Question

Given:

X          TUx      MUx    MUx/Px           Y          TUy      MUy    MUy/Py           MUy/Py’

0          0          0          0                      0          0          0          0                      0

1          250                                          1          350                                                     

2          450                                          2          550

3          600                                          3          700

4          700                                          4          800

5          775                                          5          875

6          800                                          6          900

Suppose income I = $160, Px = $20, & Py = $20.

1. Find the combination of X and Y that maximizes utility.
2. Calculate Consumers’ surplus of X, CSx = TUx – TEx, total utility minus total expenditures such that total expenditures TEx = Px.X. Do the same for commodity Y. Calculate consumers’ surplus CSy = TUy – TEy, where total expenditures TEy = Py.Y.
3. Suppose Py rises to Py’ = $40. Find the combination of X and Y that maximizes utility.
4. Calculate CSy’ the new consumers’ surplus of Y, CSy’ = TUy’ – TEy’.
5. Draw the demand curve for commodity Y. Is it downward sloping?
6. Challenging question: Find the equation for demand pertaining to commodity Y such that Py = a – bY. In other words, find the parameters a and b.

Answer 1

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