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?
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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?
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- Suppose that the cost of producing q appliances is C(q) = 500 – 4q + q? and the demand function is given by p = 14 – 2 q. The quantity that minimizes the average cost function and the corresponding price are g= 22.36 and p= -30.72 a) Why the corresponding price is negative? explain The maximum profit would be -473 b) Why the maximum profit is minus? explain what happensA firm has a linear demand function for it's product.When the price of the product is sh.20,the quantity demanded is 40 units.When the price increases to sh.240 the quantity demanded becomes 30 units.In addition,the firm's marginal cost function is giving by: Mc = 40q- 2q^2+2 Fixed cost = 5 million Where q= quantity demanded,Mc = marginal cost(sh.million) Required 1.The level of output that maximises profits 2.The maximum profit 3.The price of the product at the maximum profitWhat is the price function of output for a firm with cost function c(y) = y2+ 2y2+ 6 ? (a) y = P/6 (b) y = 4/P (c) y = 2/P (d) y = P/2
- A company manufacturing laundry sinks has fixed costs of $100 per day but has total costs of $2,500 per day when producing 15 sinks. The company has a daily demand function of q = 360 − p, where q is the number if laundry sinks demanded and p is te price of a laundry sink. (b) Find a function for the average cost of this company?A firm's demand function is Q = 16 – P and its total cost function is defined as TC = 3 + Q +0.25Q 2 . Use these two functions to form the firm's profit function and then determine the level ofoutput that yields the profit maximum. What is the level of profit at the optimum?The cost function for Acme Laundry is: TC(q)=10+10q+q^2 so its marginal cost function is: MC(q)=10+2q where q is tons of laundry cleaned. Derive the firm's average cost and average variable cost curves. What q should the firm choose so as to maximize its profit if the market price is p? How much does it produce if the competitive market price is p = 50?
- The cost of producing x teddy bears per day at the Cuddly Companion Co. is calculated by their marketing staff to be given by the formula C(x) = 100 + 37x - 0.07x2. (a) Find the marginal cost function C'(x). C'(x) = (b) How fast is the cost going up at a production level of 100 teddy bears? When they produce 100 teddy bears, the production costs are increasing at a rate of x dollars per teddy bear In other words, the cost to produce the 101st teddy bear is approximately dollars (c) Find the average cost function C, and evaluate C(100). C(x) = C(100) = So when they produce 100 teddy bears, the average cost per teddy bear is x dollars. (d) Fill in the blanks: Since the marginal cost is less than the average cost per unit, increasing production from 100 teddy bears will cause the average cost per unit to decrease.The cost function for Acme Laundry is: TC(q)=10+10q+q^2 so its marginal cost function is: MC(q)=10+2q where q is tons of laundry cleaned. Derive the firm's average cost and average variable cost curves. What q should the firm choose so as to maximize its profit if the market price is p? How much does it produce if the competitive market price is p = 50?What would it look like in excel?Find the price that will maximize profit for the demand and cost functions, where p is the price, x is the number of units, and C is the cost. Demand Function p= 78-0.1 square root x Cost Function C = 33x + 550 $ =
- Mathematical Economics If fixed cost are 20, variable cost per unit are 2 and the demand function is P+ 2Q = 24, find the profit function in terms of Q.The total revenue curve of a firm is R (q) = 40q - 12q2 and its average cost A(q) = 1/30q2 - 12.85q +20 + 400/q, where q is the firm's output. (1) Derive and expression C(q) for the firm's total cost function.The demand function for a firm is p = 320 – 3.2x, and the cost function is C(x) = 100 + 80x – 1.6x2 Required (i) Determine the profit function. (ii) Determine the output and price for maximum profit and the maximum profit. Show that it is a maximum point.
