DRAW THE GRAPH IN PART D$!$

DO NOT FORGET TO DO PART D$!$

You are the product manager for wireless headphones and your company has the exclusive license of the product. The company's marketing department models the demand function for your game as Q $=$a $+$bP $+$cM $+$dPS$,$where Q is the annual demand for your product measured in thousands of units, P is the price of the headphones, M is the average annual family income measured in thousands of dollars, and PS is the price of the stereos with the technical specifications needed to have an excellent listening experience. The output given by Excel after running a regression is given in the image attached.

a$)$What is the modeled demand function for headphones? Express it as a

function of P$,$M$,$and PS$.$

b$)$You hire an economic consultant to obtain estimates of income and the price of stereos next year. Her report calculates that average family income will be $$45,000,$and the price of a stereo $$800.$What will be your demand function next year? Express it as a function of P$.$Also$,$ solve for the inverse demand function, that is$,$solve for price in terms of quantity.

c$)$Assume that you have excess inventory and, consequently, are just worried about maximizing revenue. What price should you charge? What would be your revenue? What is the price elasticity of demand at this price?

d$)$Draw an accurate graph showing market demand, marginal revenue, and the area representing your total revenue.