Please explain the following

1. The marginal revenue for a perfectly competitive firm is equal to the market price. Why is the marginal revenue for a monopolist less than the market price for positive quantities of output? 2. What is a Nash equilibrium? Why would strategies that do not constitute a Nash equilibrium be an unlikely outcome of a game? 3. Explain how consumers in an economy can be made better off if the marginal rate of transformation does not equal consumers' marginal rates of substitution. 4. What role does consumer utility maximization play in a general equilibrium analysis? 5. At an optimal interior basket, why must the slope of the budget line be equal to the slope of the indifference curve