StudySpace: Economics in Development, 6th Edition

Worked Example: Farm Production Decisions

Standard microeconomic tools provide insight into farm production decisions and the effects of price changes. Consider a representative farmer in Basmati who owns 1 hectare (about 2¹/2 acres) of land for growing rice. The first three columns of Table 16–1 show for various amounts of chemical fertilizer (F), the required labor input (L), and the corresponding quantity of rice output (Q). Figure 16–1 portrays this technical relationship as a rice-fertilizer production function. The graph clearly shows diminishing returns to successive increments of F input.

FIGURE 16–1

Click here for Table 16-1

Technically, the seed variety being used can yield as much as 3,600 kilograms of rice per hectare. But the actual yield achieved by the farmer is an economic decision that depends on prices as well as technical conditions. Suppose that the price of fertilizer is PF = 3 rupees per kilogram, the price of rice is PR = l rupee per kilogram, and the price of labor is PL = 200 rupees per worker. At these prices, the cost of production (C), the value of output (V ), and the farmer’s net income

(Y ) can be calculated for each level of fertilizer usage. The results are shown in columns 4, 5, and 6 of Table 16–1. As can be seen, the maximum income level of Y^* = 800 rupees is achieved when F^* = 200 kilograms of fertilizer are used; it yields Q^* = 3,000 kilograms of rice. The farmer will choose to operate at point A in Figure 16–1, even though higher yields are feasible.

Has the extension worker failed to convince the farmer to use the “best” cultivation method? No. Agronomists must recognize that farmers will add fertilizer only up to the point where the extra costs are offset by the extra value of rice output. Columns 7 and 8 of Table 16–1 show the incremental cost (ΔV) for each successive 50 kilogram dose of fertilizer. These data clarify the basis for the farmer’s decision. Beyond F^* = 200 kilogram, incremental costs exceed the value of the extra rice output.

This analysis can be restated in the familiar framework of marginal cost (MC) and marginal revenue (MR), defined with respect to Q. The marginal revenue for successive units of rice output is simply PR = 1 rupee per kilogram. The marginal cost for successive units of output can be calculated as follows. The 700 kilograms of extra rice produced when F goes from 0 to 50 are obtained at an incremental cost of 350 rupees. So for this range of rice output, MC = 350/700 = 0.50 rupees per kilogram. Similarly, when F increases from 50 to 100, Q increases by 600 kilograms (from 1,500 to 2,100 kilograms) while costs rise by 350 rupees. So MC = 350/600 = 0.58 rupees per kilogram. Proceeding in this way, one obtains the MC curve shown in Figure 16–2, along with the MR curve.

FIGURE 16-2

The level of output that maximizes net income is Q^* = 3,000 kilogram, as before. This, of course, is the point where MC = MR.

Two concluding remarks: First, if all rice output were marketed, the MC curve would represent the supply curve for the representative farmer in Basmati. You can see that Q increases as a function of PR. Aggregation across farmers would generate a standard market supply curve. Second, the effect of prices on the quantity supplied is even more pronounced if one considers that the acreage devoted to rice and the share of rice output that gets marketed will both be positive functions of the market price.

Exercises

1. Now, it is your turn to analyze farm production decisions and price effects. This exercise builds upon the Worked Example, so be sure you have read it carefully.

a. Let’s redo the Worked Example using a rice price of PR = 2 rupees per kilogram, while keeping the price of fertilizer at PF = 3 rupees per kilogram and the price of labor at PL = 200 rupees per worker.

Click here for Table 16-2

(i) Table 16–2 has a format similar to that of Table 16–1. The numbers in the first three columns, which summarize the production technology, are identical. Fill in all of the blanks in Table 16–2. Some of the numbers are provided to help you with your calculations. Keep in mind that ΔC and ΔV refer, respectively, to the increase in production cost and the increase in output value per incremental 50 kilogram dose of fertilizer.

(ii) When PR changes from 1 rupee to 2 rupees, would any shifts occur in the curves shown in Figures 16–1 and 16–2? Explain.

