In Avengers: Infinity War the character Thanos seeks to use the power of the infinity stones to eliminate half the people in the universe. If output of the universe can be modeled by y= A× F(K.L) where F(K.I) = K1/3, 2/3 with an initial K = 100, L = 100, and A = 1, then how much would output change if Thanos gets his wish? (Calculate the percent change and give your answer as a decimal. It will be negative because output will be lower.)
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- Hannah 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. $The production of a product is characterised by the function f(x, y) = 16x/4y3/4, where x is the number of units of labour and y is the number of units of capital needed to produce f(x, y) units of the product. Each unit of labour costs £50 and each unit of capital costs £100. You are given a budget of £500,000 and are asked to calculate the number of units of labour that maximise the production. Enter your answer as an integer. Answer:Your business produces two products: graphics and writing assessments. However, time is finite and your business must allocate its time between the two products. If your business is producing one service, it cannot produce the other service at the same time. Based on previous experience, you know that your firm can produce 11 graphics and 20 assessments per day. Your firm could also produce 7 graphics and 40 assessments per day. Given these production possibilities, what is the tradeoff between your two services? Make sure you estimate your tradeoff (opportunity cost) in terms of how much you receive for each unit of graphics services that you give up, that is, for 1 unit of graphics given up, how many units of assessments do you gain? Make sure to express your answer to the first decimal point.
- What is a sunk cost? Provide an example of a sunk cost other than one from this book. Why are such costs irrelevant in making decisions about future actions?In recent years, the United States has experienced large increases in oil production due in large part to a new technology, hydraulic fracturing ("fracking"). Fracking involves injecting a mixture of water, sand, and chemicals into rock formations at high pressure to release oil and natural gas. An article in the Wall Street Journalindicates that economies of scale in fracking may be considerably smaller than in conventional oil drilling. If this view is correct, what would the likely consequences be for the number of firms drilling for oil in the United States?Suppose a person quits a job earning $45,000 per year and starts a business with $120,000 withdrawn from a money-market account earning 8 percent per year. The implicit cost of the business is $ for the entrepreneur's time plus $ for the entrepreneur's funds (enter your response as an integer).
- Introduction to Calculus in Economics (continued): In the previous Problem Set question, we started looking at the cost function C (x), the cost of a firm producing z items. An important microeconomics concept is the marginal cost, defined in (non-mathematical introductory) economics as the cost of producing one additional item. If the current production level is z items with cost C (x), then the cost of computing h additionial items is C (+h). The average cost of those h items (C(r+h)-C(x)) is As we analyze the cost of just the last item produced, this can be made into a mathematical model by taking the limit as h → 0, h i.e. the derivative C' (x). Use this function in the model below for the Marginal Cost function MC (x). Problem Set question: The cost, in dollars, of producing z units of a certain item is given by C (2) = 0.043 – 20x+ 350. (a) Find the marginal cost function. a ab Va a sin (a) MC (x) = E (b) Find the marginal cost when 60 units of the item are produced. The marginal…I do not understand the meaning of this question, if it is required to complete the task as soon as possible. I think it should be two people working at the same time, and according to the barrel effect, select a situation where the maximum time is short?A T-shirt screener can screen t-shirts (q) in two different ways. He can either use a fast screening machine (F) or a slow screening machine (S). Screen use is defined in terms of ”hours” running. His production function is f(F, S) = 10F + 6S. (a) The screener wants to be able to produce 120 shirts. List three feasible and efficient production plans (combinations of inputs) for doing this. (b) Graph the screener’s isoquant curve for q = 120. (c) The hourly cost of using the fast machine is $800 and the hourly cost of the slow machine is $200. What is the cost minimizing (optimal) combination of inputs for producing 120 shirts? (d) Suppose the screener must now produce 400 shirts. What is the cost minimizing combination of inputs?
- Your team can produce an output equal to Q=1000 units and you have two inputs or resources to use. These resources are labor and capital. Assume the wage rate is is $10 for labor and renting cost for a machine is $20. Suppose you have three combinations of resources available to you and these are: Option I Labor = 10 Capital = 5 Option II Labor = 4 Capital = 8 Option III Labor = 14 Capital = 2 Find the least cost method and decide which method you will select to produce Q=1000 (show your work below)Your team can produce an output equal to Q=1000 units and you have two inputs or resources to use. These resources are labor and capital. Assume the wage rate is is $10 for labor and renting cost for a machine is $20. Suppose you have three combinations of resources available to you and these are: Option I Labor = 10 Capital = 5 Option II Labor = 4 Capital = 8 Option III Labor = 14 Capital = 2 Find the least cost method and decide which method you will select to produce Q=1000Introduction to Calculus in Economics (continued): In the previous Problem Set question, we started looking at the cost function C (æ), the cost of a firm producing z items. An important microeconomics concept is the marginal cost, defined in (non- mathematical introductory) economics as the cost of producing one additional item. If the current production level is æ items with cost C (z), then the cost of computing h additionial (C(z+h)-C(z)) items is C (z + h). The average cost of those h items is . As we analyze the cost of just the last item produced, this can be made into a mathematical model by taking the limit as h → 0, i.e. the derivative C' (z). Use this function in the model below for the Marginal Cost function MC (x). Problem Set question: The cost, in dollars, of producing z units of a certain item is given by C (z) = 0.02a3 – 10z + 450. (a) Find the marginal cost function. MC (z) (b) Find the marginal cost when 50 units of the item are produced. The marginal cost when 50…