In: Economics
Lucy has just been promoted to a managerial position and given a new office. She is very fond of small Persian carpets and Native American paintings. Her utility function for carpets(x) and paintings (y) is given by: U = 100 * sqrt(xy)
Her company gave her a budget of $7,200. Persian carpets cost $700 each and Native painting costs $500. Using Excel spreadsheet, develop columns for quantity and of carpets and paintings within her budget. Use 0,1,2,....10 carpets as possible quantities. Develop columns of TU, MU, and MU/$ for carpets and paintings and answer the following questions.
At the maximum total utility level, what is the optimal number of carpets she gets and what is the optimal number of paintings she gets?
Quantity |
||||||
Persian Carpets |
Native Paintings |
Total utility |
Marginal utility for carpets |
Marginal utility for paintngs |
Mu of carpets/$ |
Mu of paintings/$ |
0 |
10 |
0.00 |
- |
0 |
- |
0 |
1 |
9 |
300.00 |
150 |
16.6666667 |
0.214286 |
0.3 |
2 |
8 |
400.00 |
100 |
25 |
0.285714 |
0.4 |
3 |
7 |
458.26 |
76.37626 |
32.7326835 |
0.327327 |
0.458258 |
4 |
6 |
489.90 |
61.23724 |
40.824829 |
0.349927 |
0.489898 |
5 |
5 |
500.00 |
50 |
50 |
0.357143 |
0.5 |
6 |
4 |
489.90 |
40.82483 |
61.2372436 |
0.349927 |
0.489898 |
7 |
3 |
458.26 |
32.73268 |
76.3762616 |
0.327327 |
0.458258 |
8 |
2 |
400.00 |
25 |
100 |
0.285714 |
0.4 |
9 |
1 |
300.00 |
16.66667 |
150 |
0.214286 |
0.3 |
10 |
0 |
0.00 |
0 |
- |
0 |
- |
The components of table can be described as follows:
U = 100*sqrt(xy)
And substituting the quantities of x and y.
And substituting the quantities of x and y.
The green color shows the maximum total utility that can be attained by Lucy for given set of possible quantities. At maximum total utility, the number of carpets demanded are 5 and number of paintings are 5.