a consummer has a revenue of I dollars. the prices of x and y are Px and Py. the utility function of the consummer is U(x,y)= x^(1/2)y^(1/2).
a) Py =4 and I =100. find the demand curve (of Marshall) and draw it. What is the elasticity demand when Px =5
b)Py =4 and Uo is the maximal level utility when Px =5, Py =4 and I =100. find the the compensated demand curve (or of Hicks) and draw it on the same graph. for what value of Px the two curves will cut? what is the elasticity of compensated demand when Px =5?
c) Px =5 and Py =4. find the Engle curve and draw it. What is the elasticity of x in function with I when I = 100?
d) Py =4 and I =100. Suppose Px falls from 5 to 2. what is the change in the demand quantity of x? Decompose this change in substitution effects and revenue. what is the change in the consummer surplus?
e) find the derivative x and Px as function of Px, Py, I and decompose it in substitution effects and revenue effects.