StudySpace: Economics in Development, 6th Edition

Worked Example: Linkage Effects in Planland

The idea of intersectoral linkages, introduced in Chapter 3 and briefly discussed in this chapter, brings out the evolving nature of the interdependence among the various branches of the economy. Planland is a fictitious developing economy whose input-output table consists of three sectors: (1) agriculture, (2) manufacturing, and (3) services. The interindustry flow matrix of an input-output table is simply an accounting framework, showing the flows output or income between branches of the economy. Looking across a row shows where the sector’s output was sold, whereas looking down a column shows where output and input were, by source and by the sector. They both add to total output for the sector. That is why the column total and the row total are identical.

Table 18–1 converts the information on output levels into a matrix consisting of coefficients. Each entry in every column of the flow matrix is divided by the total at the bottom of the column; this gives the amount of each input required per unit of output in the sector, column by column. This information will be used to estimate the direct and indirect amount of output needed, sector by sector, to meet planned targets for final output. Study the data carefully.

The first column shows that each $1 of output in agriculture requires $0.08 worth of agricultural inputs, $0.04 worth of manufactured inputs, and no services. The sum of these three figures (= $0.12) gives the direct requirement for domestically produced inputs per $1 of agricultural output. The index of direct backward linkages in this case is

Click here for Table 18-1

This value equals the figure shown in the row 4 for total domestic purchases per unit of agricultural output. For the manufacturing industry, the index of direct backward linkages can be identified in the same manner:

(The index for the service sector will be dealt with in Exercise 1.)

To calculate the index of total backward linkages, one must know the direct plus indirect production requirements, per unit of output for each sector—the rij matrix. The input-output mathematics required to compute these coefficients cannot be explained here. It suffices to understand that r23, for example, shows the total amount of industry 2 output required per $1 of final production in industry 3, including the whole chain of interindustry linkages.

For Planland, the appropriate calculations show that $1 of final demand for agricultural goods requires production of rll = $1.11 of agricultural output (of which $1.00 is the final output itself and $0.11 is the required amount of inputs from this sector). The $1.00 of final demand for agricultural goods also requires r21 = $0.08 of manufactured products and r31 = $0.01 worth of services. Note that the services requirement is entirely indirect: The agricultural sector itself uses no service inputs, but services are required for production of other inputs to agriculture. The sum of these three figures gives the total requirement for domestic production per unit of final product in agriculture. Thus, the index of total backward linkages is

For manufacturing, the corresponding figure is

Each $1.00 of manufactured product creates a requirement for $2.45 worth of domestic output, taking into account the interindustry flows of intermediate goods.

Take note that the previous sentence says “creates a requirement for.” Does this mean that $2.45 worth of direct plus indirect domestic output will occur per $1.00 increase in manufacturing-sector production? Maybe not. Domestic suppliers of intermediate goods might be undersold by imports, or they might be unable to increase production capacity to satisfy the increased demand. Also, the input requirements might be met by bidding supplies away from other uses. Or the particular input demands of a specific manufacturing activity may differ from the average coefficients displayed in the input-output table. Then again, inputs previously imported (see line 5 of the coefficients matrix) could be replaced by domestic production. In short, the index of linkages gives only a rough indication of where effective linkages may be lurking.

Exercises

1. Now, it is your turn to calculate linkages from the input-output coefficients, using the Planland data shown in Table 18–1 as your raw material.

a. (i) The Worked Example showed how to calculate the index of direct backward linkages for the agriculture and manufacturing sectors in Planland. For the service sector, one would apply the formula

Rewrite this equation, replacing the question marks with the proper symbols:

(ii) Using the appropriate numerical values from Table 18–1, the value of the index of backward linkages for the service sector is

L _b3 = .

(iii) Compare L_b3 with the corresponding index value for agriculture and for manufacturing (reported in the Worked Example). It should be clear that the sector has the largest index of direct backward linkages.

b. To calculate the index of total backward linkages for the service sector, you need to know the following r_ij values:

r₁₃ = 0.61.

r₂₃ = 0.54.

r₃₃ = 1.20.

