Suppose a firm wants to produce 50 units of output at minimum cost and it has three factories with the following marginal cost functions MC;(y1) = 40 MC2(y2) = 4y2 MC3(y3) = 8y3 How should the firm allocate production across their three factories? (Note: if you can't figure out how to do this for three factories, you can do it for factories 2 and 3 for part marks)
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- How do we calculate each of the following: marginal cost, average total cost, and average variable cost?2. Suppose a firm wants to produce 50 units of output at minimum cost and it has three factories with the following marginal cost functions MC,(y1) = 40 MC2(y2) = 4y2 MC3(y3) = 8y3 How should the firm allocate production across their three factories? (Note: if you can't figure out how to do this for three factories, you can do it for factories 2 and 3 for part marks)Suppose your dad owns a voodworking shop where he makes handmade benches. The following graph shows the marginal cost (MC) and average variable cost (AVC) for your dad's business. 100 90 80 MC 70 60 AVC 50 40 30 20 10 10 20 30 40 50 60 70 80 90 100 OUTPUT (Benohes per month) For each of the prices in the following table, use the graph to determine the number of benches your dad would produce in order to maximize his profit. Also, for each of the prices, indicate whether the firm will produce or shut down (or be indifferent between the two) in the short run. Price Output (Dollars per bench) (Benchs per month) Produce or Shut Down? 32 36 42 55 66 76 COST (D olars per bench)
- 2. Trapper Joe, the fur trader, has found that his production function in acquiring pelts is given by q = 2pH where q =the number of pelts acquired in a day, and H =the number of hours Joeís employees spend hunting and trapping in one day. Joe pays his employees $8 an hour. a) Calculate Joeís total and average cost curves (as a function of q). b) What is Joeís total cost for the day if he acquires four pelts? Six pelts? Eight pelts? What is Joeís average cost per pelt for the day if he acquires four pelts? Six pelts? Eight pelts? c) Graph the cost curves from part a and indicate the points from part b.A firm has a fixed production cost of $4000. For the first 100 units of production, the firm has a marginal cost of $50 per unit produced. Producing more than 100 units has a marginal cost of $70 per unit produced. The firm cannot produce more than 150 units. How much does it cost to produce at q=0? at q=50? at q=100? at q=125? at q=150? Graph the firm’s marginal cost functionFor a firm with a Total Cost function TC C(Q), recall that the definitions of Marginal Cost (MC) and AverageTotal Cost (ATC) are given as follows:Marginal Cost (MC) = C'(0)Average Total Cost (ATC) = C(Q)/QProve that the marginal cost is equal to the average total cost (MC = ATC) when the average total cost is at itsminimum value.(Hint: By using the definition of average cost function, find the quantity that minimizes it by applying unconstraint optimization.Show that the FOC of the minimization problem implies that MC=ATC has to be satisfied at the minimum level of average cost.)
- Noah and Naomi want to produce 300 garden benches per week in two production plants. The cost functions at the two plants are C1(Q1)=800Q1−2(Q1)^2and C2(Q2)=850Q2−3(Q2)^2The corresponding marginal costs are MC1=800−4Q1and MC2=850−6Q2What is the best assignment of output between the two plants?Instructions: Enter your answers as whole numbers.Noah and Naomi should produce benches at plant 1 and benches at plant 2.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 Journal indicates that economies of scale in fracking may be considerably smaller than in conventional oil drilling. If this view is cor- rect, what would the likely consequences be for the num- ber of firms drilling for oil in the United States?Suppose that the Acme Gumball Company has a fixed proportions production function that requires it to use two gumball presses and one worker to produce 1,000 gumballs per hour. a. Explain why the cost per hour of producing 1,000 gumballs is 2v + w (where v is the hourly rent for gumball presses and w is the hourly wage). b. Assume Acme can produce any number of gumballs they want using this technology. Explain why the cost function in this case would be TC = q(2v +w), where q is output of gumballs per hour, measured in thousands of gumballs. c. What is the average and marginal cost of gumball production (again, measure output in thousands of gumballs)? (show the complete formula) Draw the graph for the average and marginal cost curves for gumballs assuming v=3, w-5 (show working) Now draw the graph for these curves for v=6, w=5.( show working) Explain why these curves have shifted.
- Suppose that the Acme Gumball Company has a fixed proportions production function that requires it to use two gumball presses and one worker to produce 1,000 gumballs per hour. a. Explain why the cost per hour of producing 1,000 gumballs is 2v + w (where v is the hourly rent for gumball presses and w is the hourly wage). b. Assume Acme can produce any number of gumballs they want using this technology. Explain why the cost function in this case would be TC = q(2v +w), where q is output of gumballs per hour, measured in thousands of gumballs. c. What is the average and marginal cost of gumball production (again, measure output in thousands of gumballs)? Graph the average and marginal cost curves for gumballs assuming v=3, w-5 Now graph these curves for v=6, w=5. Explain why these curves have shifted.Suppose a snowboard manufacturer increases its output by 1 snowboard per day. As a result, the total cost of producing snowboards each day rises from $100 to $110. The marginal cost of producing an extra snowboard is $ . (Only enter number; the $ sign has been provide for you.) Please answer neatly n give proper explanation within 40min2. If c=3q-3q2+q3is a cost function, when is marginal cost decreasing?