Question

1. Consider the market for good x. The market demand is given by,

D(p) = 100 ? 2P (Demand)

and the supply function is given by,

S(p) = 25 + 5P. (Supply)

(a) (5 points) Solve for the equilibrium price and quantity in this market .

(b) (10 points) If the government imposes a $2 value tax on x, calculate the the after tax equilibrium (buyer’s price, seller’s price and quantity).

(c) (5 points) Which side of the market shares more burden of the tax? (Hint: Compare the loss in consumers’ surplus and producers’ surplus. A diagram would help.)

2. Consider the following production function:

f(01.02) = 21

(a) (10 points) Solve the cost minimization problem for the firm given the production function.

(b) (5 points) Show that for $\alpha =\frac{1}{2}$ the cost function can be written as $c(y)=2(w_{1}w_{2})^{\frac{1}{2}}y$

(c) (5 points) For $w_{1}=1$ and $w_{2}=4$ solve the profit maximization for the producer for the cost function given in part (b). [Hint: firm is choosing y and price of output is denoted by p.]

(d) (2 points) If p = 2 how much would the firm supply? What would be it’s profit?

(e) (2 points) If p = 4 how much would the firm supply? What would be it’s profit?

(f) (2 points) If p = 6 how much would the firm supply? What would be it’s profit?

(g) (2 points) Draw the supply function for the firm.

(h) (2 points) Calculate the elasticity of the supply function for the firm.