Write down the firm’s objective and efficiency condition. Using diagrams for this problem, calculate the dynamically efficient extractions, marginal user costs, present value of scarcity rents, and present value of total net benefits for the two periods.
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Suppose a firm is facing a two-period (t = 0, 1) depletable resource (e.g., oil) extraction problem. The inverse demand function of the resource is Pt=20–0.5Qt ; marginal extraction cost is MCt = $5/unit; resource stock is Q = 20 units and interest rate is r = 50%.
a) Write down the firm’s objective and efficiency condition. Using diagrams for this problem, calculate the dynamically efficient extractions, marginal user costs, present value of scarcity rents, and present value of total net benefits for the two periods.
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- (a) A retail company has a marginal profit curve given by: MP =-2Q 2+ 160Q + 2145. Determine the level of production, or range of production at which the company will have: (i) Increasing returns (ii) Decreasing returns (iii) Negative returns (iv) Its maximum profit (b) A production process varies only with raw materials, as all other inputs are fixed. The cost of a shipment of 8kg of raw materials is fixed at $85. It takes 5kg of raw materials to create one item of output, Q. The marginal revenue for this production process is expressed by: MR = =Q 2 + 520 – 576. 2+52Q Determine the optimal amount of raw materials to be used in this production process. (c) A production process varies with both labour, L and raw materials, M. The production function is given: Q = 1.25L 0.38 +0.9M0.68 Current production level is Q= 800 items and marginal profit is given as a fixed $16.50. Determine what profit can be expected if: (i) Labour is increased by 25%. (ii) Both labour and raw materials are…Green et al. (2005) estmate the supply and demand curves for Californa processod tomatoes. The supply function is: \[ \ln \left(Q_{s}\right)=0.200+0.550 \ln (p) \] whereQis the quantify of processing tomatoes in milions of tons per year andpis the price in dollars per ton. The demand function is: \[ \ln \left(Q_{d}\right)=2600-0.200 \ln (p)+0.150 \ln \left(p_{1}\right) . \] wherep1is the price of tornato paste (which is what processing tomatoes are used to produce) in dollars per ton. Supposept=$119Determine how the equilerium price and quantity of processing tomatees change if the price of tomato pasise tails by16%. If the price of tomato paste fals by18%, then the equaborium price will by 5 (Enter a numene response using a real number rounded to two decimal places)A manufacturer has found out that if he is to increase his current sales, he must lower his current price. His marginal revenue (MR) from an output x is given by the expression MR=148 – 2x. The marginal production cost (MC) is Ksh 36 and fixed costs amount to Ksh 1,000. Required i) Derive the revenue and total cost functions. ii) Determine the output and price that would maximize profit. iii) Compute the maximum profit.
- C&A Fast Food has four activities in serving a customer: greet customer, take order, process order, and deliver order. Each activity is staffed by one employee (for a total of four employees). The processing time for each activity is given as follows: Greet customer Take order Process order Deliver order Activity Processing time per customer 2 seconds 30 seconds 60 seconds 5 seconds Assume demand is unlimited. If one additional employee is added to the bottleneck activity, what will be the percentage change in process capacity?The business venture involves the sale of decorative jewelry cases. It costs the startup $280 to produce 40 jewelry cases a week while it costs $320 to produce 60 decorative cases per week as well. the demand, x, for your product is given as a linear function of price, p, where p(x)=15−0.02x 1.Assume that the total cost C(x),is linearly related to the output x. Find an equation for C(x).Hence, determine the Fixed Cost and Variable Cost for this startup. 2.Form the Revenue and Profit Functions based on the information given. 3.Hence, determine the Break-even points to the nearest whole number and discuss the relationship between the intersection points of the graphs of R(x)and C(x)The variable x represents the number of HDTVs manufactured and sold in a given month. The variable p is the price charged when you sell a TV. A demand curve is given by p = 660-3x. a) Find the x-intercept of this demand curve. Say what it means. Assume you must pay salaries totalling 8000$ in a month. Also, it costs $110 to manufacture one TV. b) Write a formula for your cost function C(x) c) Write a formula for your revenue function R(x) d) The profit function is M(x) = Graph the profit function and using the Maximum program, find the maximum possible profit and fill in the details (round off x to the nearest whole number): e) number of sales: f) profit: g) selling price: h) revenue: i) cost: j) check these results fit together: k) Find the range of prices you can charge and still be in the black: The lowest price you can charge is ___________ and the highest is ___________
- The marginal profit for a certain company is MP₁(x) = -x² + 18x-45. The company expects the daily production level to rise from x = 3 to x = 5 units. The management is considering a plan that would have the effect of changing the marginal profit to MP₂(x)= -x² +14x-33. Should the company adopt the plan? Determine the area between the graphs of the two marginal profit functions from x = 3 to x = 5. Interpret this area in economic terms. C Should the company adopt the plan that would make the marginal profit be MP₂? O A. Yes, because the company will make a larger profit under the new plan. B. No, because the company's profit will be smaller under the new plan. O C. It is impossible to tell using the given information. The area between the graphs of the two marginal profit functions from x = 3 to x = 5 is sq. units.Consider a firm with a production function given by y = min{yax,, bx2}. This firm can sell its product for price p and buy its inputs at input costs w1 and w2. In this situation, the conditional input demand functions are given by: 2.2 y? x,(y,W1, W2) = а %3D x2(y, W1, W2) : %3D Find the following components of the solutions to the cost minimization and profit maximization problems, and show that the required feature holds. The sequence in which the features are listed is not related to the sequence in which they need to be found. 2.2.1 The minimum cost function 2.2.2 The supply function 2.2.3 The input demand functions 2.2.4 The maximum profit function 2.2.5 Show that the maximum profit function is convex in pricesDetermining Rent in a Market with Low-Cost and High-Cost Firms Suppose firms in a competitive market for house paints have the cost function C(q)=8+2q+2q?. The market is in a long-run equilibrium. (a) What is the price of house paint? (b) Suppose a subset of the firms in the market have developed technology that reduces their costs by 50% at any output level. That means these low-cost firms have the cost function C(q)=4+q+q?. How much additional profit do these low-cost firms earn from the technology? (c) Suppose over time, more and more firms adopt the lower-cost technology. What will be the price of paints in the long run?
- Use the functions given below to solve the problem. C(x) represents the cost, in dollars, of x units of a product and R(x) represents the revenue, in dollars, from the sale of x units. Find the number of units that must be produced and sold in order to break even, C(x) = 72,000 + 43x and R(x) = 47x The number of units that must be produced and sold in order to break even is units.5) A company's cost of producing q liters of a chemical is C(q) dollars and this quantity can be sold for R(q) dollars. Suppose C(2,000) = 5,930 and R(2,000) = 7,780. a) What is the profit at a production level of 2000? b) If MC(2,000) = 2.1 and MR(2,000) = 2.5, what is the approximate change in profit if q is increased from 2000 to 2001? Should the company increase or decrease production from q = 2000 and why? %3D c) If MC(2,000) = 4.77 and MR(2,000) = 4.32, should the company increase or decrease production from q = 2,000 and why?The Hickory Cabinet and Furniture Company makes chairs. The fixed cost per month of making chairs is $7,500, and the variable cost per chair is $40. Price is related to demand, according to the following linear equation: v = 400 - 1.2p Develop the nonlinear profit function for this company and determine the price that will maximize profit, the optimal volume, and the maximum profit per month.