(iii) With PR = 2 rupees per kilogram, the income-maximizing farmer in Basmati would choose to produce an output of

Q' = kg of rice,

using F' = kg of fertilizer.

The farmer’s net income in this case would be

Y' = Rs .

(Note: By drawing the new MR line in Figure 16–2 you can confirm your result, using the MC = MR rule.)

b. To see the effects of increasing the price of rice from 1 rupee to 2 rupees, compare the outcome in part a with the outcome in the Worked Example.

(i)  As a result of the higher price of rice, the income-maximizing farmer in Basmati increases output by kilograms, or percent.

(ii) After adjusting to the high price, the farmer’s net income will increase by rupees, or percent.

(iii) Suppose that the average farmer markets rice output only in excess of 1,500 kilograms—the amount needed for family consumption. Then, the increase in PR to 2 rupees would expand the quantity of rice supplied by the average farmer to the market from to kilograms, an increase of percent.

(iv) Think about the rural labor market. Will the increase in the price of rice affect the demand curve for farm labor? What about the labor supply curve? What does this imply about the average wage for farm workers? Explain.

(v) How will the farmer’s outcome be affected by these changes in the rural labor market?

c. Return now to the original rice price of PR = 1 rupee but now suppose that the price of fertilizer is cut in half, to PF = l.5 rupees.

(i) Table 16–3 is similar to Table 16–1, but for simplicity columns 7 and 8 have been omitted. The numbers in the first three columns of Table 16–3 are identical to those in Table 16–1. Given the new price of subsidized fertilizer, fill in the blanks in Table 16–3.

Click here for Table16-3

(ii) With PF = 1.5 rupees, the income-maximizing farmer in Basmati would choose to produce an output of

Q'' = kg of rice,

using F'' = kg of fertilizer.

The farmer’s net income in this case would be

Y'' = Rs .

(iii) Explain how the effects of this fertilizer subsidy would alter Figures 16–1 and 16–2.

Before proceeding, think about the important insights that one gains from applying basic microeconomics tools to a farm enterprise—insights about price effects on food supplies and rural incomes.

2. Now let’s introduce a technical innovation, along with risk considerations.

a. The Basmati Agricultural Research Farm (never referred to by acronym) develops a new variety of rice seed that is far more responsive to fertilizer. Specifically, for each level of fertilizer use in Table 16–1, the new seed variety doubles output. The new technology also doubles the required labor input for each level of fertilizer use.

(i) On the basis of this technological information about the new biological package, fill in the blanks in columns 2 and 3 of Table 16–4.

(ii) Assuming that prices initially are the same as in the Worked Exercise (so PR = Rs1, PF = Rs3, and PL = Rs200), fill in the blanks in columns 4, 5, and 6 of Table 16–4.

(iii) Using this new variety of rice seed, the income-maximizing farmer in Basmati would choose to produce an output of

Q^* = kg of rice,

using F^* = kg of fertilizer.

The farmer’s net income (if all the output were marketed) would be Y^* = Rs .

Click here for Table16-4

b. Unhappily, this is not the whole story. In normal years farmers can expect to realize the outcome Q^* and Y^* as just calculated. But the new rice variety is highly susceptible to a periodic plant disease. When this plant disease strikes, farmers using new seeds lose 2,000 rupees because income from the poor crop does not cover the cost of fertilizer, planting, and weeding.

(i) The plant disease strikes one year out of four, on average. A farmer’s expected income with the new variety of rice is Ye = rupees. (Hint: Expected income, here, equals average income over the four-year cycle.)

(ii) Your calculations should show that expected income from using the new seed variety (Ye) still exceeds the income generated with traditional seeds (which is 800 rupees, from the Worked Example), despite the plant disease problem. Considering risk as well as income, should one expect poor peasant farmers to adopt eagerly the new variety of rice? Explain.

c. Agronomists then develop an even better seed that is not susceptible to plant disease. Even so, problems with the rural infrastructure may block successful introduction of the new variety of rice.

