Johnspends all his income (m>0) on good A and good B. Assume both a and b arebigger or equal to 0. When John consumes positive amounts of both good Aand good B, his demand for good A has the following features: [1] own-priceelasticity is always equal to -2; [2] cross-price elasticity is always equal to1; [3] income elasticity is always equal to 1; [4] when the price for good X is2 and the price for good Y is 1 and his income is 4, his demand for good X is1.

a) Find John's optimal consumption bundle as functions of pricesand income: [a(Pa,Pb,m),b(Pa,Pb,m)]

b) Are good A and good B normal goods or inferior goods? Are goodA and good B substitutes or complements?

c) Suppose John's income is 8 and the price for good Y is 3. Whenthe price for good A rises from 2 to 4, how does John’s optimal choice change?What is the substitution effect? What is the income effect?

This is your homework assignment. Provide us your answers and your reasoning for them and any work when applicable and we will tell you if you are right or not. But we do not hand you answers.

This is your homework assignment. Provide us your answers and your reasoning for them and any work when applicable and we will tell you if you are right or not. But we do not hand you answers.

I just want to know the hints to the calculation of part a using the information provided. How to synthesize the different elasticities to get the optimal choice? Much obliged.