Question

2) Consider the cost function: C(w1,w2,q)=min{w1,w2}q

Derive the production function and the conditional demand functions of the factors of production.

3) A monopolist firm operates in a market where the inverse demand function is given by P (Q) = 24-2Q. The average unit cost of production of the firm is 2. Calculate The price-quantity pair which maximizes the profit of the monopolist and calculate the elasticity of the demand, the profit of the firm and the dry loss of well-being. Suppose, in the context of the model included in the previous question, that the company requested perfect price recognition. What will the price and quantity be? Determine the new level of profit and the dry loss of social well-being

Answer 1

2) The production function will be perfect substitues input Production function

Q=X1+x2

Conditional demand of factors;,

X1=Q ,for w1≤w2. And x1=0 ,for w1>w2

X2=Q,for w2≤w2, amd x2=0,for w2>w1

3) Profit Maximizing quantity at ,MR=MC

P=24-2q

MR=24-4q

MC=AC=2{ when average cost is fixed}

24-4q=2

Q=22/4=5.5

P=24-2*5.5=13

Profit=(13-2)*5.5=60.5

Elasticity of demand={∆Qd/∆p}*(p/q)=(-0.5)*(13/5.5)=-1.18

Deadweight loss=1/2*(11-5.5)*(13-2)=30.25

If firm do perfect price discrimination,the it will charge the willingness to pay by CONSUMERs,for each QUANTITY. By doing this it can aquire all CONSUMERs surplus and total surplus will be equal to producer surplus.

And the QUANTITY sold will be equal to perfect competition equilibrium quantity.

24-2q=2

Q=22/2=11

Profit=1/2*(24-2)*11=121