DSE 2012- Question 16,29 and 30.

Posted by Ayushya Kaul on Apr 23, 2013; 7:42am
URL: http://discussion-forum.276.s1.nabble.com/DSE-2012-Question-16-29-and-30-tp7580148.html

I'll post the following questions here. I somehow couldn't wrap my head around them. Any help regarding how to go about solving it and so on, would be greatly appreciated.

30) Suppose that there are two agents in an economy with
income x1 and x2. If the richer person transfers a portion of her income
to the poorer person without changing the income ranking (that is the rich
remains richer even after the transfer) then it is called a progressive transfer.
Welfare of this economy is measured by a function W(x1; x2). W is a `good' measure of social welfare if the social welfare increases due to a progressive
transfer. Consider the following candidates for W;
W1(x1; x2) = x1 + x2 W2(x1; x2) = x1x2

(a) Only W1 is a `good' measure
(b) Only W2 is a `good' measure
(c) Both W1 and W2 are `good' measures



29) The demand curve for electricity is D(p) = 120  p. The
marginal cost of electricity production is MC1(q) = 20 + q. The marginal
cost of pollution due to electricity production is MC2(q) = 3q. Find the
competitive equilibrium output and the social optimum output.
(a) 50; 20
(b) 50; 30
(c) 60; 20
(d) 60; 30

16) The equation x^7 = x + 1
(a) Has no real solution
(b) Has no positive real solution
(c) Has a real solution in the interval (0; 2)
(d) Has a real solution but not within (0; 2)