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

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1 AAE 320 Spring 2013 Exam #1 Name: KEY 1) (5 pts.) True or False? Mark your answer. a) T F_X_ In Strategic Management, a mission and goal are the same thing. b) T F_X_ Someday I d like to have some land in Columbia County is an example of a goal as defined by Strategic Management. c) T_X F According to the research discussed in class, Ag Business undergrads generally underestimate the importance of internships and leadership experiences for increasing their starting salary. d) T F_X_ Wisconsin has many farms and most of them are large enough to generate over $250,000 in revenue annually. e) T F_X The Flat Objection Problem discussed in class argues that farmers over use input such as fertilizer and pesticides to reduce or flatten objections. 2) (10 pts.) You manage a farm and hire labor to sell manure. This table reports how many bags can be filled and ready for sale in one hour with different numbers of laborers. Laborers Hired Manure Bags/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. MP = Q/ X = (44 20)/(3 1 ) = 24/2 = 12 b) Bags of manure sell for $2.00 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. VMP = P x MP = 2.00 x 12 = $24.00 c) What optimality condition defines the profit maximizing amount of the input to use? (Be brief and to the point.) VMP = r, the cost of the input d) If wages, taxes, materials, etc. cost you $14.00/hour to hire a laborer, what is the profit maximizing number of laborers to hire? (You may need to interpolate between entries.) VMP = r at a number of laborers between 5 and 7. The simple average of $16 and $12 is $14, which is the cost of laborers (r), so go with the average of 5 and 7 or 6 laborers.

2 3) (15 pts.) Apple production as a function of the number of beehives is A = H 0.1H 2, where yield A is pounds of apples per tree and H is the number of beehives per tree. The sale price of apples is $4/pound and the price to rent a beehive is $118. a) What is the economically optimal number of beehives (H) to rent? Set up and solve this economic problem using calculus and this information. Check the second order condition. Set up: π = 4( H 0.1H 2 ) 118H FOC: dπ/dh = 4(30 0.2H) 118 = 0 Solve FOC for H o H = 118/4 = 29.5 o 0.5 = 0.2H o H = 0.5/0.2 = 2.5 Optimal H is 2.5 Hives SOC d 2 π/dh 2 = 4( 0.2) = 0.8 < 0 SOC for maximum satisfied b) When renting this number of beehives, what is apple production (A) in pounds per tree? A = H 0.1H 2 = (2.5) 0.1(2.5 2 ) = c) Besides beehive rental, the other fixed costs of managing a tree are $1800 per tree. What are net returns in dollars per tree? π = 4(674.4) 118(2.5) 1800 = =

3 4) (10 pts.) Chicks starting at 8 oz fed the following corn and soybean meal rations gain 40 oz and are ready to butcher and sell as broilers in 12 weeks. Corn (lbs) Soybean Meal (lbs) Marginal Rate of Technical Substitution Corn as X Corn as Y 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. Treating Corn as X: MRTS = Y/ X = ( )/( ) = 2.0 Treating Corn as Y: MRTS = Y/ X = ( )/( ) = 0.5 b) What optimality condition defines the profit maximizing amount of both inputs to use? (Be brief and to the point.) Use X and Y where MRTS =price ratio, or Y/ X = r X /r Y c) If corn cost $0.12/lb and soybean meal costs $0.16/lb, what is the profit maximizing level of each to feed? (Note: you may need to interpolate between entries.) Treating Corn as X: r X /r Y = 0.12/0.16 = 0.75 Treating Corn as Y: r X /r Y = 0.16/0.12 = 1.33 In either case, this occurs in the table when corn = 5.2 lbs and soybean meal = 4.0 lbs

4 5) (20 pts.) Apple production is A = L 200L N 2N 2 0.2LN, where A is apple production as pounds per tree, L is the lime applied in tons per acre and N is the nitrogen fertilizer rate in pounds per acre. The apple price is $4 per pound, the price of lime is $120 per ton and the price of nitrogen fertilizer is $0.60/lb. What is the profit maximizing amount of lime (L) and nitrogen (N) to use per acre to grow apples? (Note: you will not need to convert prices to set up the profit function.) Be sure to check the second order conditions. Set up: π = 4( L 200L N 2N 2 0.2LN) 120L 0.6N FOCs: o dπ/dl = 4( L 0.2N) 120 = 0 o dπ/dn = 4(50 4N 0.2L) 0.6 = 0 Solve FOCs for L and N any way you want, one example below o Solve FOC 1 for N o L 0.2N = 30 o L = 0.2N o N = L o Substitute this into FOC2 and solve for L o 4(50 4N 0.2L) = 0.6 o 50 4N 0.2L = 0.15 o 50 4( L) 0.2L = 0.15 o L 0.2L = 0.15 o L = 0.15 o L = o L = / = L = Optimal L is tons o Use N = L and this L to find N o N = L = (0.1688) o N = 12.4 Optimal N = 12.4 lbs SOC o d 2 π/dl 2 = 4( 400) = 1600 < 0 SOC for maximum satisfied o d 2 π/dn 2 = 4( 4) = 16 < 0 SOC for maximum satisfied o d 2 π/dldn = 4( 0.2) = 0.8 < 0 o 1600( 16) ( ) = > 0 SOC for maximum satisfied