(i) How can problems with rural credit block the successful introduction of the new variety of rice?

(ii) How can problems with rural roads block the successful introduction of the new variety of rice?

(iii) How can problems with rural extension services block the successful introduction of the new variety of rice?

 

3. This exercise investigates one more variation on the Worked Example: the effect of land tenure arrangements. You will need to refer repeatedly to the data in columns 1 through 6 of Table 16–1 for background information.

a. The income figures in column 6 of Table 16–1 implicitly assume that rice farmers are independent proprietors. Suppose, instead, that the farmers are sharecroppers who must pay 25 percent of their gross harvest as rent to the landlords, while bearing the full burden of paying input costs.

Click here for Table 16-5

(i) For each level of output shown in Table 16–5, calculate the net income retained by the sharecrop farmer after paying the landlord. Place your answers in the column labeled Sharecrop farmer. [Hint: Y = V(0.75) – C.]

(ii) What amounts of F and Q will be chosen by the sharecropper to maximize net income (after share payments to the landlord)?

F = kg of fertilizer.

Q = kg of rice.

(iii) You should have found that the sharecropper chooses less F and less Q than the independent proprietor. With reference to marginal revenue and marginal cost as shown in Figure 16–2, why does this difference occur?

(iv) Whose production decision is more efficient—the sharecropper or the independent proprietor? Briefly explain.

b. Instead of paying the landlord a fixed share of the crop, suppose that the farmer is a tenant who pays the landlord a fixed sum of 400 rupees.

(i) Calculate the net income retained by the tenant farmer for each output level shown in Table 16–5. Place your answers in the column labeled Tenant farmer. [Hint: Y = V – (C + 400).]

(ii) What amounts of F and Q will be chosen by the tenant farmer to maximize net income (after rent payments to the landlord)?

F = kg of fertilizer.

Q = kg of rice.

(iii) You should have found that the tenant chooses the same levels of F and Q as the independent proprietor. Use the analysis of marginal cost and marginal revenue conditions summarized in Figure 16–2 to explain why these two different land tenure arrangements lead to the same outcome.

c. Think again about the logic underlying Figure 16–2. What would be the effect on the sharecropper’s production decision if the landlord paid 25 percent of the input costs, as well as receiving 25 percent of the gross crop?

4. This exercise uses supply-and-demand analysis to study the effects of food price controls and subsidies. Curves Dr and Sr in Figure 16–3 are the retail market demand and supply curves for grain in the Republic of Nafaka. Curve Sf shows the farm-gate supply curve. As discussed in the text, marketing costs account for the vertical gap between Sf and Sr.

In the absence of government intervention, curves Dr and Sr establish the equilibrium price in the retail market at P0 = N$1.00 per kilogram of grain. (N$ stands for the Nafaka dollar, which is worth U.S.$0.50.) The equilibrium quantity is Q0 = 200 million kilograms of grain. Curve Sf shows that the price paid to farmers for supplying quantity Q0 is P1 = N$0.60 per kilogram. So the marketing cost of moving food from the farm gate to the retail consumer is C0 = N$0.40 per kilogram of grain.

a. Now the government of Nafaka imposes price controls: Grain must be sold in the retail market for P^* = N$0.80 per kilogram.

(i) From curve Dr you can see that the retail quantity demanded at price P^* is

Q1 = million kg of grain.

(ii) The traders still incur marketing costs of C0 = N$0.40. After these costs are deducted from the retail price, farmers receive

P2 = N$ per kg of grain.

FIGURE 16-3

(iii) At this price, farmers are willing to supply to the market only

Q2 = million kg of grain.

(iv) Consequently, a shortage (excess demand) emerges in the retail market of

Q1– Q2 = million kg of grain.

b. With the price control in effect, the government has three options for handling the excess demand. First, the government can simply live with the shortage. Second, it can import grain to satisfy the excess demand.

