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 offers two types of microphones "podcast" style and "economy" style. The following chart shows the willingness to pay and cost for each type of microphone and consumers.

1 Problem 1 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. LoG't' offers tuo types of microphones \"podcast" style and \"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 m Economy 23 El] 3D 1. Suppose that LoGi is able to tell apart professors from TAs. Then, LoG't' can choose which microphone to offer to each consumer, and what price to charge. Which microphone would LoG't' offer to professors and what price would LoG't' charge? What about the TAs? For items 2-5 below, ossurne the: Lo't' cannot tell professors sport 'om TAs. 2. Assume that in the mist of the pandemic LoG-i decides to sell economy microphones only because it is much easier to produce those. What is the equilibrium price of economy micro- phones that would maximise LoGi prots? Hint: Your creator will be a function of the number of professors and TA 's. 3. Now supme that LoGi decides to sell podcast style microphones only. Compute the price that would maximise LoGt' prots. 4. LoGt' has done some research and learned that there are 15 professors and 35 TAs at UCLA. Emed on this, LoGi wants to sell podcast mics to profwors and economy mics to TAs. What are the prices of each type of mics that allow LoGs' to do so? 5. Assume prices forth type of mic are thwe 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 s dollars to the TA. What is the minimum value of .1: such that the TAs will be indifferent between buying the economy mic and the podcast mic