a) Given the supply and demand functions: P = 300 +5Q and P = 500-5Q: Find i. The TC and TR functions. ii. The MC and MR functions. iv. V. vi. vii. Solve the MC = MR equation. The profit function, it in terms of Q. Find the maximum profit quantity. Comment on your answers to iv. and vi.
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- The Potomac Range Corporation manufactures a line of microwave ovens costing $500 each. Its sales have averaged about 6,000 units per month during the past year. In August, Potomacs closest competitor, Spring City Stove Works, cut its price for a closely competitive model from $600 to $450. Potomac noticed that its sales volume declined to 4,500 units per month after Spring City announced its price cut. What is the arc cross elasticity of demand between Potomacs oven and the competitive Spring City model? Would you say that these two firms are very dose competitors? What other factors could have influenced the observed relationship? If Potomac knows that the arc price elasticity of demand for its ovens is 3.0, what price would Potomac have to charge to sell the same number of units it did before the Spring City price cut?A firm manufactures two goods labeled 1 and 2. It sells Qi items of good i for a fixed price per unit of pi. The total cost of producing good i is ciQi2.Explain briefly why the profit function is given byπ(Q1, Q2) = p1Q1 + p2Q2 − c1Q12 − c2Q22Find the values of Q1 and Q2 which maximize π and verify that the second-order conditions for a maximum are satisfied. Find an expression for the maximum profit.. An electricity producer has a constant marginal cost of production equal to $40 per megawatt. The residual demand for its electricity is given by P (q) = a−bq, where P is the price and q is the quantity of power generated by this producer. The producer knows the slope, b, but he vertical intercept of the residual demand curve, a is unknown. Assume A and B are greater than zero. If you get stuck, you may answer any of the following questions for special case where a = 80 And b = 0.5 for partial credit. (a) What is the marginal revenue, M R(q), for this producer? b) What is the optimal q for this producer? (c) What is the electricity producer’s optimal price? (d) What is the electricity producer’s optimal bid in a uniform price Auction? e) Suppose b is equal to zero. Would the producer have an incentive to submit a bid above its marginal cost? Explain.
- A price-taking firm in a competitive industry of a good that is continuously divisible (like sand) has a total cost function TC(Q) = 3.5Q^2 + 100Q + 500. The market price for the good is p = $240. a: Carefully write out this firm’s profit maximization problem, using the particulars of thisproblem. b: Give the marginal condition (equation) that characterizes the solution to this problem. Solvethis condition for the firm’s optimal quantity Q*. c: Calculate the firm’s maximized profit. d: On a graph with quantity on the horizontal axis, neatly plot the marginal revenue curve andmarginal cost curve. Show Q* on your graph. e: Label areas on your graph using a, b, c, etc. and indicate the areas that correspond to totalrevenue and variable cost.2. The supply Qs = s(P, Pm) has the functional form of: Qs = -12 + 0.5P - 2Pm initially, the materials cost Pm_0 = 7. Find the optimal quantity to supply if the price is P=76 and P=80. At P=76, Q_0 = . At P=80, Q_0 = . 3. Now, the cost of materials changes to Pm_1 = 9. Find the optimal quantity to supply if the price is P=76 and P=80. At P=76, Q_1 = At P=80, Q_1 = Draw the second supply curve and show how supply shifted.A commodity has a demand function modeled by p = 117 − 0.5x and a total cost function modeled by C = 40x + 31.75, where x is the number of units. (a) What price yields a maximum profit? $____________ per unit (b) When the profit is maximized, what is the average cost per unit? (Round your answer to two decimal places.) $_____________ per unit
- a) What is the fixed cost? b) Assume the firm can not make any excess profit and instead aims to sales maximise. Calculate the price and quantity at that point c)Find the profit maximising price and quantity d)Calculate the total profit using the Total cost and Total revenue functions. e)Find the Consumer surplus using integration. You must show the integral before inputting numbers.James mainly sells confectionery items, newspapers, magazines and cigarettes in his convenience store. Noting his small business is not thriving, he thought of selling hot pies and rolls too. Suppose the total cost function for rolls and pies is, TC = 900 + 50Q, Q = Q1 + Q2 Where Q1 and Q2denote the quantities of rolls and pies respectfully. If P1 and P2 denote the corresponding prices, the inverse demand equations are. Q1 = 70 - P1 and 0.5Q2 = 100 - P2 a)If James decides to make a total of 48 rolls and pies per day and charges different prices as above (that is, P1 ≠ P2 ), how many of rolls and pies each should he make in order to maximize the profit of a particular day? Estimate and interpret the Lagrange Multiplier λ [note: assume second-order conditions are satisfied]. b)Using your knowledge of input-output tables, explain which components of the economy will be affected if all convenience stores, including James’, closed down for three months due to the COVID-19. What would…1) a) Solve the following inequalities:(i) 5(11 − ?) < ? + 49 (ii) 7? − 3 <10m + 23< 8 − 5m (iii) ?2 ≥ 15 − 2? b) The cost structure for iPhones are as follows, fixed cost of $25 and variable cost perunit of $2. The associated demand function isp = 20 − q .(i) Obtain an expression for the profit, π(q). (ii) Find the range of output which gives a profit of at least $31. c) Use Microsoft Word or Excel to solve the system of linear inequalities:r + 5t ≤ 57t – 2r ≤ 4 r ≥ 0(NB: clearly identify the solution set by placing a BIG enough ‘S’ to coverthat entire region).
- 1. If profit is maximum at sales of 700 units, does the firm have no choice but to limit sales at this level? Explain your answer. 2. A business firm produces and sells a particular Variable cost is P30/unit. Selling price is P40 per unit. Fixed cost is P60,000. a. What is the break-even quantity and break-even point? Show your solution. 3. A manager makes the statement that output should be expanded as long as average revenue exceeds average Does this strategy make sense? Explain. 4. Suppose that the steel firm’s costs are shown below: Complete the table and determine the optimal output to be Price of steel P17 per unit. Output (Q) TFC TVC TC MC TR MR Profit/Loss 0 500 0 1 500 50 2 500 90 3 500 140 4 500 200 5 500 270 6 500 350 7 500 450…Continuing your analysis of the competitive US manufacturing industry from Question 1, withdemand of Qd = 500 – 8P and supply of Qs = 4P – 100, suppose a technological innovationcauses the supply curve to increase, shifting the curve down by $15 for every given quantity Q. Determine the new supply equation. Solve for equilibrium price P2 and quantity Q2. Depict the original supply S1, the new supply S2, and the original demand D1 on theusual P, Q diagram. Label all intercepts (including two intercepts for the demand curveand one intercept for the supply curve). Clearly indicate and label the new marketequilibrium. Graphically indicate the areas of Consumer Surplus (CS2) and Producer Surplus (PS2)that resulted from the new market equilibrium. Compute the values of Consumer Surplus (CS2) and Producer Surplus (PS2) associatedwith the new market equilibrium, clearly indicating the units that CS and PS aremeasured in. Who has benefited from technological innovation, based on the…For problems 1 – 4: The Dolan Corporation, a maker of small engines, determines that in 2019 the demand curve for its product is P = 2,000 - 50Q where P is the price (in dollars) of an engine and Q is the number of engines sold per month. If managers set a price of $750, how many engines will Dolan sell per month? a.30 b.35 c. 20 d.25
