Donald and Mary derive utility from only two goods bananas B

Donald and Mary derive utility from only two goods: bananas (B) and milk (M). They have identical preferences. That is their utility function is U = B + 400 ln ( M ). The price of bananas (Pb) and milk (Pm) are both $1 per unit. Donald has an income of $300 per month and Mary has an income of $600 per month.

a. What quantities of B and M will maximize Mary’s utility? Please include a graph showing the budget line, indifference curve and optimal bundle.

b. What quantities of B and M will maximize Donald’s utility? Please include a graph showing the budget line, indifference curve and optimal bundle.

c. Holding Donald\'s income constant at $300, what is his individual demand curve for bananas? ( Hint: compute the equation that shows his optimal consumption of bananas as a function of Pb)

d. Assume that the price of bananas drops to $0.75 per unit. Compute Donald’s income and substitution effect (for banana’s consumption).

Solution

he Progressive Era in the United States was a period of social activism and political reform that flourished from the 1890s to the 1920s.[1] During this period activist Jane Addams and steel magnate Clayton Mark worked with to address the social and political problems.[2] Clayton Mark built a planned worker community for the employees of the Mark Manufacturing Company, named Marktown.[2] One main goal of the Progressive movement was purification of government, as Progressives tried to eliminate corruption by exposing and undercutting political machines and bosses. Many (but not all) Progressives supported prohibition in order to destroy the political power of local bosses based in saloons.[3] At the same time, women\'s suffrage was promoted to bring a \"purer\" female vote into the arena.[4] A second theme was achieving efficiency in every sector by identifying old ways that needed modernizing, and emphasizing scientific, medical and engineering solutions.
Many people led efforts to reform local government, public education, medicine, finance, insurance, industry, railroads, churches, and many other areas. Progressives transformed, professionalized and made \"scientific\" the social sciences, especially history,[5] economics,[6] and political science.[7] In academic fields the day of the amateur author gave way to the research professor who published in the new scholarly journals and presses. The national political leaders included Theodore Roosevelt, Robert M. La Follette, Sr., Charles Evans Hughes and Herbert Hoover on the Republican side, and William Jennings Bryan, Woodrow Wilson and Al Smith on the Democratic side.
Initially the movement operated chiefly at local levels; later it expanded to state and national levels. Progressives drew support from the middle class, and supporters included many lawyers, teachers, physicians, ministers and business people.[8] The Progressives strongly supported scientific methods as applied to economics, government, industry, finance, medicine, schooling, theology, education, and even the family. They closely followed advances underway at the time in Western Europe[9] and adopted numerous policies, such as the banking laws which became the Federal Reserve System in 1914. They felt that old-fashioned ways meant waste and inefficiency, and eagerly sought out the \"one best system\".