digital kitchen location with a production function of q= (L^0.3 )(K^0.5), where q is the number of chicken meals it sells, L is employee hours, and K is robot hours. Chicken sells for a price p. Employees and robots are paid w and r per hour, respectively. In the short run, Los Pollos Hermanos uses 25 robots. (a) define diminishing marginal returns to labor. (b) Does Los Pollos Hermanos experience diminishing marginal returns to labor? If so, at what number of employee hours does it occur? (c) Calculate Los Pollos Hermanos's short-run demand for labor (i.e., its short-run unconditional demand function for labor).
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- Suppose a firm engaged in the illegal copying of DVD’s has a daily short run total cost function given by: STC = (q^2)+25 If pirated DVD’s sell for $20, how many will the firm copy each day? What will its profits be? What is the firm’s short run producer surplus at P=20? Develop a general expression for this firm’s producer surplus as a function of the price of pirated DVD’s.The inverse demand for tea is given by P= 10 – 0.04Q, where Pis the price per a gram of tea and Qis the total number of grams of tea brought to market. There are two tea shops in the market. Shop 1's cost function is given by C = 0.01q,?, where qı is the number of grams of tea it brings to market. Shop 2's cost function is given by C2 = 0.01q2², where qp is the number of grams of tea it brings to market. Given that the two shops compete by setting output (Cournot), answer the following. a) Identify shop 1's reaction function to shop 2's output to within 2 decimal places (e.g. 0.33). 91= Number - Number 92 b) Identify shop 2's reaction function to shop 1's output to within 2 decimal places (e.g. 0.71). q2= Number Number 91 c) To within two decimal places (e.g. 0.63) what is the equilibrium output level of each shop and the equilibrium per gram price for tea. Shop 1 will produce Number grams of tea and shop 2 will produce Number grams of tea. The equilibrium market price is £ NumberSuppose the production function for a competitive firm is y=f(x1,x2)= x₁2x₂2/3. The cost per unit of the first input is w₁ and the cost of the second input is w₂. a. What are the returns to scale of this production function? Find the cheapest input bundle, x₁ and x2, that yields the given output level of y. b. Write down the formula of the firm's total costs as a function of y. Are the average costs increasing, constant or decreasing in y? Are the marginal costs increasing, constant or decreasing in y? Why?
- Would a cost function of 0 mean a linear line of supply curve? For example if 10 firms are on the market selling 10 goods and the cost function is 0?The inverse demand for tea is given by P = 8 – 0.03Q, where Pis the price per a gram of tea and Q is the total number of grams of tea brought to market. There are two tea shops in the market. Shop 1's cost function is given by C = 0.02q,?, where q, is the number of grams of tea it brings to market. Shop 2's cost function is given by C2 = 0.02q22, where q2 is the number of grams of tea it brings to %3D %3D market. Given that the two shops compete by setting output (Cournot), answer the following. a) Identify shop 1's reaction function to shop 2's output to within 2 decimal places (e.g. 0.33). 91= Number Number 92 b) Identify shop 2's reaction function to shop 1's output to within 2 decimal places (e.g. 0.71). q2= Number Number 91 c) To within two decimal places (e.g. 0.63) what is the equilibrium output level of each shop and the equilibrium per gram price for tea. Shop 1 will produce Number grams of tea and shop 2 will produce Number grams of tea. The equilibrium market price is £…In competitive markets, there are many small firms with each firm unable to influence the market price. Suppose company ABX operates in the wheat market. The company produces and markets wheats at a Price = $20 per container. The firm’s total costs are given as: TC = 50 +2Q + 3Q2 What is the firm Fixed Cost? Why? Also, use a graph to support your answer
- Suppose the imaginary company of Panthera is a small, Cedar Rapids-based American apparel manufacturer specializing in athleisure. The following table presents the brand’s total cost of production at several different quantities. Fill in the remaining cells of the following table. (Graph is in images)Suppose that the profit from the sale of Kisses and Kreams is given by the following, where x is the number of pounds of Kisses and y is the number of pounds of Kreams. P(x, y) = 10x + 6.6y - 0.001x² -0.025y² dollars You know from previous experience that, for such a profit function, profit will be maximized at the critical point of P(x,y). (a) Determine the amounts of Kisses and Kreams that will maximize profit. pounds of Kisses pounds of Kreams (b) What is the maximum profit? (Round your answer to two decimal places.) $Beta Industries manufactures floppy disks that consumers perceive as identical to those produced by numerous other manufacturers. Recently, Beta hired an econometrician to estimate its cost function for producing boxes of one dozen floppy disks. The estimated cost function is C = 20 + 2Q^2. a. What are the firm's fixed costs? b. What is the firm's marginal cost? Now suppose other firms in the market sell the product at a price of $10 c. How much should this firm charge for the product? d. What is the optimal level of output to maximize profits? e. How much profit will be earned? f. In the long run, should this firm continue to operate or shut down? Why? *Please show all work*
- A firm has a linear demand function for its product. When the price of the product isSh.220, the quantity demanded is 40 units. When the price increases to Sh.240, thequantity demanded becomes 30 units. In addition, the firm’s marginal cost function isgiven by:MC = 40q – 2q2 + 2Fixed cost = Sh.5 millionWhere q = quantity demanded, MC = marginal cost (Sh. million)Evaluate the level of output that maximizes profits.Sergio Lopez is a publisher of Latin American poetry. His fixed cost is $525, and the cost to produce each individual copy of his book is $3.50. Currently, Sergio is selling these books for $6 each. So far this year, he has produced x a. Write a linear cost function C for Sergio’s book production, in terms of x. b. Find the linear revenue function R for selling x copies of the book. Remember that P(x) = (price)x. c. Use and 1b. to determine the profit function P for selling x books. Write the formula in simplified form. d.Use your answer for 1c to determine the profit, in dollars, for selling 300 books.Giocattolo is a profit-maximizing firm producing toy cars, which it can produce and sell in its home country, Italy, and abroad in Spain. The average cost (AC) curve on the following graph represents Giocattolo's cost of producing toy cars within one factory, whether in Italy or in Spain. COST (Dollars per toy car) 10 1 0 10 I 1 20 30 40 50 60 70 80 QUANTITY (Thousands of toy cars) AC 90 100 Suppose that at the current market price of toy cars, the demand for Giocattolo's product is 10,000 toy cars per year in Italy and 20,000 toy cars per year in Spain. (Hint: Select each point on the previous graph to see its coordinates.) (?) Based on Giocattolo's average cost curve, within one factory it can produce 20,000 toy cars at S per toy car, and produce the total of 30,000 toy cars at S per toy car. Complete the following table by indicating Giocattolo's total production cost for each scenario. Total Production Cost (Dollars) Scenario Produce 10,000 toy cars in Italy and 20,000 toy cars in…