Q0. Answer all the following seven parts in about 100 words each : 5x7=35
(a) Economic rent is not earned when the supply of a factor is perfectly elastic. Elucidate. Use a diagram. 5
(b) Show that the elasticity of substitution is constant in a Cobb-Douglas production function. Find its value and interpret. 5
(c)
Consider the optimisation problem :
Maximize u(x1, x2)
subject to M = p1x1 + p2x2
where M, p1 and p2 are positive constants.
Write down the Lagrangian for this problem and explain why you need to assume that an interior solution exists before using the Lagrangian method to solve the problem. 5
(d) An economy has 10 slave owners and 500 slaves. Slave owners like having slaves more than not having slaves, and slaves would rather be free than remain as slaves. Explain why the institution of slavery is Pareto optimal in this case. 5
(e)
Explain with a diagram why the compensated demand curve is vertical if the consumer’s utility function is of the form :
v(x, y) = min[x, y] 5
(f) Pharmacies often give senior citizens discounts on medicines. Explain why this may be profit maximizing behaviour as opposed to pure generosity on the part of the pharmacy owners. 5
(g) Suppose that the Government as a monopoly firm produces electricity and sells it to the people at a price p per unit. The demand (q) function for electricity is q = α p−β. If the price elasticity of demand for electricity in an absolute sense is found to be 0·894, should the Government reduce the price per unit to increase the revenue ? Justify your answer. 5
