In: Economics
A consumer’s utility function is U = logx + logy2 , where and y are two consumption goods. The price of x is $2.00 per unit and the price of y $5.00 per unit. Her budget is $1000. Solve her utility maximization problem and find her optimal consumption of x and y. Will your answers change if the consumer’s utility function is U = logxy2 instead – why or why not?
When U= logx + logy2, using solver in excel where, setting utility to be maximised, changing quantities and keeping the Budget constraint to $1000 we get,
Price |
goods |
Quantities |
Budget |
Utility |
2 |
x |
92.16 |
184.33 |
|
5 |
y |
163.13 |
815.67 |
6.86 |
1000 |
When U= logxy2, using solver in excel where, setting utility to be maximised, changing quantities and keeping the Budget constraint to $1000 we get,
Price |
goods |
Quantities |
Budget |
Utility |
2 |
x |
166.67 |
333.33 |
|
5 |
y |
133.33 |
666.67 |
6.47 |
1000 |
Yes the quantities change as both equations are of different forms