(i) From Table 18–1 you can see that the required input of manufactured goods per unit of services is a23 = 0.25. What, then, is the meaning of r₂₃ = 0.54 as reported previously?

(ii) Notice that the value of r₃₃ is greater than unity. What does this mean? (Recall that the Worked Example reported values for r₁₁ and r₂₂ that also exceeded unity.)

(iii) Calculate the value of the index of total backward linkages for the service sector in Planland:

.

(iv) Comparing L_t3 with the index values for agriculture and manufacturing (reported in the Worked Example), you will find that the sector has the largest index of total backward linkages.

(v) Your results should show that the sector with the greatest direct backward linkage effect is not the same as the sector with the greatest total backward linkage effect. Briefly explain how this can occur.

c. Turn now to forward linkages. It is necessary to refer to the interindustry flow matrix for Planland rather than the coefficient matrix. Table 18–2 provides the required data.

Click here for Table 18-2

(i) Table 18–2 shows that the total value of output for agriculture is

Z₁ = $ .

(ii) The value of agricultural output used as an input is

To agriculture: X₁₁ = $ .

To industry: X₁₂ = $ .

To services: X₁₃ = $ .

(iii) Altogether, the value of agricultural output purchased as a productive input equaled

(iv) Therefore, the index of direct forward linkages for agriculture is

.

(v) Following a similar procedure, you should find that the index of direct forward linkages is L_{f 2} = .55 for manufacturing and L_{f 3} = for services.

(vi) The sector having the largest index of direct forward linkages is .

d.

(i) What does L_{f 2} = .55 mean? More specifically, if production in manufacturing increases by one unit, then the index of direct forward linkages indicates .55 what?

(ii) More generally, what does this index value say about the suitability of manufacturing as a leading sector for Planland’s economic development?

Recall the warning from the Worked Example that these indices give only a rough indication of where effective linkages may be lurking. More detailed study would be needed to determine whether the linkages actually would materialize.

2. This exercise investigates the choice of technology in industry. Three alternative technologies for producing knives are available in Republique de Couteau. The data below show the amount of capital (K) and labor (L) required to produce 1,000 knives per year by three alternative methods: the traditional handicraft technology (T1), the labor-intensive intermediate technology (T2), and the automated modern technology (T3).

a. (i) Calculate the capital-labor ratio for each technology:

For T1, K/L = .

For T2, K/L = .

For T3, K/L = .

(ii) The capital-labor ratio for the automated technology is times higher than the ratio for the intermediate technology and times higher than the ratio for the handicraft technology.

(iii) Is this range of capital-labor ratios unrealistic in comparison with the range of technology choice cited in the textbook?

b. In Figure 18–1, plot the point representing the K and L requirements to produce 1,000 knives per year, using each of the three technologies. Label the three points T1, T2, and T3, respectively. Then connect the points to form the corresponding isoquant.

c. Informal-sector firms in Couteau face a market wage that reflects the opportunity cost of labor, but their cost of capital is extremely high due to segmented capital markets. In contrast, modern-sector firms face a subsidized price of capital along with a minimum wage that is higher than the market wage. Specifically, factor prices (in francs) are as follows:

(i) Given the factor prices faced by firms in each sector, which is the minimum-cost choice of technology?

For firms in the modern sector, T .

For firms in the informal sector, T .

(Hint: You already know how much K and L are required by each technology choice.)

FIGURE 18-1

(ii) Which is the appropriate technology for the economy, that is, the one that minimizes costs in terms of shadow prices? T .

(iii) Draw a budget line showing the minimum level of costs for modern-sector firms. Label it B_m . (Hint: The line must have a slope equal to –2 = –P_L /P_K .)

(iv) Carefully draw a budget line showing the minimum level of costs for informal sector firms. Label it B_i .

(v) Carefully draw a budget line showing the minimum level of costs in terms of shadow prices. Label it B_s .

