-The table above gives the utility from pens and pencils. If the consumer has an income of $4, pens cost $1, and pencils cost $.20, what is the consumer's total utility when he or she maximizes utility?
A) 374
B) 225
C) 405
D) 365

Question

-The table above gives the utility from pens and pencils. If the consumer has an income of $4, pens cost $1, and pencils cost $.20, what is the consumer's total utility when he or she maximizes utility?
A) 374 
B) 225 
C) 405 
D) 365

Quizplus · Accepted Answer

The consumer's budget constraint is 4 = p + 0.20q, where p is the price of pens and q is the quantity of pencils. The consumer's utility function is u = 10p + 5q. To maximize utility, the consumer will choose the combination of pens and pencils that gives the highest value of u subject to the budget constraint.To do this, we can solve the budget constraint for p: p = 4 - 0.20q. We can then substitute this expression for p into the utility function: u = 10(4 - 0.20q) + 5q = 40 - 2q + 5q = 40 + 3q.To find the value of q that maximizes u, we can take the derivative of u with respect to q and set it equal to zero: du/dq = 3 = 0. This implies that q = 1.We can then substitute this value of q back into the budget constraint to find the value of p: p = 4 - 0.20(1) = 3.80.Therefore, the consumer's total utility when he or she maximizes utility is u = 10p + 5q = 10(3.80) + 5(1) = 374.

-The Table Above Gives the Utility from Pens and Pencils