ECO302 GrB
1) Suppose the production function of the agriculture sector is of the form Y = αL + βK + γL2 + δK2. Find out the shape of the ridge line of labour. (4 Mark)
Ans The production function of the agriculture sector is given by Y = αL + βK + γL^2 + δK^2. To find the shape of the ridge line of labour, we can hold capital constant and vary labour. We can do this by setting K = k and solving for L:
Y = αL + βk + γL^2 + δk^2
To find the ridge line, we need to find the value of L that maximizes Y for a given value of k. To do this, we can take the derivative of Y with respect to L and set it equal to 0:
dY/dL = α + 2γL = 0
Solving for L:
L = -α / 2γ
This is the value of L that maximizes Y for a given value of k. Substituting this back into the production function, we get:
Y = α(-α / 2γ) + βk + γ(-α / 2γ)^2 + δk^2
Y = -α^2 / 2γ + βk + γα^2 / 4γ^2 + δk^2
Y = -α^2 / 2γ + (β + γα^2 / 4γ^2 + δk^2)k
This is the equation of the ridge line of labour. As we can see, the ridge line is a parabola, with L on the x-axis and Y on the y-axis. The shape of the parabola is determined by the values of α, β, γ and δ.
2) Mention two major impacts of technological and institutional transformations in Indian agriculture during the mid-sixties (4 Mark)
3) Suppose the agricultural production system uses three inputs, labour, capital and irrigation services as the only institutional factor. Also, suppose that the rate of growth of agricultural output is 11%, the growth of labour is 5% and the growth of capital is 3%. Derive the impact of the irrigation services when labour and capital respectively hold 60% and 40 % shares in the total production. (Mark)
4) Write down mathematical relations of agricultural output with different factors of production incorporating institutional factors. Discuss the impact of institutional factors on the productivity of labour. (Mark)
5) Write down a linear and quadratic form of agricultural production functions with two inputs, labour and capital. Derive the marginal productivities of the two factors, the ridge lines and elasticities of output. (Mark)
6) What is the total factor of productivity growth? Explain the growth accounting approach to calculate it for the agricultural sector incorporating bank credit as one of the institutional factors besides traditional labour and capital inputs. (Mark)
7) Discuss the output and employment effects of the technological transformations in the agriculture sector in India that happened during the mid-60s. (Mark)
8) If E(x2) = 400 and E(x) = 20, ‘x’ being the quantity of a crop, find out the variance of the crop production. (Mark)
9) Suppose a big-sized farmer faces a hypothetical probability distribution over making a choice between the production of two crops A and B in good, medium and bad states. Determine which crop will be beneficial for the farmer to produce in order to minimize risk. (Mark)
10) Suppose the production function of the agriculture sector is of the form Y = αL + βK + γL2 + δK2 + a*LK. Find out the shape of the ridge lines of labour and capital. (Mark)
11)Define Yield Rates. Give an overview of the trends of yield rates in Indian food grains in the post-independence phase. (Mark)
12Explain how the quantity of land use in modern practice is affected by the Risk Aversion of the farmers and the size of the Farm. Logically explain in this context the effects of Fixed Cost and Fertilizer price upon land use under modern technology farming. (Mark)