Exploring the Equimarginal Principle

12. A housewife is buying four 12 ounce cans of peas for \$.60 each and three 16 ounce cans for \$.72 each. Using the equimarginal principle, determine if she is minimizing her costs of buying peas. If she is not, explain how she can shift her money to increase the amount of peas without spending more.

13. Hans Fruehstueck has \$1.00 to spend on breakfast. He must decide how many donuts and cups of coffee to buy. The utility these items give him is shown in the table below:

 Number Utility of Donuts Utility of Coffee 1 5 10 2 10 13 3 14 15 4 16 16
a) Construct a table showing the utility function similar to that in the readings, and decide what Hans should do if coffee and donuts both cost \$.25.
b) If coffee and donuts both cost \$.25, construct a table showing costs and benefits similar to that in the readings and find how many donuts he will buy by computing the marginal cost and marginal benefit of buying donuts.
c) Construct a table similar to that which the readings used to illustrate the equimarginal principle and show how it tells you what Hans should do.
d) How will you find Hans' new best position using the methods of parts a, b, and c if the price of donuts rises to \$.50? If he only has \$.75 to spend?

14. Suppose that Robinson Crusoe, isolated on his island, has figured a way to measure his utility. He has only two goods to consume, Bananas and Fish. (Ignore Coconuts for this part of the questions.) The table below shows how bananas and coconuts provide him utility:

 Coconuts Bananas Fish Number Total Utility Marginal U MU/Cost Total Utility Marginal U MU/Cost Total Utility Marginal U MU/Cost 0 0 . . 0 . . 0 . . 1 (first) 9 . . 7 . . 10 . . 2 (second) 17 . . 13 . . 20 . . 3 (third) 19 . . 19 . . 22 . . 4 (fourth) 20 . . 23 . . 22 . . 5 (fifth) 20 . . 24 . . 21 . .

a) Each item costs him two hours of effort and he has ten hours of effort to spend. How many of each will he consume? Explain how you get your answer.
b) Suppose he now discovers that coconuts grow on his island. The utility they provide is shown above. Gathering a coconut also takes two hours and he still has ten hours of effort to spend. How many of each will he consume? Explain how you get your answer.
c) Suppose bananas drop in price so they only require one hour of effort to obtain. How will he now use his time to maximize his utility? Explain how you get your answer.

15. The average number of yards gained on a pass play in the NFL is greater than the average number of yards gained on a rushing play. Does this indicate that teams should use more passing and less running than they are currently using? Explain.

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