Your firm specializes in recycling used plastics into consumer goods. You have three production opportunities: 1. You can produce plastic utensils for a revenue of $30,000 while production will cost $15,000. 2. Alternatively, you can produce lampshades: you calculate that at the optimal production, you expect to sell 2,000 lampshades every year at $10 each, and your average total cost per lampshade will be $2. 3. You also have the option to shut down your factory and produce nothing at a cost of $1,000 a year. Which opportunity do you choose?

5. The annual output for a luxury hotel chain is given by Q = 30K²/5 L¹/2 R¹/4, where K, L and R are the capital, labor and real estate inputs, all measured in $1,000,000 s, and Q is the average number of rooms rented per day. The hotel chain's annual budget is B = $69 million. (a) How should they allocate this budget to the three inputs in order to maximize their annual output? What is the maximum output? (b) What is the approximate change in the firm's maximum output if their annual budget increases by $500,000? Explain your answer.

Jacques lives in Detroit and operates a small company selling bikes. On average, he receives $773,000 per year from selling bikes. Out of this revenue from sales, he must pay the manufacturer a wholesale cost of $452,000. He also pays several utility companies, as well as his employees wages totaling $277,000. He owns the building that houses his storefront; if he choose to rent it out, he would receive a yearly amount of $3,000 in rent. Assume there is no depreciation in the value of his property over the year. Further, if Jacques does not operate the bike business, he can work as a nurse and earn a yearly salary of $32,000 with no additional monetary costs, and rent out his storefront at the $3,000 per year rate. There are no other costs faced by Jacques in running this bike company. Identify each of Jacques's costs in the following table as either an implicit cost or an explicit cost of selling bikes. Implicit Cost Explicit Cost The wages that Jacques pays The wholesale cost for the…

Question 37 [ DIFFICULT] Consider two firms, both producing the same product, using the same production technology given by: q = √√K This production technology implies the following MRTS: K MRTS=AY ΔΧ L where K is the amount of capital used and L is the amount of labour used to produce output. It can be shown that this production technology implies the following minimised total cost function: TC = 2q√w√r where w represents the per-unit cost of labour and r represents the per-unit cost of capital. Suppose each firm can hire labour at $1 per unit and capital at $9 per unit. Each firm produces 90 units of output. One firm (Firm 1) chooses its input combination to minimise costs of production. However, Firm 2 instead produces output using twice as much labour as Firm 1. Compared to Firm 1, how much higher are Firm 2's cost of production? a) $270 b) $67.50 c) $275 d) $135 e) $132 Hint: It can be shown that the cost-minimising quantities of capital and labour (chosen by Firm 1) are K = 30…

.(a) A firm has production function q(k,l) = k'/³1²/3, where k denotes the capital used and I denotes the labour employed. Suppose that each unit of capital costs v dollars and each unit of labour costs w dollars, so that the capital and labour costs are vk + wl. Use the Lagrange multiplier method to determine the values of k and I that minimise the cost of producing Q units of the firm's good. Find the corresponding minimised value, C, of this cost and the value, X*, of the Lagrange multiplier corresponding to the optimising values of k and l. Show that d* =

Suppose a local developer has built 24 houses so far this year at a total cost to the company of $4.8 million. If the company builds the 25th house, its total cost will increase to $5 million. Which of the following is correct? - all of the above - the marginal cost of the 25th house, if it is built, will be $200,000 - if the company can sell the 25th house for $250,000, then it should build it - for the first 24 houses, the average cost per house was $200,000

QUESTION 3 Zeus owns a factory which makes guitars which sell for $400 each. The number of guitars he can make in a month depends on the size of his crew. He pays each person on his crew $1500/month. He also pays rent on a building, which he has leased for the remainder of the year for $2000/month. The table below indicates how many guitars can be built, as a function of the size of his crew (the crew size excludes himself). You may assume all other cost, such as materials, are 0. Size of Crew Total # of Guitars 1 4 2 8 3 19 4 28 5 40 6 50 7 58 8 earns without a dollar sign and without a comma). 64 The size of the crew that maximizes the firm's profits is 9 67 10 70 11 72 12 The Marginal product of labor is the additional output per worker. Crew member delivers the greatest marginal product. 74 13 and Zeus dollars in profit per month (please record your answer 75

Suppose that Flamerock Tires must decide where to produce one million tires: the US, where wages are 30 and the cost of capital is 5; or China, where wages are 5 and the cost of capital is 25. Production in each location follows the same technology (production function) given by: Q = f(L, K) = L^0.25 K^0.75 Computationally solve the cost - minimizing input levels in each location to produce the goal of 1 million tires

Suppose that for a company manufacturing calculators, the cost, revenue, and profit equations are given by x² C = 70,000 + 30x, R=200x - A) Costs are increasing at the rate of $ (Simplify your answer.) where the production output in 1 week is x calculators. If production is increasing at a rate of 600 calculators per week when production output is 5,000 calculators. Find the rate of increase (decrease) in cost, revenue, and profit. B) Revenue is decreasing at the rate of $ (Simplify your answer.) C) Profits are (Simplify your answer.) 20 at the rate of $ P=R-C per week at this production level. per week at this production level. per week at this production level.

Assume a company expects to sell 6 million packages of Pop-Tarts Gone Nutty! in the first year after introduction but expects that 70 percent of those sales will come from buyers who would normally purchase existing Pop-Tart flavors (that is, cannibalized sales). The price for a package of Pop-Tarts Gone Nutty! is $1.30 and its variable cost is $0.65, when the price for a package of original Pop-Tart is $1.10 with variable cost of $0.30. Assuming the sales of regular Pop-Tarts are normally 300 million packages per year and that the company will incur an increase in fixed costs of $450,000 during the first year to launch Gone Nutty! will the new product be profitable for the company? Determine the unit contributions and the loss for every package cannibalized from the original product. (Round to the nearest cent.) Unit contribution original Pop-Tarts $ Pop-Tarts Gone Nutty! Loss for every package cannibalized S