5 6) (10 pts.) Currently you own and operate a small acreage, plus hold a regular job. Your typical annual farm revenue is $60,000 and annual operating costs are $40,000, plus you pay an additional $2,500 for the mortgage. Your farm s market value is $100,000, but you still owe $50,000 for the mortgage. You are thinking about alternatives to farming the land yourself. You think you could continue paying the mortgage costs of $2,500, but rent the land for $10,000 per year to a different farmer and increase your hours at your regular job to earn an extra $8,000. If you sold the land, you could invest your equity and earn 2% annually. a) Given these numbers, what is your economic profit for owning and operating the small acreage? Revenue 60,000 Operating Costs 40,000 Mortgage 2,500 Opportunity Cost of Time Rent given up 10,000 Job income given up 8,000 Opportunity Cost of Capital 50,000 2% 1,000 1,500 b) Based on these calculations, what is your best option and how much better is it in terms of $? These numbers imply that you are losing $1,500 per year in potential income by operating the farm yourself, so the best option would be to rent the land and earn more at work (hoping you were earning more than 2% on the land investment). c) Suppose you refinance the land mortgage and reduce your annual mortgage costs from $2,500 to $1,000. Now what is your best option and how much better is it in terms of $? If you refinanced, the mortgage payment for interest would drop to $1,500 and so you d have zero economic profit. In this case, either option is the best : run the land yourself or rent it out and work more at your regular job.

6 7) (15 pts.) The table below reports the cost of producing eggs on a farm. Eggs Fixed Variable Total Marginal Average Average (dozen/week) Cost Cost Cost Cost Variable Cost 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. TC = FC + VC = = 207 MC = TC/ Q = ( )/( ) = 0.78 AVC = VC/Q = 107/190 = 0.56 ATC = TC/Q = 207/190 = 1.09 b) What optimality condition defines the profit maximizing amount to produce? (Be brief and to the point.) P = MC c) If the farmer can sell eggs for a price of $0.88 per dozen, what is the profit maximizing number of eggs to produce? (Note: you may need to interpolate between entries.) P = MC at 207 dozen eggs d) At this price, is the farmer making a profit? How do you know? At this price, the farmer is losing money because the price is less than the ATC. Note that the price is above the AVC, so the farmer is better off continuing to sell eggs and covering part of the FC, otherwise he/she will lose all the fixed cost.

7 8) (10 pts.) The figure below illustrates Average Total Cost and Average Variable Cost for a hypothetical farm, where the two dots represent the minimum of each curve. a) (4 pts.) On the figure below, draw in a hypothetical marginal cost curve and clearly mark the profit maximizing supply curve the quantity the profit maximizing farm will produce at any given price. Clearly indicate the bottom end of the supply curve the lowest price a profit maximizing farm will operate at and the quantity it will supply. (Note that the points labeled A, B and C may not be and do not have to be on the profit maximizing supply curve you draw, but are for use in later questions.) Average Total Cost Price or Cost ($) A Average Variable Cost B C Supply curve in brown: passes through the two points that are the minimum of the ATC and avc curves. At minimum AVC, supply curve ends and jumps to the vertical axis, i.e., minimum of AVC is the lower end of the supply curve. This question concerns interpreting a farm s profit if it produced the output and input combinations implied by three price-quantity points labeled A, B, and C in the diagram above. Each point is an output sold by the farm as measured by the horizontal axis, at the price as measured by the vertical axis. b) (2 pts.) At point A, does the farm earn positive, negative or zero profit? Positive profit because price > ATC c) (2 pts.) At point B, does the farm earn positive, negative or zero profit? Negative profit because price < ATC d) (2 pts.) At point C, does the farm earn positive, negative or zero profit? Negative profit because price < ATC Output Q