Question

+ A consumer finds only three products, X, Y, and Z are for sale. The amount of which the consumption will yield is shown in the table below. Assume that the prices of X Y and are $10.32 and S8, respectively, and that the consumer has an income of $74 to spend Product X Product Y Product (Price $10) (Price $2) (Price $8) Marginal Utility per $ 4.2 Marginal Utility per $ Marginal Utility pers Quantity Utility Quantity Utility Quantity Utility 1.0 40 4.0 25 (a) Complete the table by computing the marginal utility per dollar for successive units of X, Y, and Z to one or two decimal places. Remember the marginal utility per dollar would be calculated by first getting the marginal utility which is the change in utility as quantity increases and then dividing it by the price. When doing Quantity 1 you are going from 0 units to 1 unit. The utility for units would be so (b) How many units of X, Y. and Z will the consumer buy when maximizing utility and spending all income? Show this result using the utility maximization formula. (Meaning they need to spend all of their income of $74) (c) Why would the consumer not be maximizing utility by purchasing 2 units of X, 4 units of Y, and 1 unit of Z?

Answer 1

ANSWER a. It is correctly done in the table.

MUn=TUn-TUn-1

MUx/Px= Marginal utility per dollar

b. Utility maximizing combination of X,Y and Z is where marginal utility per dollar is equal for all goods X, Y and Z.

X= 4 units

Y= 5 units

Z= 3 units

As Marginal utility per dollar is equal to 3.

Also, it satisfy the budget constraint:

4*10+5*2+3*8= 40+10+24= $74 which is equal to the income.

c. When X= 2 units

Y= 4 Units

Z= 1 Unit

2*10+4*2+1*8= 20+8+8= $36< $74 income.

Consumer is not maximizing utility in the above case as the consumer is not satisfying the budget constraint. The consumer can afford to consume more of each good.

So it is not utility maximizing choice.