Please answer a) through d)!

Problem 1 A tech company sells laptops (x) and tablets (v) to a number of business customers. An innovation reduces the cost of producing tablets. An executive at the company is concerned that lowering the price of tablets to pass on the cost saving to customers might affect demand for laptops (it) also sold by her firm. Suppose the tech executive is considering lowering the price of tablets by a percentage (I so that after the price reduction tablets cost p'y = (1 41) py. a) In a graph measuring the number of tablets along the vertical axis, illustrate how the lower price of tablets would affect the budget constraint of a customer with a budget of M to spend on x and y. b) Suppose the customer considers laptops (x) and tablets (y) perfect substitutes with laptops twice as effective as tablets (u(x,y) = 2x + y). Suppose also that initially the price of a laptop was twice the price of a tablet, px = 2py. In your graph, illustrate how the lower price of tablets would affect the customer's demand for laptops. c) Now, suppose instead the customer considers x and y perfect complements and u(x,y) = min[2x, 37]. How would the discount affect the customer's purchases of x and y in this case? Illustrate in a separate graph. d) Last, suppose the customer considers laptops and tablets imperfect substitutes and u(x,y) = 11237 d.1) Using calculus, derive the demand for x and the demand for y as a function of prices pit and py, M, and (1. d2) How does the reduction in the price of y affects the demand for x in this case