Economics homework help

Economics homework help. For questions 3) – 9), show at least some of the steps of your calculation, not only the end result!
 
1) For a linear preference function u (x, y) = x + 2y, calculate the utility maximizing consumption bundle, for income m = 90, if,

1. a)p_x= 4 and p_y = 2
2. b)p_x= 3 and p_y = 6
3. c)p_x= 4 and p_y = 9

 
2) When an agent maximizes utility given a certain budget, how can we solve the problem graphically? Show a general case for what Banerjee calls ‘Cobb-Douglas preferences’. (In other words, what is the condition that has to be met between budget line and indifference curve in order to maximize an individual’s utility?)
3) For a demand function u (x, y) = xy, show the demand functions for good x and good y. (Remember that MRS = (du/dx) / (du/dy) = p_x / p_y in the point of interest, the tangency point of budget line and indifference curve. The budget condition is given by p_xx + p_yy = m).
 
4) Calculate the own-price elasticities as well as the income elasticities of demand for goods x and y based on your results in 3).
 
5) Follow the same steps as in 3) for u (x, y) = x^1/3 y^2/3.
 
6) Show the individual’s demand for good x and good y that follows from their utility function u (x, y) = x^1/2 y^1/2.
 
7) For the values in 5), assume income m = 30, p_x = 2, p_y = 1. How many units of each good does the individual consume? Calculate the same using the function from 6).
 
 
 
8) Show the individual’s demand for good x and good y that follows from their utility function
u (x, y) = x^ay^1-a  , with 0 < a < 1.
 
9) Use your result from 8) to calculate the own-price elasticity of demand for both goods.
 
10) Briefly explain why we assume that it makes sense that demand functions are homogeneous of degree zero in income and prices.
 
 
 

Economics homework help