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Charlie's Cherries grows and sells cherries on a small farm

Economics Dec 12, 2020

Charlie's Cherries grows and sells cherries on a small farm. Next door, Frank's Fish Farm grows rainbow trout in small, manmade ponds. Occasionally, the ponds must be drained and refilled. The wastewater from the ponds is perfect for watering Charlie's cherry trees. The cost of producing a pound of fish is given by cf(F) = cto so the marginal cost is MC-(F) = 0.20F. The cost of producing a pound of cherries is given by ccC) = dio- F so the marginal cost is MCCCC) = 0.200. If the two goods were produced by a single firm the cost would be aC,F) = çifo+ fo- F. The marginal cost of producing a pound of cherries in this scenario is as before, or MCCC) = 0.20C. The marginal cost of producing a pound of fish, on the other hand, has an extra term included now and is given by MCAF) = 0.20F - 1. Both firms sell their products in a competitive market where the price of cherries is $4 per pound and rainbow trout are $12 per pound. V 1st attempt Part 1 (2 points) See Hint If Charlie and Frank both operate independently, Charlie will produce pounds of cherries and Frank will produce pounds of rainbow trout in equilibrium. Give your answers to two decimal places. Part 2 (2 points) See Hint Suppose Charlie and Frank decide to merge their operations. They form a new company called Chank's Cherries and Rainbows. If Chank's is profit maximizing, it will produce pounds of cherries and pounds of rainbow trout. Give your answers to two decimal places.

Expert Solution

Marginal cost of cherry for Charlie = 0.20C

Marginal cost of fish for Frank = 0.20F

Price of cherries = $4

Price of fish = $12

(a) In perfect competition, p = MC

For cherry, 0.20C = 4 which gives C = 20 pounds

For fish, 0.20F =  12 which gives F = 60 pounds

(b) If they merge the compnay, water from fishery can be used for watering cherry and new cost structure would be :

Marginal cost of cherry for Charlie = 0.20C

Marginal cost of fish for Frank = 0.20F - 1

In perfect competition, p = MC

For cherry, 0.20C = 4 which gives C = 20 pounds

For fish, 0.20F - 1 =  12 which gives F = 65 pounds

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