Bela has the quasi-linear utility function

U(q1,q2) = 64q1^1/2 + q2

a) Assuming p2 = 1 and Y = 100, find the consumer's compensating variation for an increase in p1 from $1

to $2.

[HINT: DETERMINE THE DEMAND FUNCTIONS FOR q1 AND q2, WHICH ARE THE OPTIMAL

QUANTITIES, IN TERMS OF P1 FIRST. THEN USE THE DEFINITION OF COMPENSATING

VARIATION FOR THE CALCULATION]

b) Draw a graph of the optimal bundle for Bela with q1 on the X-axis. Make sure to label all the curves

and the axes appropriately. Indicate the optimal quantities using numbers you got in part a).

IT IS NOT NECESSARY TO DRAW THE CURVES USING THE FUNCTIONS GIVEN. FREE HAND /

GENERAL GRAPH OF THE RELEVANT CURVES AND LINES WOULD BE PERFECTLY OKAY.

NOW Suppose that the government chooses to give Bela a gift in kind (that is, q1).

c) On the same graph you have drawn for part b) of this question, show that Bela is better off with the

gift. Explain your answer with the help of the graph you have drawn.