Answer to Question #187738 in Microeconomics for Rida Awwal

Question

Given Utility function U=20Q-2Q^2, what quantity of good gives highest utility for the consumer? What will happened if the consumer obtains more quantity than the one you computed?

Answer 1

Utility(U)=$20Q-2Q^2$

1.Quantity of good that gives highest utility

For utility maximization we use  $\frac{\delta U}{\delta Q}$ and put $\frac{\delta U}{\delta Q}=0$

$\frac{\delta U}{\delta Q}$ =$20-4Q$

$-20=-4Q$

$Q=5$

2.The consumers utility is maximized at obtaining 5 units of the good beyond which the marginal utility becomes negative. This means the consumer will not get any additional satisfaction or enjoyment in obtaining more quantity of the good than the one obtained above