The graph reveals that T1 is the minimum-cost technology choice for informal-sector firms and that T3 is the minimum-cost choice for modern-sector firms but only because both groups of producers face distorted factor prices. Budget line B_s shows that T2 is much less costly for the economy in terms of appropriate shadow prices.

d. Altogether in Couteau there is a market for 1 million knives per year. Keep in mind that the isoquant in Figure 18–1 is drawn for Q = 1,000 knives per year.

(i) How many units of capital are required to produce 1 million knives per year with the technology used?

In the modern sector, K = thousand.

In the informal sector, K = thousand.

(ii) How many workers are required to produce 1 million knives per year with the technology used?

In the modern sector, L = thousand.

In the informal sector, L = thousand.

(iii) Valuing labor and capital at shadow prices, what is the total factor cost for producing 1 million knives per year?

Using modern-sector technology, F million.

Using informal-sector technology, F million.

Using appropriate technology, F million.

(iv) Compared to production in the informal sector, producing 1 million knives per year in the modern sector requires times as much capital, creates only percent as many jobs, and has an opportunity cost (at shadow prices) that is percent higher.

e.

(i) Given the actual factor prices prevailing in each sector, what is the factor cost per 1 million knives?

In the modern sector, F = .

In the informal sector, F = .

(ii) Given the distorted factor prices that prevail, the sector can easily underprice the sector in market competition. So producers in the sector will be driven out of business.

(iii) Is this an efficient development trend? Explain.

Before going on, think about the loss of efficiency—and the loss of jobs— caused by distorted factor prices in this one small sector of the economy.

3. This exercise examines the relationship between scale economies and the size of the market. Figure 18–2 shows the long-run average cost (including a normal return on capital) for brick production in Amigo. The figure clearly exhibits economies of scale, since long-run average cost declines with the capacity of the production unit.

FIGURE 18-2

a. Brick production entails a number of processes, including mixing clays, molding the bricks, firing the bricks in a kiln, and drying the bricks, in addition to handling, storage, and business operations.

(i) Identify two plausible reasons for the presence of scale economies in the brick industry.

(ii) What output capacity is the minimum efficient scale (MES) of operation for producing bricks in Amigo?

MES = thousand tons per year.

(iii) The graph shows that a production facility with a capacity of 1/2 MES has an average cost that is percent higher than at the MES.

(iv) A production facility with a capacity of 1/4 MES has an average cost per ton of bricks that is percent higher than at the MES.

b. At the market price of P100,000 (P = pesos) per ton, the quantity demanded in Amigo is 2 million tons of bricks per year.

(i) The MES in the brick industry equals percent of the annual market volume in Amigo.

(ii) What does this number imply about the possibility of developing an efficient, competitive brick industry in Amigo?

(iii) Suppose that brick producers in Amigo can export bricks to El Toro, a neighboring country that lacks high-quality clays. Including exports, the market for Amigoan bricks would equal 8 million tons per year. How would the presence of this export market alter the prospects for developing an efficient, competitive brick industry in Amigo?

c. The main capital goods that are needed to produce bricks in Amigo are clay presses. A study shows that one clay press is needed per 10 thousand bricks and that domestic demand in Amigo is growing by 200 thousand bricks per year.

(i) To meet the annual growth of domestic demand for bricks, the brick producers have to buy new clay presses each year.

(ii) Brickmakers also require 50 clay presses per year for replacement purposes. Altogether, then, there is a demand for clay presses per year.

(iii) Figure 18–3 shows the long-run average cost curve for producing clay presses. The MES in the clay-press industry is reached with a production level of presses per year.

(iv) How does the domestic demand for clay presses compare with the MES for producing these presses? What does this imply about the cost of producing clay presses locally for the domestic market? Give specific numerical answer.

FIGURE 18–3

d. The government is considering banning imports of these presses to take advantage of the backward linkage effects from brickmaking.

(i) If the government decides to ban imports of clay presses to promote domestic production, would the domestic clay-press industry be competitive or monopolistic? Explain.

(ii) How would the brickmakers be affected by this government decision?

 

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