The pandemic has shift teaching from the classroom to the Zoom room and with it has made Professors and TAs to adjust their teaching tools. Assume that LoGi is the only company selling microphones to UCLA. LoGi oEers two types of microphones I"podcastl' style and I"economy\" style. The following chart shows the willingness to pay and cost for each type of microphone and consumers. Willingness to pay Microphone Costs Professors TAs Podcast 4|] 200 1 20 Economy 23 BI] 30 1. Suppose that LcGi is able to tell apart professors from TAs. Thu, LcGi can choose which microphone to offer to each consumer, and what price to charge. 1Which microphone would LoGr' offer to professors and what price would LoGi charge? 1|What about the TAs? For items 9-5 below, assume rst LoGr' cannot tell professors apart from TAs. 2. Assume that in the mist of the pandemic LoG decides to sell economy microphones only because it is much easier to produce these. What is the equilibrium price of economy micro phones that would maximize LoGIT prots? Hint: Your answer will tie a function of the number of professors and TA '5. 3. Now suppose that LoGrZ decides to sell podcast style microphones only. Compute the price that would maximize LoGi prots. 4. LoG has done some research and learned that there are 15 professors and 85 TAs at UCLA. Based on this, LoG-i wants to sell podcast mics to professors and economy mics to TAs. 1What are the prices of each type of mics that allow 1500:" to do so? 5. Assume prices for each type of mic are those that you computed in the previous question. The Econ department knows that the TAs are buying the economy mics at this price and wants to give them incentives to buy the podcast mics. So, they come up with the following rule, if a TA buys an economy mic she will have to pay for if out of pocket, but if the TA buys a podcast mic, the department will reimburse 1 dollars to the TA. What is the minimum value of I such that the TAs will be indifferent between buying the economy mic and the podcast mic