From the previous analysis, you can determine that as Musashi increases his production of tea towels, his opportunity cost of producing one more tea towel decreases increases remains constant
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From the previous analysis, you can determine that as Musashi increases his production of tea towels, his
decreases
increases
remains constant
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- Juan Valdez owns a coffee farm in Colombia. His production function is: f(x1,x2)=(x1−1)^0.25 x2^0.5 Assume the price of input 1 is r and the price of input 2 is w. (a) Write down an expression for the technical rate of substitution. (b) Find Juan's demand for inputs conditional on the quantity y of coffee Juan wants to produce. (c) Find Juan's cost function. (d) What is the supply function of Juan's firm?10) Suppose a firm is currently producing 100 units of good A for a total cost of $75,000 and 100 units of good B at a total cost of $30,000. If the firm finds that it can produce the two goods together, what is the savings in total cost (in percentage terms) that the firm can achieve by exploiting economies of scope?You manage two chocolate factories. Using only these two factories, you must produce exactly 420 kgs of chocolate daily at lowest possible cost. Mathematically, you have: Q1 = Quantity produced at Chocolate Factory #1 Q2 = Quantity produced at Chocolate Factory #2 Daily total overall production: Q1 – Q2 = 420 At present, each factory produces half the overall requirement. This means that Q1 = 210, Q2 = 210 a) Following your logic , you realize that as long as the marginal cost is different between the two factories, you can lower overall cost while maintaining production at 420 kgs. So, to reduce the overall cost to the lowest possible, you decide to move more than 1 kilogram from one factory to another. As a result, each factory will produce a different quantity of chocolate while the overall daily production remains at 420 kgs. To minimize overall cost, how many kilograms will you order/instruct Factory #1 to produce? Q1 = ____________kgs And how many kilograms would you…
- Suppose that Marie produces milk q using her own labor l and cattle k using the production functionq = f(k, l) = k2/3ℓ1/3Although Marie does not need to pay anyone to use either input, the opportunity costs of labor and cattle are w = 1 and v = 16, respectively, and P is the price of milk. a) Suppose that Marie’s stock of cattle is fixed at k0 = 8. Set up her short run cost minimization problem and find her labor demand ℓ(q) and cost function SC(q). b) Find Marie’s short run marginal cost SMC(q) and average cost SAC(q) functions and find the quantity at which short run average cost is minimized. c) Set up Marie’s short run profit maximization problem and find her short run supply curve q(P).Assume an economy producing only two goods (shoes and computers) with a fixed amount of productive resources and technology and employing all its productive resources to the maximum.Production in this economy is subjected to the law of diminishing marginal returns and resourcesare assumed to be fully optimized. In addition, the cost of sacrificing shoes for computers andvice versa is 1. On the basis of the foregoing assumptions, answer the following questions: Assume now that the sacrifice ratio is greater than 1, show what will happen to the shape of the production possibility frontier.Consider a firm that produces widgets according to the following Cobb-Douglas production function: Q = A * L^α * K^β where: Q is the quantity of output, L is the quantity of labor, K is the quantity of capital, A is a scale parameter (total factor productivity), α and β are the output elasticities of labor and capital respectively. Given that A = 1, α = 0.6, β = 0.4, L = 16 and K = 9, a) Calculate the quantity of output Q. b) If the firm increases the quantity of labor (L) to 20 while keeping the quantity of capital (K) constant, what will be the new quantity of output?
- Ike's Bikes is a major manufacturer of bicycles. Currently, the company produces bikes using only one factory. However, it is considering expanding production to two or even three factories. The following table shows the company's short-run average total cost (SRATC) each month for various level of production if it uses one, two, or three factories. (Note: Q equals the total quantity of bikes produced by all factories.) Number of Factories. Q = 50 1 140 2 230 3 320 Q = 100 60 110 160 Average Total Cost (Dollars per bike) Q = 150 Q = 200 40 40 80 80 40 40 Q = 250 160 110 60 Q = 300 320 230 140 per bike. Suppose Ike's Bikes is currently producing 300 bikes per month in its only factory. Its short-run average total cost is $ Suppose Ike's Bikes is expecting to produce 300 bikes per month for several years. In this case, in the long run, it would choose to produce bikes using one factory one factory On the two factories its SR plot the three SRATC curves for Ike's Bikes from the previous…The Cobb-Douglas production function for a particular product is N(x,y) = 80x0.6.0.4, where x is the number of units of labor and y is the number of units of capital required to produce N(x, y) units of the product. Each unit of labor costs $40 and each unit of capital costs $60. Answer the questions (A) and (B) below. (A) If $150,000 is budgeted for production of the product, determine how that amount should be allocated to maximize production, and find the maximum production. (B) Find the marginal productivity of money in this case, and estimate the increase in production if an additional $50,000 is budgeted for the production of the product. C (A) If $150,000 is budgeted for production of the product, determine how that amount should be allocated to maximize production, and find the maximum production. Production will be maximized when using units of labor and units of capital.The profit function of our firm is a piecewise function depending on 2 goods: II(Q₁, Q₂) = AQ² - 3Q² + Q1Q2 + 35Q₁ + 82Q2 − 245 if Q₁ ≤ 5 Unfortunately, we don't know have any information about the profit function when Q₁>5. As we don't have any information when the quantity produced of good 1 is greater than 5, we use the total differential equation to make estimations when Q1>5. Currently, we are producing 5 units of good 1 and 10 units of good 2. a) What is the value of A knowing that our estimation of profit, using total differential equation, is 500 when Q₁=7 and Q₂=10? A = b) Assuming that we still produce 5 units of good 1 and 10 units of good 2. Using total differential equation, how many units of good 1 should we produce in total to increase profit by 38% if we decrease production of good 2 to 8 units? (If needed, round your answer to 2 digits after the decimal point). Q₁=
- A firm uses inputs L and K to produce output Q and the production function is Q = 5LK. The firm is currently using inputs L = 6 and K = 8. If the firm reduces its capital purchase to only 2 units, how much additional K must it purchase to keep output constant? Group of answer choices 12 14 16 18Let y = f(x1, x2)=x11/2 + x1x2 be a firm’s production function, where x1≥0, x2≥0. Write down the firm’s production possibility set, and its input requirement set. Is this production function concave, quasi-concave? Is this production function homogenous? Find its returns to scale when x1=1, and x2=1.Ike's Bikes is a major manufacturer of bicycles. Currently, the company produces bikes using only one factory. However, it is considering expanding production to two or even three factories. The following table shows the company's short-run average total cost (SRATC) each month for various levels of production if it uses one, two, or three factories. (Note: Q equals the total quantity of bikes produced by all factories.) Average Total Cost (Dollars per bike) Number of Factories Q = 50 Q = 100 Q = 150 Q = 200 Q = 250 Q = 300 1 180 100 80 120 200 360 2 270 150 80 80 150 270 3 360 200 120 80 100 180 Suppose Ike's Bikes is currently producing 50 bikes per month in its only factory. Its short-run average total cost is $ per bike. Suppose Ike's Bikes is expecting to produce 50 bikes per month for several years. In this case, in the long run, it would choose to produce bikes using