Economic Assignment

1. The demand function for bicycles in Holland has been estimated to be Q=2000+15Y-5.5P, where Y is income in thousands of eruos, Q is the quantity demanded in units, and P is the price per unit. Answer the following questions when P=150 euros and Y=15(000) euros.

(1) Does Demand Law suffice in the case?

(2) Determine the price elasticity of demand.

(3) Determine the Income elasticity of demand.

2.

Suppose Adam has 100 dollars and consumes 2 products only, x and y. Price of x is 1 and price of y is 2. His utility can be best captured by the function of x0.5+y0.5.

(1) Write down the Lagrangian function for Adam’s optimization problem. Is it L=x0.5+y0.5+λ(100-x-2y)?

(2) Solve the optimal consumption bundle for Adam. Is it x=50,y=25?

(3) Now the price of y decreased to 1. Write down the Lagrangian function for Adam again.

(4) Facing the new price, what is Adam’s optimal consumption bundle? Is it x=50,y=50?

(5) Facing the new price and holding the original consumption bundle in (2), how much money does Adam leave? Is it 25?

(6) Calculate the optimal consumption bundle if Adam faces the constrain of x+y=75. Is it x=37.5,y=37.5

(7) How much does Adam change the consumption of x and y due to the price change? (Use income effect and substitution effect to describe)

(8) Draw a graph to show (7).