Consider the consumption decisions of R.B. Turbo, a new student at T University. Ms. Turbo has only available $1,000 in monthly income to spend on food and housing. In terms of food, Ms. Turbo, a vegetarian, has found there is a nice restaurant called Veggies that offers vegetarian meals. She wants to buy food from this restaurant and is considering their monthly dinner plan, which costs $125.00 per meal served every day in the month (she can consume more than one meal a day). In addition, Ms. Turbo is looking for housing. She has found a cheap apartment building in a polluted area of New Jersey where the monthly rental of a one-bedroom apartment is $250.00, a 2-bedroom is $500,00, a 3-bedroom is $750.00, a 4-bedroom is $1,000 and so on. Assume That Turbo has preferences that can be described by the following utility function:
U = X_{1}^{0.5}X_{2}^{0.5}
Where X_{1} is the quantity consumed of food per month (number of meals served every day in a month), and X_{2} is the number of bedrooms in her apartment.
A. Calculate the number of bedrooms that Ms. Turbo's apartment will have (give a numerical answer and explain how it is obtained, including any derivations).
B. Compute the number of meals that Ms. Turbo will consume every day at Veggies (again, provide a numerical answer and specify how it is obtained).
C. Suppose that Ms. Turbo suddenly receives a $500 increase in monthly income. Would there be any changes in her consumption of housing and food? (assume that she has the ability to upgrade to better apartments (with more bedrooms) and to change her monthly meal plan if she wants, so as to increase or decrease the number of meals she eats a day).
D. What is Ms. Turbo's income elasticity of demand for housing?
E. Suppose that Ms. Turbo has an income of $1,000 (as in parts A and B) but that, all of a sudden, Veggies decides to increase the price of its monthly program of meals from $125 per meal to $150. How many dishes will Ms. Turbo consume each day under the new program? Will she keep the same type of apartment (the same number of bedrooms)?
F. What is Turbo's price elasticity of demand?