Microeconomics questions.

The sign of own price elasticity of demand for maize is the same as that of cross price elasticity of demand for maize and rice.

Concisely define price discrimination and state the necessary conditions for price discrimination.

Under what condition do oligopolists behave like monopolists in the market.

What are the welfare and efficiency implications, when monopolists charge high prices by restricting output in the market? discuss.

Does individual`s preference for cars and fuel or electrical appliances and electricity obey the convexity characteristic of indefference curve? Explain.

If the utility function of an individual consumer is U(X,Y)=(X+2)² +(Y+3)³, find:

1. The marginal utility function for each of the commodities X and Y
2. The value of the marginal utility of the first commodity when four units of each commodity are consumed.

You are given the utility function U=q₁q₂ and the budget constraint is p₁q₁+p₂q₂=y

1. Set up the Lagrangian equation for this problem
2. What are the first order conditions for a maximum
3. Solve for the equilibrium values of q₁,q₂ and 
4. Show the effect of an increase in income on the quantity of good1

Show mathematically that the criteria for profit maximization with respect to output and input levels are similar.

The cost function for a perfectly competitive firm is specified as:

1. Derive the first order condition for profit maximization of the firm expressed as p(q).
2. If the market demand is given by q(p)=9 units, how much profit(loss) would the firm make?
3. Suppose the cost function above is for a pure monopolist operating at a point where price elasticityof demand for q is equal to 2, what would be the optimal quantity of output at P =464?

What are the major determinants of the elasticity of supply of commodities?