Consider the following information: Q = min{ 65 L, 4 K} PL=9, PK 10, P=18 and C-3058 What is the profit maximizing level of labor?

1) The Cobb-Douglas production function is y = 12 with a > 0 and 3 > 0. Show that MP₁ = ay/2₁, MP₂= By/22. What is the MRT S21? How does it vary with: (a) y: (b) 2/1. 2) Show that the cost function for a firm with the constant returns Cobb-Douglas production function y = Actis given by C(p, y) = ypip-B, where B is a function of A and a only. Derive the conditional input demands.

When the quantity of a variable input is increased from 3 units to 4 units the total output increases from 70 units to 85 units the marginal product of the variable input is 15 units? True/False

FarFlung make computer keyboards. They use both labour, L, and materials, M, in their production of keyboards. The production method they use requires that at least one labour and one material is always employed. FarFlung have a Cobb-Douglas technology which means that their production function is: Q(L, K) = LM. (a) FarFlung can make and sell 160000 computer keyboards. If fixed costs are £1000000 then what is the short run total cost of production and the short run average cost of production?  (the price of labour is £100 and the price of materials is £25?) (b) FarFlung could move to a new factory, where they will be able to manufacture 360000 computer keyboards. They are confident they can sell all the keyboards, but they will need to reduce price from £20 to £10. Whilst they will be able to use the same technology, the fixed costs will increase to £2000000.   i. What is the new level of short run average costs? What does this imply about the shape of the long run average cost curve?…

(2 ex Production function is flu, X2)=min (x,, 2-x) Dwhat are the conditional factor demand of y = 10 OVA the firm faces w, and w₂ as input prices, what is the cost function?

Firm ABC has estimated that it has the following production function: Q = 1.5LK – 0.3L2 – 0.15K2 Labor (L) has a price of €60 and capital (K) has a price of €75. ABC wants to maximize the production with a total cost of €2025. (a) Determine the quantities of labor and capital the firm should use. (round results to 2 decimal places) (b) What quantity of output will be produced at the optimal combination of factors of production?

A firm has the following information on production and costs from past data: Output (Y) 0 12 18 6 Total Cost (TC) 9 2775 5361 8199 If the total cost function is known to be TC = aY' + bY ² + kY + ƒ , and the demand for the product of the firm is Y = 320-(1/2). P answer the following: • Determine the coefficients of the cubic cost function. • Derive all cost and revenue curves and the profit function. Show that the MC cuts the AVC when AVC is at its minimum point. Plot the relevant graph indicating all points. Calculate the break even and profit maximizing levels of output and price. • What is the relationship between price, marginal revenue and own price elasticity of demand at the profit maximization point.

A firm’s only variable factor is labour and it produces a single product, X. It also has fixed costs. The short-run production function is; X=-0.1L3 + 6L2 + 12L. Where X is the output in tons, and L is the number of persons employed. What is the quantity of X when average variable cost is minimized? If the weekly wage is $360 and the price of X is $30 per ton, how much X should be produced to maximize profits?

a b and c please

dien There are two factors in a production function y = x 113 x₂¹1³. The market price of each unit ofy is p=3, and the factor prices are w₁=1 and W₂=2 for x₁ and X₂ respectively. variable (a). Calculate your cost function as a function of y if X, and x₂ are both barible factors. (b). Now derive the functions of average and marginal cost and plot them against quantity (C). Solve for your optional output of y. Calculate the ratio of two factors (X₁/X₂) (d). In the short run the fixed factor is set at X₂=1. What is the new optimal output level now?