Ten villagers graze cows in a common field. It costs $10 to buy a c produces. With c cows grazing on the field, total value ("benefit") of their milk is 100c¹2 (hence the total value of milk per cow is 100cc). The total benefit is increasing in c (upward sloping) because each additional cow generates revenue (which goes to the villager who owns the cow) but the slope is decreasing c because for every additional cow in the field, there is less grass available for the other cows, who therefore won't produce as much milk. The marginal revenue ("benefit") per additional cow grazing on the field is 50c 12 a. How many cows should the village raise to maximize total profits (i.e., what is the optimal c*?)?

Ten villagers graze cows in a common field. It costs $10 to buy a c produces. With c cows grazing on the field, total value ("benefit") of their milk is 100c¹2 (hence the total value of milk per cow is 100cc). The total benefit is increasing in c (upward sloping) because each additional cow generates revenue (which goes to the villager who owns the cow) but the slope is decreasing c because for every additional cow in the field, there is less grass available for the other cows, who therefore won't produce as much milk. The marginal revenue ("benefit") per additional cow grazing on the field is 50c 12 a. How many cows should the village raise to maximize total profits (i.e., what is the optimal c*?)?

Exploring Economics

8th Edition

ISBN:9781544336329

Author:Robert L. Sexton

Publisher:Robert L. Sexton

Chapter2: Economics: Eight Powerful Ideas

Section: Chapter Questions

Problem 19P

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