Reference no: EM133620263

Question 1: A firm faces the demand schedule P = 53.5 - 0.7Q and the total cost schedule:

C(Q) = 400 + 35Q - 6Q² + 0.1Q³, what price will maximize its profit?

Question 2: A monopolist producing a single output has two types of customers. If it produces Q₁ units for customers of type 1, then these customers are willing to pay a price of P₁ = 50 - 5Q₁ dollars per unit. If it produces Q₂ units for customers of type 2, then these customers are willing to pay a price of P₂ = 50 - 5Q₂ dollars per unit. The monopolist's cost of manufacturing Q units of outputs is C(Q) = 90 + 20Q dollars, where Q = Q₁ + Q₂

i) In order to maximize his profit, how much should the monopolist produce for each market? What is the maximum profit?

ii) If there is no price discrimination, compute the demand function for the market as a whole? Compute the firm's profit maximization output for this situation and compute the profit?

Question 3: A firm uses two inputs to produce a single product. If its production function is

Q = x^1⁄4y^1⁄4

and if it sells its output for a dollar a unit and buys each input for 4 dollar a unit, find its profit maximization input bundle. Check the second order condition.

Question 4. A firm has a production function Q(L, K) = 5L^1⁄2K^1⁄3, where L is the labour unit used and K is the number of units of capital involved with an output of Q units. If P_L = 4 dollar and P_K = 5 are price of labour and capital per unit in dollar, respectively. Compute units of abour and capital which will produce an output of 200 units at minimum cost.

Required:
i) Write the objective function.
ii) Write the Lagrangian function.
iii) Solve the problem (use Bordered Hessian determinant to show that we have maximum at the stationary point)
iv) Find the Lagrange multiplier and interpret the result.