a. Specify the first order condition for the firm's profit maximization problem. b. Suppose there is a differentiable function x(p) that satisfies the implicit function above. Using the chain rule, find x' (p). c. Specify conditions on the function f(x) so that x' (p) > 0.
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- (b) You are the CEO for a lightweight compasses manufacturer. The demand function for the lightweight compasses is given by p = 40 – 4q²where q is the number of lightweight compasses produced in millions. It costs the company $15 to make a lightweight compass. (i) Write an equation giving profit as a function of the number of lightweight compasses produced. (ii) At the moment the company produces 2 million lightweight compasses and makes a profit of $18,000,000, but you would like to reduce production. What smaller number of lightweight compasses could the company produce to yield the same profit? Problem з(b) You are the CEO for a lightweight compasses manufacturer. The demand function for the lightweight compasses is given by p 40 – 4q²where q is the number of lightweight compasses produced in millions. It costs the company $15 to make a lightweight compass. (1) Write an equation giving profit as a function of the number of lightweight compasses produced. (11) At the moment the company produces 2 million lightweight compasses and makes a pre of $18,000,000, but you would like to reduce production. What smaller number of lightweight compasses could the company produce to yield the same profit? Σ BIUG G |卡 三 = 9 ..(b) You are the CEO for a lightweight compasses manufacturer. The demand function for the lightweight compasses is given by p = 40−4q2where q is the number of lightweight compasses produced in millions. It costs the company $15 to make a lightweight compass. (i) Write an equation giving profit as a function of the number of lightweight compasses produced. (ii) At the moment the company produces 2 million lightweight compasses and makes a profit of $18,000,000, but you would like to reduce production. What smaller number of lightweight compasses could the company produce to yield the same profit?
- 8. Daisy's Doggie Treats has a marginal profit function given by m(x) = 0.34e0.02x dollars per bag of treats, where x is the number of bags of treats produced and sold each month. If production and sales increase from 200 to 250 bags each month, then profit will increase by which of the following? a) $31.90 b) $1,594.86 c) $72,242.76 d) $1,653.27 e) None of the above1. Consider a two-product firm under pure competition. With pure competition, the prices of both commodities will be taken as exogenous, denoted by P₁ and P₂. The production cost is C (Q₁, Q2) = Q +3Q/²2 where Q₁ and Q₂ represent the output levels of product 1 and product 2. (e) Find the maximum proifit that this firm can earn as a function of P₁ and P₂.A firm knows that its marginal cost for a product is MC = 2x + 15, that its marginal revenue is MR = 51 − 4x, and that the cost of production of 60 units is $4,660. (a) Find the optimal level of production. units(b) Find the profit function. P(x) = (c) Find the profit or loss at the optimal level. There is a ---Select--- profit loss of $ .
- 6.10. Firm supply and industry supply. A firm's marginal cost curve is given by MC(q) = 1+1 q. The minimum of the firm's aver- age cost is given by 2.5. (a) Plot the firm's marginal cost function. (b) Derive the expression of the firm's supply curve. (c) Determine the firm's optimal output level when p 4. (d) Determine the firm's optimal output level when p = 2. (e) Suppose that the industry in question comprises 200 firms like the one above. Derive the industry supply curve.[F] The profit function of a business firm is 1 3 T = f(q) = -³ + 6q² – 11q – 50. (i) What output q should the business firm produce to maximize the profit? (ii) What is the maximum profit the business fırm can generate?A7 You are the manager of a bakery that produces and packages gourmet muffins, and you currently sell muffins in packages of 3. A consultant’s report has estimated the (inverse) demand of a typical consumer to: P = 3 − 0.5Q If your cost of producing bran muffins is C(Q) = Q: (a) What is the marginal cost of muffins? (b) Draw the demand and marginal cost on a diagram. (c) Determine the optimal number of muffins to sell in a single package. (d) What price should the firm charge for each park?
- The figure deplcts the demand curve for Beautiful Cars, and the marginal cost and Isoprofit curves of the car manufacturer. The quantity and price at polnt E are (Q*. P*) - (30, 5,500). Suppose now that the firm Increases the price to 5,550 and chooses the corresponding level of output from the demand function at the new price. Based on this Information, whlch of the following Is correct? 8,000 Demand curve 100 Quantity of cars, O O The firm will sell 30 cars at the higher price. O The firm's profit remains the same. O The quantity of cars produced reduced. O Tho firm's profit is now incroasod Price, Marginal cost ($)(1). derive and sketch the optimization condition for profit maximization.1. Estimated Demand. You are the manager of a firm that sells packs of coffee pods for coffee makers. You typically sell the packs for $24 and sell an average of 2,470 packs per month. You decide to raise the price to $28 per pack. When you do this your monthly sales fall to 1,482 packs per month. a. Assuming that your firm’s demand function is linear (i.e., takes the form QP=a-bP), calculate the linear demand function for the packs 2. Markups and elasticities. The marginal cost (MC) of producing your product is $16 a. Using the estimated demand curve from the previous question, calculate the point price elasticities of demand at the two price from question 1 b. Use the markups and elasticities and indicate whether the two prices are higher or lower than the profit maximizing price. NOTE: YOU DO NOT NEED TO CALCULATE THE PROFIT MAXIMIZING PRICE YET.