Consider a shrimp restaurant at Fisherman’s Wharf in San Fransisco. The chef at the restaurant chooses whether to use farm-raised or wild-caught shrimp to produce the main dish – shrimp balls. Suppose the price per shrimp is $0.25 for farm-raised shrimp and $0.50 for wild-caught shrimp. Furthermore, suppose that one farm-raised shrimp contains enough meat to produce one shrimp ball while wild-caught shrimp are half the size of their farm-raised brethren – thus two wild-caught shrimp are required to produce one shrimp ball. The meat from the two types of shrimp is perfectly substitutable. For each of the following, put farm-raised shrimp on the horizontal axis and wild-caught on the vertical.
(a) Draw the $5 isocost line.
(b) Draw the ten shrimp ball isoquant curve. Add to this graph the lowest cost isocost line corresponding to the cheapest combination of inputs to produce ten shrimp balls – how many wild-caught and farm-raised shrimp will the chef use to produce ten shrimp balls? What will be the cost?
(c) Suppose the rent for the restaurant is $2,500. What is the chef’s cost function for shrimp balls?
(d) Suppose farm-raised shrimp are found to pollute the water in the region where they are farmed. As a result, the local government imposes a tax of $1 per farm-raised shrimp, which the restaurant must pay when purchasing farm-raised shrimp. Thus the price of farm-raised shrimp becomes $1.25. What is the restaurant’s new cost function?