Problem #2 A 2-product firm is known to have the following demand functions: Q1 = 40 – 2P, - P2 Q2 = 35 – P – P2, The firm's cost function is C = Q? + 2Q3 + 10. Calculate the firm's profit maximizing levels of output and the corresponding prices. What is the maximal profit"
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- Assume that marginal revenue equals rising marginal cost at 100 units of output. At this output level, a firm's average total cost is $11 and its total variable cost is $600. If the price of the product is $3 per unit and the firm follows its optimal strategy, the firm will earn an economic profit equal toA 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).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.
- 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?A firm in a perfectly competitive market has a fixed cost of $5 and a MC function of 9X, where X is the firm's output choice, for X = 0,1,2,3 and 4 units. The current market price of X is P = $30. In this case, the optimal X* for the firm is ______ units, and at this output, the firm faces a total cost of _____. Group of answer choices 3; $59 3; $95 4; $59 4; $95Consider the following price-demand function: P = 80 − 4Q, {Q/0 ≤ Q ≤ 10} (i) Sketch the price-demand function(ii) Find the revenue function.(iii) Suppose C = 20 + 5Q , find the profit function(iv) Calculate the profit if Q=8(v) Find the break-even level of output You have to solve iv and v
- You are the manager of a bakery that produces and packages bran buns. According to the new research, a typical consumer's inverse demand function for your bran buns is P = 4-0.5Q . Your cost of producing bran buns is C (Q) = 1Q . a) Determine the optimal number of bran buns to sell in a single package and the optimum package price. Find profits you earn. b) Suppose your company sells buns charging per-unit price. Find the profit-maximizing price. c) Compare profits your company would earn using the strategy of one price (b) with profits generated in (a).A firm has the following demand and average total cost functions: Q = 30 − PATC =7/Q− 6 +1/2 Q Find the level of output that will maximize revenue and minimize total cost and the profit function and the level of output that maximize profitsYou are the manager of a firm that sells its product in a competitive market with market (inverse) demand given by P = 50 − 0.5Q. The market equilibrium price is $50. Your firm's cost function is C = 40 + 5Q2. Your firm's marginal revenue is Multiple Choice MR(Q) = 50 − Q. indeterminable based on the information in the question. MR(Q) = 10Q. $50.
- (i) If the demand function 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 (a) The revenue R(x) and profit Π(x). (b) All values of x for which production of the commodity is profitable. (ii) The total cost of manufacturing x units during the daily production run at a factory,is C(x)= x2+ x+900 dollars. Usually,x(t)=25t units are manufactured during the first t hours of production. (a) Express the total manufacturing cost as a function of t. (b) How much will have been spent on production by the end of the third hour? (c) When will the total manufacturing cost reach $11,000?Suppose that the manager of a firm operating in a competitive market has estimated the firm’s average variable cost function to be AVC = 10 – 0.03Q + 0.00005Q2, TFC = 60. What is the MC function? What is the output where AVC is minimum? What is the optimum profit?A new restaurant – Chang – has just opened in Austin. It is serving the upscale market, with truly outstanding pasta that is flown in overnight from Bologna, Italy. Chang offers a fixed-price menu with appetizer, three dishes of pasta, and a delicious tiramisu for dessert. The restaurant faces the following demand function: Q = 600 - 4P. where Q is the number of guests per day. The marginal cost is constant at $50 per customer (including expenses for ingredients and personnel). The restaurant is paying a rent of $2,000 per day. What is the proft mazimixing number of guests and what price should Chang charge to maximize profits?