a) Find expressions for TR, (profit) x , MR, and MC in terms of Q. b) Solve the equation dn dQ and hence determine the value of Q which maximizes profit. c) Verify that, at the point of maximum profit, MR=MC.
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- Consider the demand function d(p)=300e^−0.01p^2 items purchased when charging p dollars per item. Currently the price is 9 dollars per item. Use marginal analysis to estimate the decrease in demand when the price increases by 0.3 dollars per item. Demand would decrease by approximately _____ items. Round your answer to three decimal places.a) The demand and supply functions of a particular good are given by the equations 5pq = 10 5p + 5q +15A firm sells two goods (X and Y) that are related in consumption. The estimated demand and cost conditions are: PX = 20 − 0.1QX− 0.05QY PY = 70−0.3QY−0.1QX MCX = 1 + 0.1QX MCY = 2 + 0.25QY MRX = 20 − 0.2QX− 0.05QY MRY = 70 −0.6QY− 0.1QX What are the profit-maximizing levels of output for the two goods? a. QX = 51, QY = 74 b. QX = 41, QY = 24 c. QX = 20, QY = 10 d. None of the choices are correct e. independent
- 4) An economic consultant for MCM corporation recently provided the firm’s marketing manager with this estimate of the demand function for the firm’s product: Qxd = 12,000 − 3Px + 4Py − 1M + 2Ax where Qxd represents the amount consumed of good X, Px is the price of good X, Py is the price of good Y, M is income, and Ax represents the amount of advertising spent on good X. Suppose good X sells for K200 per unit, good Y sells for K15 per unit, the company utilizes 2,000 units of advertising, and consumer income is K10,000. 4 (i) How much of good X do consumers purchase? 4 (ii) Are goods X and Y substitutes or complements? 4 (iii) Is good X a normal or an inferior good?No written by hand solution Suppose that the market for video games is competitive with demand function Qd = 170 – 4p + 2Y + 3pm – 2pc, where Qd is the quantity demanded, p is the market price, Y is the monthly budget that an average consumer has available for entertainment, pm is the average price of a movie, and pc is the price of a controller that is required to play these games. Given that Y = $100, pm = $30 and pc = $30, use Excel to calculate quantity demanded for p = $10 to p = $80 in $5 increments. Using Excel’s spreadsheet Find Qd = ________ when P=$30. Find Qd = ________ when P=$45. Now, Y increases to $120. Re-calculate the demand schedule and find Qd = ________ when P=$20. Let Y = $100 again, but pm increases to $40. Re-calculate the demand schedule and find Qd = ________ when P=$25. Let Y = $100, pm = $30, and pc increases to $40. Re-calculate the demand schedule and find Qd = ________ when P=$50.1. Which of the following might increase product price from P3 to P5? a. An improvement in production technology. b. A decline in the price of a substitute good. c. An increase in the price of a complementary good. d. Rising incomes if the product is a normal good. 2. An increase in price from P3 to P5 would: a. shift this firm’s MC curve to the right. b. mean that MR5 exceeds MC at Q3 units, inducing the firm to expand output to Q5. c. decrease this firm’s average variable costs. d. enable this firm to obtain a normal, but not an economic, profit. 3. At P4: a. this firm has no economic profit. b. this firm will earn only a normal profit and thus will shut down. c. MR4 will be less than MC at the profit-maximizing output. d. the profit-maximizing output will be Q5. 4. Suppose P4 is $10, P5 is $15, Q4 is 8 units, and Q5 is 10 units. This firm’s: a. supply curve is elastic over the Q4–Q5 range of output. b. supply curve is…
- The market research conducted by a firm in the drinking water industry shows that the demand for water has a constant elasticity equal to − 1/? where ? is 9 a) Express the demand function in the form of a differential equation b, Find the general solution for the differential equation by expressing Q (the quantity demanded) as a function of P (the product price). c, ) Suppose that the demand for bananas has a constant elasticity equal to – 9. Explain in words (without providing any calculation) how decreasing the price would affect a banana seller’s total revenue and profits. Please help me. Thank you so much.2. Suppose your marketing research department estimates the demand for your company’s product as Qx= 500-11Px+0.5Y, where Qx is the quantity demanded per week, Px is the price of product X, and Y is the average household income per week in the city. R2=0.87, the standard error of the coefficients of the price (Px) and household weekly income (Y) are 2 and 0.1, respectively. a. Are the coefficients of Px and Y statistically significant? b. Given the initial values Px=$10 and Y=$1000, find price elasticity (Ep) and income elasticity(EY), respectively. Is the demand for the company’s product price and income elastic, or inelastic? c. What action should the manager take to increase the company’s operating revenue? d. Is the company’s product a normal good? How do you know? e. Interpret what R2=0.87 meansAssume that the demand function is equal to: QD = 5000 - 1000P Where the price range is P1.00 to P5.00, derive the demand schedule economics
- Given the following demand function for beef (kg), P = 200 – 5Q i) By how much would the price have to fall for consumers to be willing to buy 1 more kg of beef per day? ii) If the price decreases by N$0.9, by how much will the demand changed?The following relations describe monthly demand and supply for a computer support service to small businesses: Qd=3000-10P Qs=-1000+10P whrer Q is the number of businesses that need services and P is the monthly fee, in dollars. a. at what average monthly fee would demand equal zero? b. at what average monthly fee would supply equal zero? c. plot the supply and demand curves. d. what is the equilibrium price/output level? e. Suppose demand increases and leads to a new demand curve: Qd = 3500 - 10P f. Suppose new suppliers enter the market due to the increase in demand so the new suply curve is Q=-500+10P. What are the new equilibrium price and equilibrium quantity? g. Show changes on the graph.Market Equilibrium A retail chain will buy 900 cordless phones if the price is $10 each and 400 if theprice is $60. A wholesaler will supply 700 phonesat $30 each and 1400 at $50 each. Assuming that thesupply and demand functions are linear, find the market equilibrium point and explain what it means.
