A firm's total cost function is: C = 6x2 - xy + 10y2 + 30, subject to the production quota x + y = 34. Construct the Lagrange function and solve for the equilibrium values. Calculate the total cost. What is the value of the determinant of the bordered Hessian matrix?
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- Say the the aggregate inverse demand function is D(Q) = 100 - Q, where Q = q1+q2. Both firms have the same cost c(q)=cq. Only firm q1 is allowed to participate. Therefore, q2 = 0. Find the function that maximizes welfare. What is the demand and price when welfare is maximized?The demand function for a firm is; Qd = 122,000 - 500P + 4M +10,000PR where, Qd is quantity demanded, P is price per unit. M is income, and PR the price of a related good. The estimated the valueS of M and PR will be Rs 3200 and Rs 4, respectively. The firm's estimated average variable coSt function IS; AVC = 500 - 0.03Q + 0.000001Q2 a. Find the profit maximizing level of output of the firm and the price to charge. b. Should the manager continue production or shut down? Explain your answer. c. Find the level of output at which the average variable cost is at its minimum.Consider an imperfectly competitive service provider, Muscat Automotive Repair Services (MARS), whose total cost of production is C = 30Q +0. 165Q2. Also, MARS faces two different market segments, A and B, whose demands can be linearly expressed as QA = 240 − PA and QB = 120 − 0.5PB . (Hint: the marginal cost is the slope of the total cost function). 4. If MARS decides to segment the market in accordance with the demands of groups A and B, find the profit-maximizing prices and quantities (PA, QA) and (PB, QB).5. What is the value of the consumer surplus for each group A and B, under this segmentation strategy?6. Draw the situation described in (4) and (5) above, clearly showing each group’s profitmaximizing price and quantity, and the areas that correspond to their consumer surpluses.7. Verify the inverse elasticity rule under each of the scenarios described (1) and (4) above.
- The 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)Consider a manufacturing firm with total cost function: TC = 250,000 + 40Q + 0.01Q2, and market demand function: P = 940 – 0.02Q (a) Determine the firm’s profit function. (b) Determine the firm’s OPTIMAL output level. (c) Find the market price of the output at optimal operation?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 firm faces inverse demand function p(q) = 120 - 4q, where q is the firm's output. Its cost function is c(q) = c * q. a. Write the profit function b. Find the profit-maximizing level of profit of unit cost c. c. Find the comparative statics derivative dq/dc. Is it positive or negative?The marginal profit function of a firm (profit (Π), point (Q) rate change depending on quantity) is MΠ = Π ^ '= dΠ / dQ = -2Q + 120. The fixed costs of the firm produced by the company are 1000 TL. In addition, the company is known to sell the goods it produces for 200 TL. Accordingly, answer the following questions.a) Find the firm's profit function.b) Find the cost function of the firm.denton productions limited utilizes statistical analysis to determine the optimal price for its sales to customera, during july 2020, the company was provided with the following demand and cost functions by a statistical research company, p=200-6Q, where p=price in dollars; and Q=quantitity of units in thousands TC=5Q2 + 24Q + 150, where TC is total costs in thousands of dollars a. determine the optimal output for july 2020 b. find the price that maximized profit
- Suppose both cooperatives are price-takers; with PG=12 and PF =10 being the market prices of gold and fish respectively. The cost of producing G units of gold is cg(G,x)=G2+(x−4)2; where x is the quantity of mercury effluent discharged into the dam. The cost of producing F units of fish is cF(F,x)= F2 + xF ; where cF(F,x) is an increasing function of x. a) Determine the profit maximizing level of gold output, profit and level of mercury effluent discharged into the dam. Comment and explain your results. b) What is the fishing cooperative’s profit maximizing level of fish output and profit? Explain your results. c) Suppose the two cooperatives were merged to operate as a single firm; determine the socially optimal level of gold and fish output, mercury effluent and profit. Explain, comment on and contrast your results with those obtained in a and b above. d) Suppose property rights to the dam water are created and assigned to the fishing cooperative. Does this induce efficiency and…A firm's demand and total cost function are given by the expression: P = 20 - Q/2 (1) TC = 0.5Q2 + 36 (2) Where P is price per unit in £ TC = total cost in £ Q is quantity demanded and produced. Find the profit-maximising level of output using the profit function and calculate how much profit is made at this output level.Marginal cost is given by the function :- 2Q2 - 130 And the equilibrium quantity is 10 so calculate the marginal cost.