Answer to Question #188194 in Microeconomics for Rida Awwal

Question

Given Utility function U=20Q-2Q^2what 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 is the satisfaction derived by any consumer by consuming a good or service.

$U=20Q-2Q^2$

U

For utility maximization find $\frac{dU}{dQ}$ put $\frac{dU}{dQ}=0$

$\frac{dU}{dQ}=20-4Q$

Now, $\frac{dU}{dQ}=0$

$20-4Q=0$

$20=4Q$

$Q=5$

Therefore, the 5 units would give the highest utility for the consumer.

If the consumer obtains more quantity than the 5 units then his marginal utility will become negative which means the additional utility from the consumption of additional units of the good will be negative for the consumer. The negative marginal utility of the consumer will decrease its total utility and result in a reduction in the satisfaction of the consumer.