3) Assume that a fim which produces an output according to the following function is attempting to minimize cost in the long run: q = f (K, L) = (0.5KV2 +0.5LV2)/2 a) Assuming K is fixed at 36, P=16, v=1, and w=1, what is the firm's short run cost function? Compute this firm's profit maximizing demand of L in the short run b) Compute this firm's cost minimizing (quantity constant) input demand functions. c) What are the firm's total cost and supply functions?
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- 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?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.Suppose that demand for a particular style of handmade Rwandan baskets is Qd = 1700 – 10P. Each basket maker has the following cost function: TCi = 1000 + 50 qi + .1 qi^2. Given this information, find the market outcomes under the various market structures below Perfect competition, long-run. Given the same cost functions above, find the long-run equilibrium quantity per firm, the LR market price, market quantity and equilibrium number of firms. What is the profit or loss per firm? What is MCi and ATCi?
- Habib Bank Limited estimates equation of demand of its product as: Q = 55 – 0.5P - (where P = price and Q = Quantity of output), and its total cost of production as TC = 20 + Q + 0.2Q2 Where TC = total cost and Q = Quantity of output) Write the equations of the firm’s costs, as a function of Q: Average Total Cost ATC? Average Variable Cost AVC? Average Fixed Cost AFC.? Marginal Cost MC? The output level that will maximize total profit and the amount of revenue and profit that Habib Bank would receive at optimal level of production.? The output level that minimizes average total cost.? please answer all questionsFor a company with (inverse) demand function P = 4,510 - 55Q and cost function C = 88,000 + 660Q, let QR, QU, and QP denote, respectively, the quantities that maximize revenue, per-unit profit, and overall profit. Which of the following statements is true?A. QU > QP > QRB. QP > QU > QRC. QU > QR > QPD. QR > QU > QPA firm sells its output in a PCM. The firm’s short-run cost function is given by SC = Q3/300 - 0.2Q2 + 4Q + 10 1. Derive the short-run supply function of a typical firm in this industry. 2. Assuming that there are 100 identical firms in this industry, derive the short-run market supply function. 3. If currently the market demand for these firm’s product is Q = 8,000 – 200P1⁄2 , determine the short- run equilibrium market price. 4. At this equilibrium market price, calculate the level of output and profit that each firm produces in the short-run. With this information, comment on the potential entry/exit of firms in this industry in the long-run.
- When Apple introduced its first portable media player, the iPod, its constant marginal cost of producing the top-of-the-line model was $200 (iSuppli), its fixed cost was approximately $736 million, and we estimate that its inverse demand function was p = 600 - 25Q, where Q is units measured in millions. Be sure to express your answers in the proper units, where needed. a. What was Apple's average cost function? b. Assuming that Apple was maximizing its short-run monopoly profit, what was its marginal revenue function? c. What were its profit-maximizing price, quantity, profit and Lerner Index? d. What was the price elasticity of demandDefine Q to be the level of output produced and sold, and assume that the firm’s cost function is given by the relationshipTC = 20 + 5Q + Q2Furthermore, assume that the demand for the output of the firm is a function of price P given by the relationshipQ = 25 - Pa. Define total profit as the difference between total revenue and total cost, and express in terms of Q the total profit function for the firm. (Note: Total revenue equals price per unit times the number of units sold.)b. Determine the output level where total profits are maximized.Suppose that the total revenue function of a firm is defined as TR= (P)(Q) where TR= f(Q). The usual notation applies. 1. . Find the total revenue function TR(Q) if the inverse demand function is given by P(Q) = 80-0.2Q2. What is the shape of the total revenue function if graphed? State your basis.
- a. Find the input demand (x), output supply (y), and profit function for the technology, y = ln(x), where y = 0 for x ≤ 1. b. Use Hotelling’s Lemma on the profit function in part (a) to find the input demand for x and the output supply for y.Define Q to be the level of output produced and sold, and assume that the firm’s cost function is given by the relationship TC = 20 + 5Q + Q2 Furthermore, assume that the demand for the output of the firm is a function of price P given by the relationship Q = 25 - P a. Define total profit as the difference between total revenue and total cost, and express in terms of Q the total profit function for the firm. (Note: Total revenue equals price per unit times the number of units sold.) b. Determine the output level where total profits are maximized. c. Calculate total profits and selling price at the profit-maximizing output level. d. If fixed costs increase from $20 to $25 in the total cost relationship, determine the effects of such an increase on the profit-maximizing output level and total profits.A firm's short-run production function is q=3L0.2 , while its cost function is C = 2L. Furthermore, the firm can sell its output in a perfectly competitive market at p = 40. 6.1 Find the value of the firm’s profit when L = 50 . 6.2 Calculate the level of L that satisfies the first-order condition for profit maximization. 6.3 Calculate the value of the second order derivative (SOD) that ensures profit is being maximised at the value of L found in 6.2 .