Marginal Utility, and Costs

Marginal utility decisions

$1$

$.$

$$Suppose Maria's preferences for eggs and milk can be described by the following marginal utility schedules. Both eggs and milk cost $

$2$

; Maria has allocated $

$12$

$$to the purchase of these two products. Show the MU

$/$

P values.

$$ Eggs MU

$/$

P Milk MU

$/$

P

Units of Product Marginal Utility Marginal Utility

First

$2436$

$$

Second

$2030$

$$

Third

$1624$

$$

Fourth

$1218$

$$

Fifth

$812$

$$

Sixth

$46$

$$

a

$.$

$$How should Maria allocate her $

$12$

$$between eggs and milk so as to achieve maximum utility?

b

$.$

$$Suppose the price of milk rises to $

$3$

$.$

$$What amounts of eggs and milk maximize her utility at the new price of milk?

$2$

$.$

$$Suppose Susan's preferences for Diet Coke and Ice Cream can be described by the following marginal utility schedules. Both Diet Coke and Ice Cream cost $

$4\mathrm{.}50$

; Susan has allocated $

$27$

$$to the purchase of these two products. Show the MU

$/$

P values.

$$ Diet Coke MU

$/$

P Ice Cream MU

$/$

P

Units of Product Marginal Utility Marginal Utility

First

$6345$

$$

Second

$4536$

$$

Third

$2727$

$$

Fourth

$918$

$$

Fifth

$4\mathrm{.}59$

$$

Sixth

$00$

$$

a

$.$

$$How should Susan allocate her $

$27$

$$between Diet Coke and Ice Cream so as to achieve maximum utility?

b

$.$

$$Suppose the price of Diet Coke falls to $

$3$

$.$

$$What amounts of Diet Coke and Ice Cream maximize her utility at the new price of Diet Coke?

Cost formulas and problems

$1$

$.$

$$Write down the formulas for:

a

$.$

$$Total Costs:

b

$.$

$$Average Total Costs

$($

both formulas

$)$

:

c

$.$

$$Average Fixed Costs:

d

$.$

$$Average Variable Costs:

e

$.$

$$Marginal Costs:

f

$.$

$$Total Revenue:

g

$.$

$$Profit:

$2$

$.$

$$The BeachBum Water Ski Company manufactures skis for beginners and more advanced skiers. Variable costs are listed in the table below. Fixed costs are $

$100$

$.$

$$Fill in the table below for Fixed Costs, Total Costs, Average Variable Costs, Average Total Cost, and Marginal Cost.

Quantity Variable Cost Fixed Cost Total Cost Average Variable Cost Average Total Cost Marginal Cost Marginal Revenue Total Revenue Profit

$00$

$$

$1$

$$$

$10200$

$$

$2$

$$$

$25300$

$$

$3$

$$$

$45350$

$$

$4$

$$$

$70375$

$$

$5$

$$$

$100395$

$$

$6$

$$$

$135410$

$$

$$Based on your answers in the above table,

a

$.$

$$What is the company

$$

s optimal level of production?

b

$.$

$$What is the company

$$

s profit?

c

$.$

$$How can you tell at a glance what quantity to select?