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Consider an industry in which firms produce undifferentiated commodity for which
where Y is the level of output and a is some constant from (0, 1), K is the amount of capital employed, and L is the amount of labor employed. The
(a) Suppose precisely six firms are in this industry, all of which maximize profits taking prices as given. What is the equilibrium in this case?
(b) Suppose there is free entry into this industry, with all of the firms having the production function given above. What is the equilibrium in this case?
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- Consider that a company has a total cost function TC = 3Q3+2Q2+6. a.What is the average and marginal cost function and what are their values ifQ = 8?b. If the (inverse) demand function facing the firm is P = 6 - 2Q, what value must the slope of the isobenefit curve take for the firm to maximize its profit? Indicate the generic condition as well.A competitive firm has a single factory with the cost function C(q) = 3q2 + 62 and produces 25 units in order to maximise profits. Although the price of output does not change, the firm decides to build a second factory with the cost function C(q) = 7q2 + 44. To maximise its profits, how many units should it produce in the second factory?Suppose that the production function is Q=2K+5L for a firm. If price per unit of labor is 5 Turkish Liras (), price per unit of capital is 10 Turkish Liras () and the financial capasity of firm for production is 600 Turkish Liras (), find the maximum amount of output (production). (Hint: please be careful about the production function as it is linear which means that the inputs (capital and labor) are perfect substitutes, so here you have to remember the equilibrium conditions for perfect substitutes.)
- A firm's demand and total cost function are given by the expression: P = 20 - Q/2 (1) TC = 0.5Q2 + 36 (2) Where P is price per unit in £ TC = total cost in £ Q is quantity demanded and produced. Find the profit-maximising level of output using the profit function and calculate how much profit is made at this output level.Making dresses is a labor-intensive process. Indeed, the production function of a dressmaking firm is well described by the equation Q = L − L2∕800, where Q denotes the number of dresses per week and L is the number of labor hours per week. The firm’s additional cost of hiring an extra hour of labor is about $20 per hour (wage plus fringe benefits). The firm faces the fixed selling price, P = $40. Over the next two years, labor costs are expected to be unchanged, but dress prices are expected to increase to $50. What effect will this have on the firm’s optimal output? A- Increase B- Decrease C- No EffectA competitive firm produces its output, y according to the production function: y = F(K, L), where K and L are capital and labour inputs. Let the prices of output K and L be given by p, w, and s, respectively. Assume that K is fixed in the short run. In addition, assume that the production function exhibits constant returns to scale in K and L. Show that the firm’s short-run supply function is linear in L.
- Assume that a competitive firm has the total cost function: TC=1q3−40q2+880q+2000 T C = 1 q 3 - 40 q 2 + 880 q + 2000 Suppose the price of the firm's output (sold in integer units) is $550 per unit. Create tables (but do not use calculus) with columns representing cost, revenue, and profit to find a solution. How many units should the firm produce to maximize profit? Please specify your answer as an integer. What is the total profit at the optimal output level? Please specify your answer as an integer.Consider a price-taking firm whose production function is given by q = 3 L1/5 K1/9 where L and K denote respectively the amount of labour and capital the firm uses to produce q units of output. Suppose the price of labour is w = 16, the price of capital is 24 and the price of the firm's output is p=225 . Find the firm's cost function. Then enter below the value of the firm's marginal cost at the point where q = 100.A competitive firm’s production function is given by y= f(x1,x2)=x1ax2b If a=b=0.5 , the price of factor 1 is 12, and the price of factor 2 is 3, find the cost minimizing input combinations and the total cost of producing 40 units of output. Redo part (1), this time by first deriving the firm’s conditional factor demand functions and the cost function.
- Suppose that a firm is an imperfect competitor in the product market and a perfect competitor in the input markets and uses two variable inputs: Derive mathematically the first order condition showing how much of each input the firm should use to maximize total profitsA competitive firm produces output using three fixed inputs and one variable input. The firm’s short-run production function is q = 200x − 3x^2, where x is the amount of variable input used. The price of the output is $5 per unit and the price of the variable input is $10 per unit. In the short run, how many units of x should the firm use?Consider two firms that produce a single output good,y, using two inputs :Capital, K , and labor, L, the prices of each unit of capital and labor are r and w,respectively. The output good y sells for $p per unit. Firm A's production function is y = fa(K,L) = K1/4L1/4. The profit function is equals to : K1/4L1/4 - rK -wL. a) FInd the profit maximizing levels of K and L as functions of r,w, and p. b) Suppose that r = w= $1 and p =$4 . What is the profit maximizing level of output,y?
