Assume that this is the cost function for a perfectly competitive firm: Cost (q) = 5 q² + 20 For this cost function, Marginal Cost = MC = 10 q. (45) Fill in the table with your values from your cost function. Total Cost AVC AFC ATC MC 2. 3. 4 LO
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- Month (m): 4 Day (d): 1 Use the two numbers above, m and d, to complete the cost function for a perfectly competitive firm: Cost (q) = m q2 + d = (30) For a cost function like yours, Marginal Cost (MC) = 2 m q . Specifically, what are the following for the cost function you wrote out above? Fixed Cost = Average Total Cost = Cost (q)/q = Variable Cost = Average Fixed Cost = FC/q = Marginal Cost = 2 m q = Average Variable Cost = VC/q = (15) Fill in the table with your values from your cost function. q Total Cost AVC AFC ATC MC 0 0 0 -- -- -- 1 2 3 4 5 6The total cost function of a perfectly competitive firm is TC=100+10*Q+5*0^2 For what time period does the function apply? What is the equation of the marginal cost function? If the market price is 50, what is the optimal production quantity of the firm? What is the value of total revenue at the profit maximum? What is the value of total cost at the profit maximum? Will be negative or positive value of the profit at the profit maximum? In the short run, does the company decide to produce (at profit max level)? Which minimum value indicates the shutdown point? Use the following set of options to answer the above questions: long run 100 short run AVCmin ACmin maybe 4 220 positive yes MCmin no 100 years 10+5*Q 200 10+10*Q QminConsider the perfectly competitive market for titanium. Assume that, regardless of how many firms are in the industry, every firm in the industry is identical and faces the marginal cost ( MCMC ), average total cost ( ATCATC ), and average variable cost ( AVCAVC ) curves shown on the following graph
- Exercise 1: For the production function from the previous homework: y = Kα Lα Assume that the firm is in the long run (so you can use the long-run cost function you found in the previous homework) to answer the following: a. Consider the case of α = 1/(3 + A), where A is the last digit of your ASU ID#. Also, assume that the market operates under perfect competition. Obtain long-run quantity produced and profits for the firm (as a function of parameters w1, w2 and p). Also obtain the (long-run) unconditional input demands (as a function of the same parameters). b. For the case of α = 1/2 obtain the long-run output price p (as a function ofQ. 4 For a firm with a Total Cost function TC = C(Q), recall that the definitions of Marginal Cost (MC) and Average !3! Total Cost (ATC) are given as follows: Marginal Cost (MC) = C'(Q) Average Total Cost (ATC) = C(Q)/Q Prove that the marginal cost is equal to the average total cost (MC = ATC) when the average total cost is at its minimum 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.)What happens to a competitive firm whose cost function exhibits decreasing marginal cost everywhere? Construct a concrete cost function of this type and carry out the search for the profit-maximizing output.
- A perfectly competitive firm has the following total cost function: Total Output(Units) Total Cost(₨)0 201 302 423 554 695 846 1007 117 How much will the firm produce if the price of the product in the market is ₨ 14 per unit? How will itchange its output if price rises to ₨ 16 per unit?Suppose a company's revenue function is given by R(q)=−q3+400q2R(q)=-q3+400q2 and its cost function is given by C(q)=550+12qC(q)=550+12q, where qq is hundreds of units sold/produced, while R(q)R(q) and C(q)C(q) are in total dollars of revenue and cost, respectively.A) Find a simplified expression for the marginal profit function. (Be sure to use the proper variable in your answer.) MP(q)=MP(q)= B) How many items (in hundreds) need to be sold to maximize profits? Answer: hundred units must be sold. (Round to two decimal places.)The cost function for Acme Laundry is: TC(q)=10+10q+q^2 so its marginal cost function is: MC(q)=10+2q where q is tons of laundry cleaned. Derive the firm's average cost and average variable cost curves. What q should the firm choose so as to maximize its profit if the market price is p? How much does it produce if the competitive market price is p = 50?What would it look like in excel?
- Consider a firm with a total cost function TC = q^2 + 20q + 225. a) In a diagram, measuring quantity along the horizontal axis, draw the firm’s Marginal Cost and Average Cost curves. Suppose that the government introduces a $10 per unit seller tax. b) What is the firm’s new total cost function? In the same diagram as above, illustrate how the tax affects the firm’s MC and AC curves. Does the tax affect the firm’s MC? Does it affect the firm’s minimum efficient scale? Suppose instead that the government introduces a new licensing fee that raises the firm’s recurring fixed cost to 400. C) In a new diagram draw the firm’s MC and AC before and after the introduction of the licensing fee. Does the fee affects’ the firm’s MC? Does it affect the firm’s minimum efficient scale?The total cost function of a firm producing Jeans is TC = 0.5Q3− 15Q2 + 175Q + 100, where Q is output. a.What are the total variable cost (TVC) and the total fixed cost (TFC) in this case? b.The average cost is given by AC = TC/Q, the average variable cost is AVC = TVC/Q and the average fixed cost is AFC = TFC/Q. Find the AC, AVC and AFC functions. c. If the marginal cost is MC = 3(0.5)Q2 - 2(15)Q + 175, then roughly sketch the graph of MC, AVC and AC (If you know how to use Excel, then you can get more accurate graphs). What relationship do you observe between the three cost curves?Suppose that there is an industry with a big number of firms, each of them with the cost function ci(w₁,w₂,y)=(yi²+1)w₁+(yi²+2)w₂a.Find the average cost of each firm.b.Which is the supply function curve in the short run of each firm?c.Describe the necessary input set of a firm.
