Section A
Q1. Answer all the following seven parts :
(a) In a two-commodity framework, the marginal rate of substitution is everywhere equal to 2. The prices of the two goods are equal. Draw a diagram to identify the utility maximizing equilibrium.
(b)
The cost-minimizing demand for labor is L = (Q)/(50) √((r)/(w)) and that for capital is
$
K = (Q)/(50) √((w)/(r))
$
where w and r denote wage and price of capital respectively. Find the production function.
(c) Explain the principle of average cost pricing in the context of a natural monopoly.
(d) Find a monopolist's demand function for labor when the labor market is perfectly competitive.
(e) Explain the concept of external economies in the context of marginal social benefits and marginal social costs.
(f)
Suppose that the Leontief input-output coefficient matrix is
$
A = \beginbmatrix
0.1 & 0.4 \\ 0.2 & 0.5
\endbmatrix
$
and the final demand vector is
$
\beginbmatrix
1 \\ 1
\endbmatrix
$
. Find the total direct and indirect requirement of the second input to satisfy the final demand.
(g) Show that in the regression model Yi = α + β Xi + Ui; i = 1, 2, ..., n, the covariance between the regressor and the error term is zero under ordinary least squares method of estimation.
