ASRB NET and ARS / SMS / STO recruitment · India · Agricultural Scientists Recruitment Board (ICAR)
Original practice questions written to the published syllabus · not past papersThe economics of turning inputs into farm output: production functions, the three basic relationships, optimum input use, efficiency, scale and risk.
In the exams: agricultural master's entrance examinations, factor-product relationships (heavy); agricultural economics PhD entrance and fellowship examinations, production economics (heavy); agricultural scientist eligibility tests (heavy)
How our questions for ASRB NET and ARS / SMS / STO recruitment spread across the units of Agricultural Production Economics. Difficulty: 9 easy, 58 medium, 25 hard.
| Forms of production function and their estimation | 9 | |
| Technical and allocative efficiency and production frontiers | 9 | |
| Types of risk and enterprise combination under risk | 9 | |
| Optimum input use: MVP equals MFC | 8 | |
| Duality among production, cost and profit functions | 8 | |
| Cost minimisation | 7 | |
| Economies of scale and size | 7 | |
| Technological change | 7 | |
| Theory of the family farm | 7 | |
| Law of variable proportions and the three stages of production | 5 | |
| Product-product relationship | 5 | |
| Factor-product relationship | 3 | |
| Factor-factor relationship | 3 | |
| Isoquants and isoclines | 3 | |
| Scope of production economics compared with farm management | 2 |
Choose an answer, then open the working. Each explanation says why the right answer is right and why the others are not.
Under constant returns to scale, stage I for the variable input corresponds to which stage for the fixed input?
A. Stage III, where the fixed input's marginal product is negative
With linear homogeneity the two stages are symmetric: where the variable input is too scarce relative to the fixed one (stage I), the fixed input is in excess and its marginal product is negative (its stage III). This is a second reason stage I is irrational.
Further reading: Doll and Orazem, Production Economics: Theory with Applications
With Y = 10X^0.5, output price 2 and input price 1, the profit-maximising input level is
A. 100 units
MPP = 5X^-0.5, so MVP = 2 x 5/sqrt(X) = 10/sqrt(X). Set equal to MFC = 1: sqrt(X) = 10, X = 100. Stopping at sqrt(X) gives 10; forgetting the 0.5 in MPP gives 400. Ignoring the output price (setting MPP = 1) gives 25.
Further reading: Debertin, Agricultural Production Economics
A resource-use-efficiency study finds the ratio MVP/MFC for fertiliser is 1.8. The correct interpretation is that fertiliser is
D. under-used, and increasing its use would raise profit
A ratio above one means the last unit returns more than it costs, so more should be used until the ratio falls to one. A ratio below one indicates over-use. Stage III would give a negative MVP and so a negative ratio.
Further reading: Heady and Dillon, Agricultural Production Functions
The expansion path is the
D. isocline along which MRTS equals the input price ratio
Every point on the expansion path is a least-cost point for its output at the given prices. Ridge lines are the boundaries of the economic region; the expansion path is one particular isocline within it.
Further reading: Debertin, Agricultural Production Economics
A farm's estimated Cobb-Douglas elasticities for all inputs sum to 1.15. What happens if one tries to find a profit maximum along the expansion path at constant prices?
C. No finite profit maximum exists, as marginal cost keeps falling with output
With increasing returns to scale the cost function is concave in output and marginal cost declines, so MC = P gives a profit minimum, not maximum. Cost minimisation is still possible for any given output; Cobb-Douglas has no output maximum.
Further reading: Beattie, Taylor and Watts, The Economics of Production
A production function is homogeneous of degree 0.8. If all inputs are doubled, output
A. rises by a factor of 1.741
Homogeneous of degree k: f(tX) = t^k f(X) = 2^0.8 = 1.741. Multiplying 2 x 0.8 = 1.6 is the common slip.
Further reading: Chambers, Applied Production Analysis: A Dual Approach
Efficiency scores from a frontier analysis of 200 farms in one district are best interpreted as
C. relative to the best performers in that sample, not absolute measures of efficiency
Frontiers are built from the observed farms, so a score of 1.0 means best among those observed. Scores from different samples or methods are not directly comparable.
Further reading: Coelli, Rao, O'Donnell and Battese, An Introduction to Efficiency and Productivity Analysis
Tractors and combine harvesters are examples of technology that is mainly
B. labour-saving
Mechanical technology raises output per worker and substitutes capital for labour, so it is labour-saving (capital-using). Improved seed and fertiliser are the classic land-saving (biological-chemical) technologies.
Further reading: Hayami and Ruttan, Agricultural Development
In Chayanov's theory of the peasant family farm, the family applies its labour until
B. the marginal drudgery of work equals the marginal utility of the extra consumption
Chayanov's family does not pay itself a wage; it balances the disutility of extra work against the benefit of extra consumption. Setting MVP of labour to the wage is the capitalist (separable) rule.
Further reading: Chayanov, The Theory of Peasant Economy
A cost function is C = 2y(w1 w2)^0.5. At y = 10, w1 = 4 and w2 = 9, the cost-minimising demand for input 1 is
B. 15
By Shephard's lemma, x1 = dC/dw1 = 2y x 0.5 x w1^-0.5 w2^0.5 = y(w2/w1)^0.5 = 10 x (9/4)^0.5 = 10 x 1.5 = 15. 120 is total cost; inverting the price ratio gives 6.667; forgetting the 0.5 from differentiation gives 30.
Further reading: Chambers, Applied Production Analysis: A Dual Approach
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