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Profit-maximization: Non-competitive Market
A monopolist in the makeup industry produces two makeup products F and G for which the demand functions, respectively, are:
1. Find the profit-maximizing quantity of output for each product.
2. Find the profit-maximizing price for each product.
3. What is the maximum profit that the firm could earn?
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- a） Find the equation of the total cost function if total costs are 5200 when ? = 8.A cost function, Cix), is given below. Find the average cost per item when the required number of iteros are produced. C(x)=22x+1200, 1000 items What is the average cost per item? $23.20Write the MC function if the total cost function is TC = 100 + 120q + q^2
- The average cost function is given as:- AC = 2.5Q2 - 40 Calculate the average cost for the 8th unitA study of 86 savings and loan associations in six northwestern states yielded the following cost function. C� = 2.38 - 0.006153Q� + 0.000005359Q2�2 + 19.2X1�1 (2.86) (3.08) (3.68) (2.96) where C� = average operating expense ratio, expressed as a percentage and defined as total operating expense ($ million) divided by total assets ($ million) times 100 percent. Q� = output; measured by total assets ($ million) X1�1 = ratio of the number of branches to total assets ($ million) Note: The number in parentheses below each coefficient is its respective t-statistic. Which of the variable(s) is (are) statistically significant in explaining variations in the average operating expense ratio? (Hint: t0.025,70=1.99�0.025,70=1.99.) Check all that apply. Q� Q2�2 X1�1 What type of average cost-output relationship is suggested by these statistical results? Quadratic Cubic Linear Based on these results, what can we…The average cost function is:- 3Q² - 14Q + 20 Find the total cost function
- If AFC=60 and ATC=120 when output is 100, then total variable cost must be: 60 40 6000 8000A company makes solar panels. The company's revenue function, in dollars, is R(n) =10n, where n is the number of panels produced. The cost function is C(n) 100 (2)30. R and C are shown on the graph below. 1000 800 600 400 200 1 20 40 60 80 100 in Number of Panels a) Estimate from the graph i) the break-even points ii) the number of panels that should be produced for maximum profit b) Write the equation for the profit function P. c) Graph P. d) Use your graph of P to estimate the number of panels that give maximum profit. e) How would your answers for break-even points and maximum profit change if ) the number of dollars of revenue per panel is increased slightly? ii) the cost function is changed to C(n) 100(2)35? f) What does the number that was changed in part e) ii) represent?| %3D DollarsA study of 86 savings and loan associations in six northwestern states yielded the following cost function. C = 3.12 - 0.006768Q + 0.000005359Q2 +21.1X1 (3.12) (2.61) (2.89) (2.96) where C = average operating expense ratio, expressed as a percentage and defined as total operating expense ($ million) divided by total assets ($ million) times 100 percent. Q = output; measured by total assets ($ million) X1 = ratio of the number of branches to total assets ($ million) Note: The number in parentheses below each coefficient is its respective t-statistic. Holding constant the effects of bank branching (X1), what is the level of total assets that minimizes the average operating expense ratio? $1,262.92 million $1,558.81 million $631.46 million $460.99 million What is the average operating expense ratio for a savings and loan association with the level of total assets determined in the previous part and 1 branch? 1.17% 3.15% 1.02% 5.63% What is the ratio with 10 branches instead? 5.93% 1.47%…
- MC=500Q2√Q3+5 (b) Find the total cost functionA company manufactures and sells book-cases .The selling price is $54.90 per book case.The total cost.The total cost function is linear, and cost amounts to $50,000 for 2,000 book-cases and $32,120 for 800 book-cases. (a)Write the equation for revenue.(b)Write the equation for total cost. (c)Find the break even point.A study of 86 savings and loan associations in six northwestern states yielded the following cost function. C� = 3.69 - 0.007999Q� + 0.000005359Q2�2 + 25.0X1�1 (3.69) (3.08) (3.42) (3.50) where C� = average operating expense ratio, expressed as a percentage and defined as total operating expense ($ million) divided by total assets ($ million) times 100 percent. Q� = output; measured by total assets ($ million) X1�1 = ratio of the number of branches to total assets ($ million) Note: The number in parentheses below each coefficient is its respective t-statistic. Holding constant the effects of bank branching (X1�1), what is the level of total assets that minimizes the average operating expense ratio? $746.31 million $1,562.70 million $1,492.63 million $461.31 million What is the average operating expense ratio for a savings and loan association with the level of total assets determined in the previous part and 1 branch?…
