Problem 1 (a) Teddy J is a manufacturer of dish washing liquid. If his monthly demand function for 750ml size is q = 4000 – 250p and his total cost function is C(q) = 500 + 0.2q. %3D (i) Derive an expression, R(q) for Teddy J's total revenue curve. (ii) Derive an expression, II(q) for Teddy J's profit function. (iii) Determine whether Teddy J's profit is increasing or decreasing when he produces 5 hundred, 750ml bottles of dish washing liquid. (iv) How many 750ml bottles of dish washing liquid should Teddy J produce per month if he wishes to maximize his profits. (b) A firm has an average cost function 125. q? - 4. A(q) + 16 where q is the firm's output. (i) Determine the level of output for average costs are minimum. (ii) Hence determine the range of values for which average costs are decreasing. (iii) What part of the decreasing range is practically feasible? (iv) Write an equation for the total cost function. (v) Hence calculate the level of output for which total costs are minimum.
Problem 1 (a) Teddy J is a manufacturer of dish washing liquid. If his monthly demand function for 750ml size is q = 4000 – 250p and his total cost function is C(q) = 500 + 0.2q. %3D (i) Derive an expression, R(q) for Teddy J's total revenue curve. (ii) Derive an expression, II(q) for Teddy J's profit function. (iii) Determine whether Teddy J's profit is increasing or decreasing when he produces 5 hundred, 750ml bottles of dish washing liquid. (iv) How many 750ml bottles of dish washing liquid should Teddy J produce per month if he wishes to maximize his profits. (b) A firm has an average cost function 125. q? - 4. A(q) + 16 where q is the firm's output. (i) Determine the level of output for average costs are minimum. (ii) Hence determine the range of values for which average costs are decreasing. (iii) What part of the decreasing range is practically feasible? (iv) Write an equation for the total cost function. (v) Hence calculate the level of output for which total costs are minimum.
Microeconomics: Private and Public Choice (MindTap Course List)
16th Edition
ISBN:9781305506893
Author:James D. Gwartney, Richard L. Stroup, Russell S. Sobel, David A. Macpherson
Publisher:James D. Gwartney, Richard L. Stroup, Russell S. Sobel, David A. Macpherson
Chapter11: Price-searcher Markets With High Entry Barriers
Section: Chapter Questions
Problem 14CQ
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Relevant Course Objectives:
1. Apply the knowledge of functions to problems involving, supply, demand , production,
revenue and cost.
2. Identify the appropriate functions, equations and sequences which are to be used in
problem solving in the Social Sciences.
3. Use solutions to linear, quadratic, exponential and logarithmic equations to determine
market equilibrium price and quantity.
4. Solve problems involving rates of change and marginal change by the use of
derivatives
5. Write a linear system of equations in matrix form as a simple way to represent
multiple linear equations before solving them using a matrix approach.
6. Find and classify extreme points of a function for the purpose of identifying what
represents a minimum, a maximum or a point of inflexion.
7. Determine continuity or discontinuity of a function throughout its domain, since some
functions are not defined for all real numbers.
8. Solve a system of simultaneous equations with 3 variables using matrix inversion and
the Cramer's Rule.
9. Compute and interpret the value of the derivative of a function
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