11. An editor has been allotted $60,000 to spend on the development and promotion of a new book. It is estimated that if x thousand dollars is spent on development and y thousand dollars on promotion, approximately f(x,y) = 20x2y copies of the book will be sold. How much money should the editor allocate to development and how much to promotion in order to maximize sales? What is the marginal effect on sales of an increase in the development and promotion budget? 12. Consider a consumer with the utility function z = ln x + B In y, where I 0 and M is 1+r a positive constant. For economic interpretation, imagine that the consumer faces a two-period horizon, and that x is first period consumption,y is second period consumption, M is the present value of lifetime income, and is the relative price of future consumption. 1+r a. Solve for the values of x and y that maximize utility. Make sure to show that the solution is a relative maximum. Don't worry about verifying that the solution is an absolute maximum. b. At the optimum, what is the marginal utility of lifetime income (M)? In other words, how does (maximum) utility change if lifetime income is increased by an infinitesimal amount? Is there diminishing marginal utility to lifetime income? 11. An editor has been allotted $60,000 to spend on the development and promotion of a new book. It is estimated that if x thousand dollars is spent on development and y thousand dollars on promotion, approximately f(x,y) = 20x2y copies of the book will be sold. How much money should the editor allocate to development and how much to promotion in order to maximize sales? What is the marginal effect on sales of an increase in the development and promotion budget? 12. Consider a consumer with the utility function z = ln x + B In y, where I 0 and M is 1+r a positive constant. For economic interpretation, imagine that the consumer faces a two-period horizon, and that x is first period consumption,y is second period consumption, M is the present value of lifetime income, and is the relative price of future consumption. 1+r a. Solve for the values of x and y that maximize utility. Make sure to show that the solution is a relative maximum. Don't worry about verifying that the solution is an absolute maximum. b. At the optimum, what is the marginal utility of lifetime income (M)? In other words, how does (maximum) utility change if lifetime income is increased by an infinitesimal amount? Is there diminishing marginal utility to lifetime income