize total contribution? How many cars will she sell during the month? 6. Suppose unit cost is \$5 and price response is linear (as shown below). Find the optimal single price to charge and the total margin at that price. p p d 500 10000 ) (-=...
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