(i) To satisfy the excess demand created by the price controls, the government has to import Qm = million kilograms of grain. If the world price of grain is U.S.$0.50 = N$1 per kilogram, these imports entail a foreign exchange cost of U.S.$ million.

(ii) In domestic-currency terms, the government would be buying imported grain for N$1.00 per kilogram and selling it to consumers for P^* = N$0.80. So the government would be providing a subsidy to consumers of S0 = N$ per kilogram of imported grain. Altogether this subsidy would cost the government

Qm ×S0 = N$ million.

c. Alternatively, the government can eliminate the shortage by raising farm prices enough to induce domestic grain production that will match demand at Q1.

(i) Curve Sf shows that domestic farmers will increase output to Q1 only if they are paid

P3 = N$ per kg.

Adding in marketing costs, the total procurement price of grain would have to be

P4= P3+ C0 = N$ per kg.

(ii) If it pays P4 per kilogram of grain and then sells the grain for P^*= N$0.80, the government provides a subsidy of S1 = N$ per kilogram of grain produced and consumed. The total cost of the subsidy to the government is

Q1 ×S1 = N$ million.

(iii) Compare the two policies—boosting farm prices versus covering the shortage with imports—in terms of budget costs.

(iv) Compare the two policies in terms of their effect on incentives for agricultural development in Nafaka.

5. This exercise uses isoquant analysis to examine how factor productivity in agriculture can depend on factor endowments. North Nasi and South Nasi are identical in terms of land fertility and farmers’ capabilities. They have the same agricultural technology, as depicted in Figure 16–4. Isoquant QQ shows the alternative combinations of land (D) and labor (L) that can be used to produce 10 tons of rice. For simplicity, we ignore other inputs, such as capital and fertilizer.

a. In other ways, the two countries do differ. In North Nasi, the currency is the dollar, whereas South Nasi uses pesos. (You need not know the exchange rate.) Also, in North Nasi land is plentiful relative to the population. The annual rental cost of land is $200 per hectare, while the wage is $300 per year. South Nasi, in contrast, is heavily populated. There, the annual land rent is P1,800 per hectare, while wages are P300 per year.

(i) The optimal factor proportions for a farmer in North Nasi can be determined by finding the point on QQ that lies on the lowest possible isocost line. For a cost of C = $1,200, a farmer in North Nasi can afford hectares of land with zero labor, workers with zero land, or any other combination of L and D costing a total of $1,200.

(ii) In Figure 15–4, draw the C = $1,200 isocost line faced by a farmer in North Nasi.

(iii) You should find that the line is tangent to isoquant QQ. Label the point of tangency point N^*.

(iv) For a farmer in North Nasi, the optimal technique for producing 10 tons of rice involves the use of D = hectares of land, and L = workers.

(v) For farmers operating efficiently in North Nasi, land productivity is tons of rice per hectare; labor productivity is tons of rice per worker.

b. Now consider the optimal factor proportions for a farmer in South Nasi, where the wage is P300 and the land rent is P1,800 per hectare.

(i) In Figure 16–4, construct a few representative isocost lines for a farmer in South Nasi. (Hint: Try cost levels of P1,800 and P3,600.)

(ii) Find the point on isoquant QQ that is tangent to an isocost line for farmers in South Nasi. Label the point of tangency point S^*.

FIGURE 16-4

(iii) For a farmer in South Nasi, the optimal technique for producing 10 tons of rice involves the use of

D = hectares of land

L = workers.
(Hint: The answer involves only integers.)

(iv) For farmers operating efficiently in South Nasi, land productivity is tons of rice per hectare and labor productivity is tons of rice per worker.

c. Farmers in each country are adapting optimally to their respective factor costs. Yet factor proportions and factor productivity levels are very different.

(i) Output per hectare of land is much higher in Nasi.

(ii) Output per worker is much higher in Nasi.

(iii) What can one conclude from these differences in factor productivity about the relative efficiency of rice production in North and South Nasi? Briefly explain.

 

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