Question

2) A consumer's utility function is a(x,y) =- 3x3 y (a) Find the consumer's optimal choice for x as a function of income I and prices pa,Py. (The answer is a little messy.) (b) Sketch the demand curve for x as a function of income I when prices are Pz 2,Py-32. (It may be easiest to plot a few points.)

Answer 1

The utility function of a consumer is 11 (x, y) The budget constraint of the consumer will be P 1 Maximize the utility function subject to budget constraint St. : Rx+8 ! a) Set the Lagrange for utility maximization: 3x y Take first derivative of L w.rt to x, y and then and equate it zero oL ox OL 1 ax y Equate both l

Substitute the values of prices 2x*32y' Now take the derivative of lagrange with respect to λ and equate it with zero on Put the value of P pu t value of x in above equation Hence the optimal choice of x isD

b) The price of x Px-2 and price of y Py-3.2 -16,7 2x + 32y =1 Put the value of y 2x+321 2x+8x2=1 The demand curve for x as a function of income I when prices are P-2, Py-32 is shown below:

Good x