For the following total-profit function of a firm: = 144X – 3X² – XY – 2Y² + 120Y – 35 Determine the level of output of each commodity at which the firm maximizes its total profit. Determine the value of the maximum amount of the total profit of the firm.
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For the following total-profit function of a firm:
= 144X – 3X² – XY – 2Y² + 120Y – 35
Determine the level of output of each commodity at which the firm maximizes its total profit.
Determine the value of the maximum amount of the total profit of the firm.
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from Profit = 144X – 3X² – XY – 2Y² + 120Y – 35
to get the Marginal profit of X = d(Profit)/dX
X = 144 - 6X - Y
show the complete solution
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- For the following total-profit function of a firm: = 144X – 3X² – XY – 2Y² + 120Y – 35 Determine the level of output of each commodity at which the firm maximizes its total profit.Determine the value of the maximum amount of the total profit of the firm. show a step-by-step complete solutionA 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.Firm A and Firm B sell identical goods The total market demand is:Q(P) = 1,000-1.0P The inverse demand function is therefore: P(QM) = 10,000-10QM QM is total market production (i.e., combined production of firm’s A and B). That is: QM = QA + QB As a result, the inverse demand curve for each firm is: P(QA,QB) = 10,000-10QA-10QB The difference between this example and the example in class is that the two firms have different costs. Firm A has the same cost as in class, but firm B has a different cost function: TCA(QA) = 5000QA TCB(QB) = 5000QB Using the demand function and the cost functions above, what is firm A’s profit function? Using the profit function above and assuming that firm B produces QB, calculate what firm A’s best response is to firm B’s decision to produce QB. (Note: Firm A’s best response should be a function of QB) Using the demand function and the cost functions above, what is firm B’s profit function? Using the profit function above and assuming that firm A…
- Two farmers produce milk for local town with local milk demand given by Q=100-1/3P (P denotes price measured in Rands, Q denotes the quantity measured in litres). Both farmers have the same cost function given by TC=150+2q (where q denotes output)a. What if farmer 1 is a leader and farmer 2 a follower, determine the price, quantity and profits made by these two farmersConsider two firms that produce a single output good,y, using two inputs :Capital, K , and labor, L, the prices of each unit of capital and labor are r and w,respectively. The output good y sells for $p per unit. Firm A's production function is y = fa(K,L) = K1/4L1/4. The profit function is equals to : K1/4L1/4 - rK -wL. a) FInd the profit maximizing levels of K and L as functions of r,w, and p. b) Suppose that r = w= $1 and p =$4 . What is the profit maximizing level of output,y?Suppose that a firm produces identical commodities and sell them in two separate markets charging two different prices. The demand for the commodity in two markets are (1) P1 = 100 - Q1 and (2) P2 = 80 - Q2, where P1 and P2 are the price of the product that the firm charges, while Q1 and Q2 are demand in each market. Suppose that the firm's cost of production is C(Q) = 6Q. (1) What is the firm's total profit function in terms of the quantity of output? How much should this firm sell each product in two separate markets to maximize total profits?
- Suppose the (inverse) demand for a firm’s product is given by P = 10−2Q and the cost function is C(Q) = 2Q What is the profit-maximizing level of output and price for this firm?Consider an HMO with a demand curve of the following form: Q = 100 – 2 P. Suppose that its marginal and average costs were $20. If the firm maximizes profits, determine its price, output, and profits.A firm has revenue given by R(q) = 160q - 3q2 and its cost function is C(q) = 500 + 40 Q What is the profit-maximizing level of output? What profit does the firm earn at this output level? The firm maximizes profit by producing q = _______. (Enter your response as a whole number.) Corresponding profit is pi = $_________. Enter your response as a whole number).
- (i) If the demand curve for a particular commodity is p = −0.09x + 51 and the total cost function C(x) = 1.32x2 + 11.7x + 101.4,where x is the level of production. Find: 1. All values of x for which production of the commodity is profitable.Suppose you are given the following information about a particular industry: QD = 6500 – 100P Market Demand QS = 1200P Market Supply TC(q) = 722 + q2/200 Individual firm’s total cost function MC(q) = q/100 Individual firm’s marginal cost function Assume that all firms are identical and that the market is characterized by perfect competition. Find an individual firm’s supply curve. How many firms are there currently in the market? Find the equilibrium price and equilibrium market quantity. How much is output supplied by each firm, and how much profit does each firm make in the short run? Would you expect to see entry into or exit from the industry in the long run? Explain. What effect will entry or exit have on the market equilibrium? Find the long-run equilibrium price, the number of firms, and the amount of output each firm produces in the long run.The golden rule of profit maximization states that any firm maximizes profit by producing where: