You are a monopolist that sells textbooks to undergraduate students. currently you sell 100 books at a price of $100 each, for revenue of $10,000. each book is essentially costless to print, so you ignore costs and focus on maximizing revenue. based on research by your marketing team, you learn that some students will not buy the book if the price goes up. also, if you cut the price more students will buy the book.

1. if the elasticity of demand is 0.5, what will be your new revenue if you raise the price by 10%?

2. if the elasticity of demand is 2, should you raise the price or lower the price? briefly explain without performing any calculations.

3. saving two consumers, larry and jeff, have utility functions defined over the two periods of their lives: middle age (period zero) and retirement (period 1). they have the same income in period 0 of m dollars and they will not earn income in period 1. the interest rate they face is r. larry’s and jeff’s utility functions are as follow. = 0.5 + 0.5 and = 0.5 + 0.5 for each person is between zero and one and represents each consumer’s temporal discount econ 340: intermediate microeconomics. ben van kammen: purdue university. rate. a. write the budget constraint that applies to both jeff and larry in terms of consumption in each period and ), interest rate, and m. b. what is larry’s and what is jeff’s marginal rate of intertemporal substitution? c. what is the slope of the budget constraint? d. write each consumer’s condition for lifetime utility maximization. e. re-arrange the conditions from part (d) to solve for the ratio, . f. if > which consumer will save more of his middle age income? g. if > 1 1+ , in which period will larry consume more: = 0 or = 1?