1. Given the Cobb- Douglas production function for Preshzo Company limited as follows:

=^0.250.75

She estimates that the cost of labour is k3 and the cost of capital k4. You are required to do the following:

a) If she wants to produce 50kg of are output, formulate both the objective and constraint functions for Preshzo Company limited.

b) Find the minimum cost for both labour and Capital required to produce 50 kg units of output.

c) Find the shadow price lambda and interpret the coefficient of lambda.

d) Prove that the maximum unit produced at the lowest cost is 50 kg

2. Let the market demand be given by the inverse demand function

()=502 where =1+2. The cost function for each of the two firms in the industry is ()=2. Firms are courtnot competitors.

a. Discuss the assumptions of courtnot model.

b. Define the best response function of a firm. Find the best response function for each firm.

c. Find for each firm in the Cournot equilibrium firm output and firm profits. What is the price that clears the market?

3. Given the constant elasticity demand function as :

=

a. Show that Marginal Revenue of this function is proportional to the price

(let =(1/)^1/b). To simplify the equation.

b. calculate the Marginal Revenue when ==2 and when b=-10