Consider an industry with identical firms. Suppose the cost function of firm i, i=1,...,n, is given by C₁ (9₁) = 6 q² + 91 What is the minimum value of the individual firm's average cost? (As usual, you must enter a number below, not a ratio, not an expression with symbols..., just a number. Don't roun even if rounding makes sense.
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- Suppose there are 5 firms in this industry, each of which has the cost curves previously shown.Consider that a company has a total cost function TC = 3Q3+2Q2+6. a.What is the average and marginal cost function and what are their values ifQ = 8?b. If the (inverse) demand function facing the firm is P = 6 - 2Q, what value must the slope of the isobenefit curve take for the firm to maximize its profit? Indicate the generic condition as well.Assume that a competitive firm has the total cost function: TC=1q3−40q2+880q+2000 T C = 1 q 3 - 40 q 2 + 880 q + 2000 Suppose the price of the firm's output (sold in integer units) is $550 per unit. Create tables (but do not use calculus) with columns representing cost, revenue, and profit to find a solution. How many units should the firm produce to maximize profit? Please specify your answer as an integer. What is the total profit at the optimal output level? Please specify your answer as an integer.
- An economist estimated that the cost function of a single-product firm isC(Q) = 100 + 20Q + 15 Q^2 + 10 Q^3Based on this information, determine:c. The total cost of producing 10 units of output.Suppose the short-run cost function of Tyrell Corporation is c=5000+100q+8q2 a. Find the level/s of q that satisfies/satisfy the first-order and second-order conditions for the minimisation of Tyrell’s average cost(ac) Show that average cost ( ac) equals marginal cost (mc) at the level/s of obtained in (a)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?
- An economist estimated that the cost function of a single-product firm isC(Q) = 100 + 20Q + 15 Q^2 + 10 Q^3Based on this information, determine:b. The variable cost of producing 10 units of output.Trotter Inc is a polling company. Trotter uses both labor, L, (measured in hours worked) and capital, K, (measured in phone lines) to conduct surveys. The production function of Trotter’s is given by Q=10L^0.25 K^0.25 where Q is measured in surveys completed per hour. The price of a unit of L is $16 per hour and the price of a unit of K is $1 per hour. Trotter’s has additional fixed costs of $227 per hour. For parts (a) – (b) below assume that the number of phone lines is fixed in the short run. In particular, Trotter's has 16 phone lines (so K = 16). This results in additional fixed costs in the short run of $16 (ie in addition to the 227). a) In the short run what is Trotter’s (compensated) demand curve for labor? What is the variable cost curve? What is the total cost curve? b) In the short run, what is the marginal cost curve of Trotter’s? What is the average cost curve? What is the optimal size of the firm? Illustrate the short run marginal and average cost curves. For parts (c)-…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 total cost equation for a firm producing two products is TC(Q1, Q2) = 25 + Q12 + 4Q22 + 5Q1Q2 (a) Do cost complementarities exist for this firm? (b) Under what circumstances do economies of scope exist for this firm? (c) Suppose that Q1 = Q2 = 3. Do cost complementarities exist? (d) Suppose that the firm is currently producing 5 units of Q1, and 10 units of Q2, What is the firm's total cost of production? e) Suppose that the firm divests itself of the division selling Q1 to a competitor. How much will it cost the firm to continue producing 10 units of Q2? What is the total cost of producing both Q1 and Q2 if the firm producing Q1 produces 5 units?Bitcom, a manufacturer of electronics, estimates the following relation between marginal cost of production and monthly output: MC= $150+ 0.005Q What does this function imply about the effect of the law of diminishing returns on Bitcom’s short-run cost function? Calculate the marginal cost of production at 1,500, 2,000, and 3,500 units of output. Assume Bitcom operates as a price taker in a competitive market. What is this firm’s profit-maximizing level of output if the market price is $175? Compute Bitcom’s short-run supply curve for its product. Provide a 100 word summary of how this can be applied to the current economy. Show Calculations and can it be done in Excel?Suppose a firm has the following total cost function TC = 100 + 2q2. If price equals $20, what is the firm’s output decision? What are its short-run profits?
