Consider the following functions of the market for a good x. Q = 20 P - 1000. Q = 6000 - 30 P.
Identify the demand and the supply functions
Find the equilibrium price and quantity both algebraically and graphically.
What would happen ( Surplus or shortage) if this market was imposed :
A price ceiling of 100?
A price ceiling of 200?
A price floor of 180?
A price floor of 50?
Calculate the elasticities of demand and supply at the following prices
Price P = 75
Price P =150
Are your results in line with the theory of elasticity at lower (higher) prices for both demand and supply?
Consider the following market for good x (finely divisible). Q = 2 P; and ; Q=16/√P; Identify the demand and the supply functions
Find the equilibrium price and quantity
What would happen (Surplus or shortage) if this market was imposed:
A price of 5 dollars per unit?
Calculate the elasticity of demand at the price P= 8. (Elastic or Inelastic? Why?)
Consider the following cost and benefit functions: C(X, Y) = 150 X + 30 X2. B(X, Y) = 400 X - 10 X2 + 200 Y - 5 Y2 + 10 X Y . For Y = 5
Derive the benefit function
Derive the marginal benefit function
Derive the marginal cost function
Find the value of x for which the net benefit is maximized.
Calculate the values of the benefit, cost and net benefit for this value of x.
Graph the marginal benefit and marginal cost and show this equilibrium graphically. (Excel)
Graph the benefit and cost functions and show the net benefit maximizing value for x. (Excel)
Graph the following indifference curves for the given utility levels:
U (x, y) = x + y for U = 5, 6, 7, , 8, 9 and 10. (What kind of relationship exists between these goods? Substitutes, Complements?
U (x, y) = min { 3x, y} for U = 3, 6, 9, 12, and 15. (What kind of relationship exists between these goods? Substitutes, Complements?
Consider the utility function for a utility maximizing individual consuming two goods X and Y. U (X,Y) = X2Y + 15. This person pays 3 dollars for good X and 5 dollars for good Y with an income of 150 dollars. ( 3 X + 5 Y ≤ 150) Budget constraint.
Derive the marginal utility for good x. Ux
Derive the marginal utility for good Y. Uy
Find the marginal rate of substitution between x and y.
Find the amounts of good X and Y that maximizes this utility.
Compute the utility.