A consumer has 100 to spend on two commodities x and y what

Question

Question -

a. If the price elasticity of demand is given by the expression E(p) = -p²/(p² + 3p + 2). Find the demand function q^D(p) given that q^D(1) = 8.

b. A consumer has $100 to spend on two commodities X and Y. Commodity X costs $2 per unit and y commodity Y costs $1 per unit Suppose that the utility derived by the consumer from x units of commodity X and y units of commodity Y is given by U(x, y) = ln(x + 3) + ln(y + 2).

i. Find the values of x and y that will maximise utility.

ii. What is likely to be the impact on consumer's utility if the budgetary allocation was $101?