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A firm produces two goods in pure competition and has the following total revenue and total cost functions:
TR = P1Q1 + P2Q2 and
TC = 2Q12 + Q1Q2 +2Q22
Where, P1 = 12 and P2 = 18.
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- A firm produces two goods in pure competition and has the following total revenue and total cost functions: TR = P1Q1 + P2Q2 and TC = 2Q12 + Q1Q2 +2Q22 Where, P1 = 12 and P2 = 18. Form the profit function and identity the critical value Q1*. Identity the critical value Q2*. Construct the Hessian matrix and calculate the value of |H1|. Calculate the value of |H2|. Based on the values of Hessian, what can you say about the profit?Given the following total revenue (TR) and total cost (TC) functions for a firm, write down the firm’s profit function. Determine the level of output the firm should produce in order to maximize profits by using the first-order condition. Confirm that this quantity represents maximum profits by using the second-order condition.TR=4000Q−33Q2TC=2Q3−3Q2 +400Q+5000The price-demand equation for the production of bluetooth speakers is: p = 250 - 1/20x, for 0 is less than or equal to x and x is less than or equal to 5000 where x speakers can be sold at $p per each speaker. The cost to produce x speakers is given as C(x) = 150,000 + 30x, where both C(x) and p are represented in dollars ($). - find the profit function and the marginal profit and interpret the quantity P'(4500) - find the marginal cost and interpret the quantity C'(3000) - find the revenue function and the marginal revenue and interpret the quantity R'(3000)
- Mizuno Corporation produces and sells running shoes. The marketing division (the downstream division) of Mizuno faces the following the direct market demand equation as follows: Q = 392 – 2P, where Q is the number of pairs of shoes and P is the price of a pair of shoes. Production of each pair of shoes requires 1 square yard of leather. The leather is shaped and cut by the Form division of Mizuno (the upstream division). The Form division’s only customer is the marketing division. The total cost function for leather is TCU = 0.5QU2 +10 QU +2 where QU is the quantity of leather produced. The total cost of assembling and selling shoes (excluding the leather) is TCD = 2Q2 + 6Q + 4. a) Write down the profit equations of downstream division, upstream division and total profits b) Calculate the profit-maximizing quantity of shoes (Q*), quantity of leather (Qu) and price of shoes (P*) c) Determine the optimal transfer price (PU∗)Mizuno Corporation produces and sells running shoes. The marketing division (the downstream division) of Mizuno faces the following the direct market demand equation as follows:Q = 392 – 2P,where Q is the number of pairs of shoes and P is the price of a pair of shoes. Production of each pair of shoes requires 1 square yard of leather. The leather is shaped and cut by the Form division of Mizuno (the upstream division). The Form division’s only customer is the marketing division. The total cost function for leather is TCU=0.5Q2U+10QU+2,where QU is the quantity of leather produced. The total cost of assembling and selling shoes (excluding the leather) isTCD = 2Q2 + 6Q + 4. a) Write down the profit equations of downstream division (πD), upstream division (πU), and total profits (π). b) Calculate the profit-maximizing quantity of shoes (Q*), quantity of leather (Q*U ) and price of shoes (P*)c) Determine the optimal transfer price (P*U).d) Using the profit equations of your answer in a),…Mizuno Corporation produces and sells running shoes. The marketing division (the downstream division) of Mizuno faces the following the direct market demand equation as follows:Q = 392 – 2P,where Q is the number of pairs of shoes and P is the price of a pair of shoes. Production of each pair of shoes requires 1 square yard of leather. The leather is shaped and cut by the Form division of Mizuno (the upstream division). The Form division’s only customer is the marketing division. The total cost function for leather is TCU=0.5Q2U+10QU+2,where QU is the quantity of leather produced. The total cost of assembling and selling shoes (excluding the leather) isTCD = 2Q2 + 6Q + 4. a) Write down the profit equations of downstream division (πD), upstream division (πU), and total profits (π). b) Calculate the profit-maximizing quantity of shoes (Q*), quantity of leather (Q*U ) and price of shoes (P*)c) Determine the optimal transfer price (P*U).d) Using the profit equations of your answer in a),…
- A firm faces the following average revenue (demand) curve: P = 100 - 0.01Q. where Q is weekly production and P is price, measured in cents per unit. The firm’s cost function is given by C = 5Q +2000. Assuming the firm maximizes profits production, determine the price and total profitper week.A two - product firm faces the following demand and cost functions: Q1 = 40 - 2P1 - P2 Q2 = 35 - P1 - P2 C = Q 2/1 + 2Q 2/2 + 10 (a) find the output levels that satisfy the first order condition for maximum profit. (use fractions) (b) check the second - order sufficient condition. Can you conclude that this problem possesses a unique absolute maximum? (c) What is the maximal profit?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?
- The total revenue curve of a firm is R(q) = 40q − 12q2 and its average cost A(q) = 1/30 q2 − 12.85q + 20 + 400/q , ,where q is the firm's output. Is the rate of change of profit increasing or decreasing when the output level of the firm is 10 units?For 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 > QPWhen economists talk about a barrier to entry, they are referring to a.the downward-sloping portion of the long-run average total cost curve. b.a factor that makes it difficult for potential competitors to enter a market. c.the opportunity cost of equity capital that is incurred by a firm producing at minimum total cost. d.the declining output experienced as additional units of a variable input are used with a given amount of a fixed input.
