c) What optimality condition defines the profit maximizing amount of the input to use? (Be brief and to the point.)

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1 AAE 320 Spring 2012 Exam #1 Name: 1) (5 pts.) True or False? Mark your answer. a) T F Wisconsin s cranberry industry is minor compared to other states. b) T F Setting the output price equal to the average marginal product is the optimality condition for finding maximum input use. c) T F In Wisconsin, about half of those whom the USDA classifies as farmers have less than $10,000 in revenue from selling agricultural products. d) T F In Wisconsin, the average farm size has remained fairly constant over the last 5 years. e) T F According to What it Takes to Be Great, it takes 3-5 years of deliberate practice for a person to become great at something like chess. 2) (10 pts.) You manage a melon farm and hire labor. This table reports how many watermelons can be picked and prepared for sale in one hour with different numbers of laborers. Laborers Hired Watermelon/Hour Marginal Product Value of Marginal Product a) Using numbers given in this table, show below how to calculate the Marginal Product for one example, and then fill in the Marginal Product column in the table above. b) Watermelons sell for $10.00 each. Using numbers from this table, show below how to calculate the Value of Marginal Product for one example, and then fill in the Value of Marginal Product column in the table above. c) What optimality condition defines the profit maximizing amount of the input to use? (Be brief and to the point.) d) If wages, taxes, materials, etc. cost you $25.00/hour to hire a laborer, what is the profit maximizing number of laborers to hire? (You may need to interpolate between entries.)

2 3) (15 pts.) Carrots as a function of potassium fertilizer is C = K 0.01K 2, where yield C is tons/ac of carrots and the potassium rate K is lbs/ac. The price of carrots is $100/ton and the price of potassium fertilizer is $0.50/lbs. a) What is the economically optimal potassium rate? Set up and solve this economic problem using calculus and the given information. Be sure to check the second order condition. b) At the potassium rate you derived in part a, what is yield (tons/ac)? c) Besides the cost of potassium, other fixed costs are $2000/ac. What are net returns ($/ac)?

3 4) (10 pts.) Pigs starting at 30 lbs fed the following corn and soybean meal rations gain 220 lbs and are ready to butcher and sell as fat hogs in 4.5 months. Corn (lbs) Soybean Meal (lbs) Marginal Rate of Technical Substitution a) Using numbers from this table, show below how to calculate the Marginal Rate of Technical Substitution between corn and soybean meal for the second row in the table and then fill in the missing entries in the table above. b) What optimality condition defines the profit maximizing amount of both inputs to use? (Be brief and to the point.) c) If corn cost $0.15/lb and soybean meal costs $0.30/lb, what is the profit maximizing level of each to feed? (Note: you may need to interpolate between entries.)

4 5) (20 pts.) Carrot production is C = 3 + 6K 0.6K 2 + 7N 0.5N 2 0.1KN, where C is carrot yield as tons/ac, K is the potassium fertilizer rate (lbs/ac) and N is the nitrogen fertilizer rate (lbs/ac). The carrot price is $100/ton, the price of potassium fertilizer is $0.50/lb, and the price of nitrogen fertilizer is $0.60/lb. What is the profit maximizing amount of potassium (K) and nitrogen (N) to use per acre to grow carrots? (Note: you will not need to convert prices to set up the profit function.) Be sure to check the second order conditions.

5 6) (10 pts.) You own and manage a farm. Your typical annual farm revenue is $380,000 and all annual costs are $320,000. Your farm s market value is $500,000, but you owe $300,000 for the mortgage. You are thinking about alternatives to farming for a living. You think you could get a job earning $45,000 nearby and could invest the farm equity and earn 3% annually. a) Given these numbers, what is your economic profit for owning and operating the farm? b) For this question, suppose in part a above you find that your economic profit as a farmer is negative, say $10,000. Explain what this means in terms of the income you earn. Specifically, does it mean your farm is not making any money?

6 7) (15 pts.) The table below reports the cost of producing mink for a farm. Minks Fixed Variable Total Marginal (mink/year) Cost Cost Cost Cost 900 5,000 83, ,000 91,000 1,070 5,000 99,000 1,140 5, ,000 Average Variable Cost Average Total Cost a) Using numbers from this table, show below how to calculate Total Cost, Marginal Cost, Average Variable Cost, and Average Total Cost for the second row and then fill in the missing values in the table. b) What optimality condition defines the profit maximizing amount to produce? (Be brief and to the point.) c) If the farmer can sell mink for a price of $100 for fur, what is the profit maximizing number of mink to produce? (Note: you may need to interpolate between entries.) d) If the farmer can sell mink for a price of $107 for fur, what is the profit maximizing number of mink to produce? (Note: you may need to interpolate between entries.)

7 8) (10 pts.) Short Answer: Answer each of the short questions below. a) (1 pt each) Classify each of the following as a Mission, a Strategy, or a Goal. i) To own and milk 500 dairy cows in Marathon County, WI within 3 years. ii) To earn a reasonable income as a dairy farmer. iii) To improve the land I farm and pass it on to my children better than when I bought it. iv) To pursue high volume/low margin production of commodity grains. v) To sign up 5 restaurants to directly buy grass-fed beef from my farm for one year. vi) To have a full-time job off farm and work evenings/weekends on my hobby farm. b) (2 pts.) Why would a profit maximizing farm choose to operate in the short run at a price below Average Total Cost and above Average Variable Cost? (Be brief and to the point.) c) (2 pts) Briefly explain what I call the Flat Objective Problem and what it means for input use in crop production.