Question

In the good old times, Old McDonald’s farm produced unprocessed tomato exclusively. Every year, the farm produced 100,000 tons and sold it at a profit margin of $2.1 per ton. In January 1998, Old MacDonald decided to start exporting processed tomato (tomato pulp) to Europe. At that time, the price of tomato pulp was $6 per ton.

In order to produce tomato pulp, Old McDonald bought a machine capable of processing 100,000 tons per year. The machine cost $200,000 and was paid for with retained earnings that had been earning a rate of return of 8% per year. The machine had a useful life-time of 2 years - at the end of the first year the machine’s market value drops to $50,000 and then to zero at the send of the second year. In addition to the machine cost, there is a $2.2 per ton of labor cost (for harvesting and processing).

1. (a) Calculate the opportunity cost (or user cost of capital) for the machine in the first year of operation.

2. (b) Calculate average cost, marginal cost and profit margin in the first year of operation.

3. (c) Did Old McDonald make a profitable decision to switch from selling tomatoes to tomato

   pulp?

A few months later there was some bad news for Old McDonald. In December of 1998, the European Union increased its tariff on imported tomato pulp, implying that the net price received by American exporters is now only $5 per ton. An accounting consultant advices Old McDonald to sell the machine right away and go back to producing unprocessed tomatoes. Old McDonald needs to decide if to take the advice or not.

4. (d) What advice would you give Old McDonald as an economist? (Hint: Calculate the economic profit/loss, remembering to account for the opportunity cost of keeping or selling the machine.)

5. (e) Would you change your advice if the price of unprocessed tomato were expected to be $.50 per ton higher that described above? Show your calculations.

Answer 1

1. The opportunity cost (or the user cost of capital) of the machine in the first year of operation is the sum of cost of capital and the fall in the asset's value Opportunity cost- Cost of capital + Fall in the value of machine Machine's value in the beginning of year -Machine's value at the end of year - Cost of capital+ (8% of $200,000)-($200,000-$50,000) = $ 16,000 + $150,000 - S166,000 2. Calculate average cost, marginal cost and profit margin as follows: Total cost in the first year Number of units Average cost per ton in the first year- Opportunity cost for machine + Labor cost Number of tons produced S166,000 +($2.20x100,000) 100,000 $166,000 + $220,000 100,000 $3.86 - $3.86 Marginal cost per ton in the first year Per unit labor cost S2.20 Profit margin = Revenue per unit-Average cost - $6.00- $3.86 - $2.14 3. The profit margin from unprocessed tomatoes is $2.10. In the business of processed tomatoes, the profit margin is higher at S2.14. Hence, the company made a profitable decision to switch from selling tomatoes to tomato pulp 4. Calculate the opportunity cost of machine in the second year

Opportunity cost- Cost of capital + Fall in the value of machine Machine's value in the beginning of second year achine's value at the end of second year - Cost of capital+ (8% of $50,000)-($ 50.000-$0) - $4,000+ $50,000 - $54,000 Calculate average cost in the second year as follows Total cost in the second year Number of units Average cost per ton in the second year- Opportunity cost for machine + Labor cost Number of tons produced $54,000+ (S2.20x100,000) 100,000 S54,000+$220,000 100,000 - $2.74 Profit margin- Revenue per unit in second year - Average cost in second year $5.00- $2.74 - $2.26 (S5.00- $2.74)x100,000 - $2.26x100,000 - $226,000 Economic profit Since the profit margin in the business of tomato pulp is higher in the second year despite the fall in net price, the company should not go back to selling unprocessed tomatoes and should keep selling tomato pulp 5. The profit margin from unprocessed tomatoes was $2.10. If price of unprocessed tomato rises by $0.50, then the profit margin from unprocessed tomatoes will be $2.60 (-$2.10 + S0.50). As known from the solution to the previous part, in the second year, the profit margin in the business of processed tomatoes is lower than this at $2.26. This means that if the price of unprocessed tomatoes were expected to be S0.50 higher, then the company should go back to producing unprocessed tomatoes