Functional forms of producing beef (in lb) from corn (bu) are given as below. Beef is y and corn is x. y = x² for x=0,1,2,3,4 and y = -(x-7)² + 25 for x=5,6,7,8,9, and above. What is the output level when x=5? 25 21 9 24 16
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- Consider the following two systems of production, which produce the same quantity. A (assemble by hand) requires: 35 workers 1 robot B (assemble by robot) requires: 5 workers 4 robots Price of one unit of inputs (thousands): worker: £2 robot: £50 Draw the axes of a cost diagram as follows: · units of labour on the x-axis, with a scale from 0 to 70 · units of capital on the y-axis, with a scale from 0 to 5. Now mark system A and system B as points on this diagram. Draw an isocost line at C = £120. Comment on which system you would choose, and why.Midtown Manufacturing Company makes trash cans and plastic buckets, both of which requires labor hours along with time on two machines. Producing a unit of trash cans requires 50 hours of labor, 5 hours on Machine A, and 10 hours on Machine B, while producing a unit of buckets requires 20 hours of labor, 8 hours on Machine A, and 2 hours on Machine B. The Company has available 2000 labor hours, 560 hours for Machine A, and 350 hours for Machine B. Each unit of trash cans brings in $20 in profit for the company and each unit of buckets brings in $3 in profit. Be sure to write out the system of inequalities expressing these conditions and graph the feasible region. Find the profit maximizing combinations of trash cans and buckets this company can and should produce.Consider a firm with production function in the Cobb-Douglas form q = K^.5L^.5 Suppose that one unit of capital costs r=12.5, whereas one unit of labor costs w=8. Determine the optimal input mix that leads to an output of q = 2. Determine the firm’s cost function, that is, the minimum cost required to produce output q.
- Modified True or False: State whether each statement is true or false. If the statement is false, briefly explain why it is so, and then restate it to make it true. The shapes of long-run cost curves follow directly from the assumption of a fixed factor of production, which implies diminishing returns. The optimal scale of plant is the scale of plant that maximizes average cost. In the long-run competitive equilibrium, each individual firm chooses a scale of operations that minimizes its long-run average cost. Answer correctly and explain within 30mins will give you positive feedback.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 profitsHannah and Sam run Moretown Makeovers, a home remodeling business. The number of square feet they can remodel in a week is described by the Cobb-Douglas production function Q=F(L,K) Q=10L^0.5K^0.5,where L is their number of workers and K is units of capital. The wage rate is $250 per week and a unit of capital costs $250 per week. Suppose that when initially producing 100 square feet a week, they use 10 units of capital.a. What is their short-run cost of remodeling 1,000 square feet per week? Instructions: Enter your answer as a whole number. $ b. What is their long-run cost of remodeling 1,000 square feet per week? Instructions: Enter your answer as a whole number. $
- *** Please answer e, f, g,h** An ice cream company finds that at a price of $4.00 for each pint, they can sell 4000 pints of ice cream per day. For every $0.25 decrease in price, daily demand increases by 200 units. The company’s cost function is C(q)=0.01q2-90q+211600, where C represents their daily costs (in dollars), and q is the number of pints sold per day. a)Find the demand function q(p). b) Find the revenue function R(q). Hint: first you will need to solve for p in terms of q from the demand function.) c) How many pints should the company sell per day if they want to maximize their revenue? d) what price should the company charge for each pint if they want to maximize their revenue? e)Use the criteria MC(q)=MR(q) to determine how many pints the company should sell per day if they want to maximize their profit. f)What is the maximum profit the company can earn per day? g)Find the average cost function. h)How many pints should the company sell per day if they want to minimize…Where average costs of production are lowest when all output is produced by a single firm.A firm is jointly owned by Juan and Roda. The firm’s production function requires two inputs: effort by Juan, denoted by x, and effort by Roda, denoted by y. Effort is only observable by the person who exerts it. The cost to Juan of a unit of his effort is c j = 2 and the cost to Roda for a unit of her effort is cr = 2. The price received for the goods is p = 2. The production of the firm is given by Q = 10(ln(x + 1) + ln(y + 1)). Assume that both Juan and Roda are risk-neutral rational agents.a) What are the socially optimal amounts of effort x* and y*? What is the total surplus in that case? (Hint: Solve the problem of a social planner that cares equally for Juan and Roda.)b) Suppose that Juan and Roda have a contract that specifies that Juan pays a fixed amount w = 15 to Roda and that Juan gets to keep and sell all the output. What is the total surplus now? How much of that surplus goes to Juan? To Roda?c) Now suppose that the contract between Juan and Roda specifies that the total…
- A firm has access to two production processes with the following marginal cost curves: MC1 = 0.25x and MC2 = 6+0.1y, where output in production process 1 is x, output in production process 2 is y and hence total output produced is Q = x+y. Show your work to answer the following questions. (i) If it wants to produce 20 units of output, how much should it produce with each process? (ii) If it wants to produce 38 units of output, how much should it produce with each process? (iii) If it wants to produce 108 units of output, how much should it produce with each process?A research study published in Social Science Medicine, “Production Functions for General Hospitals,” estimated the following general hospital production function in the Netherlands: Q = 5*Staff.34*Beds.64*Drugs.04*Specialists.02, where Q is a measure used by the authors for patient care. Suppose a hospital currently utilizes the following inputs: Staff =20, Beds = 120, Drugs = 60, Specialists =10. Use a spreadsheet to find the following or otherwise. If the hospital increases its specialists by one (1), that is, employs an 11th specialist, the increase in Q (marginal product) will be:Distinguish between economies and diseconomies of scale, ensuring to differentiate between internal and external economies and diseconomies of scale.
