Questions by xspencer - Page 21

On March 2, 2020, Zoe Moreau, Karen Krneta, and Veronica Visentin start a partnership to operate a personal coaching and lifestyle consulting practice for professional women. Zoe will focus on work-life balance issues, Karen on matters of style, and Veronica on health and fitness. They sign a partnership agreement to split profits in a 3:2:3 ratio for Zoe, Karen, and Veronica, respectively. The following are the transactions for SUNLAND Personal Coaching:2020 Mar. 2 The partners contribute assets to the partnership at the following agreed amounts:Z. Moreau K. Krneta V. VisentinCash $14,900 $10,100 $19,700 Furniture 17,500 Equipment 18,700 13,900 Total $33,600 $27,600 $33,600 They also agree that the partnership will assume responsibility for Karens note payable of $5,200.Dec. 20 Zoe, Karen, and Veronica each withdraw $30,100 cash as a "year-end bonus." No other withdrawals were made during the year.31 Total profit for 2020 was $109,000.2021 Jan. 5 Zoe and Veronica approve Karens request to withdraw from the partnership for personal reasons. They agree to pay Karen $14,850 cash from the partnership.6 Zoe and Veronica agree to change their profit-sharing ratio to 4:5, respectively.Dec. 20 Zoe and Veronica withdraw $42,400 and $45,800 cash, respectively, from the partnership.31 Total profit for 2021 was $123,750.2022 Jan. 4 Zoe and Veronica agree to admit Dela Hirjikaka to the partnership. Dela will focus on providing training in organizational skills to clients. Dela invests $31,000 cash for 25% ownership of the partnership.
Klay and Jaylen have preferences over basketballs (b) and MuscleMilk (m). Klays preferences can be described by Uk(bk,mk) = bk^1/5 mk^4/5 and Jaylenss preferences can be described by Uj(bj,mj) = bj^4/5 mj^1/5 . Klay has an endowment of 10 basketballs and 20 bottles of MuscleMilk while Jaylen has 20 basketballs and 10 bottles of MuscleMilk.(a) Solve for the contract curve in this economy and plot it in an Edgeworth Box with basketballs on the horizontal axis and Klays origin at the bottom right. Once youve derived the Edgeworth Box, feel free to use Desmos or another graphic calculator to plot the function.(b) Solve for the competitive equilibrium price ratio and each individuals final consumption. Show this outcome and the endowment point in your Edgeworth Box. Which consumer is a net supplier of basketballs? Of MuscleMilk? Reminder: you can choose one good and set that goods price equal to $1. Generally, its easier if you choose the y-axis good, so in this case pm = $1. Then solve for the price of basketballs relative to the price of MuscleMilk.(c) Verify that the allocation obtained in the competitive equilibrium is on the contract curve by plugging your solutions from part (b) into what you found in part (a). At this competitive equilibrium, what is each consumers marginal rate of substitution?(d) Klay tears a ligament in his knee and is no longer able to enjoy basketballs. Suppose new preferences are summarized by the utility functions Uk = mk for Klay and Uj = min(bj,mj) for Jaylen. Is the original allocation Pareto efficient? Why or why not?