Compute the price elasticity of demand
Not what you're looking for?
Question 1:
Demand for a product produced by a firm is given by the expression: P = 60 ? 5Q. Fixed cost is 20. Variable costs of producing Q units are VC (Q) = ? Q2 + 16Q.
(I) Find expressions for total, average and marginal costs. Find expressions for total, average and marginal revenue. Find an expression for profit.
(II) Find an output that maximizes the total revenue. Compute the price elasticity of demand at this output. Explain the economic reasons for the value of the price elasticity of demand found at this level of output. How big is the maximum possible total revenue?
(III) Find an output that maximizes the profit. Compute the elasticity of demand at this output. Check if the demand is elastic or inelastic at this output and explain the economic intuition for the answer found. How big is the maximum possible profit?
Purchase this Solution
Solution Summary
Demand for a product is considered.
Solution Preview
Hello!
(I) Total cost is the sum of average costs and fixed costs. I'll assume here that the "Q2" you wrote in the VC(Q) expression is actually Q squared, which I'll write as Q^2. Furthermore, there is a "?" in the VC(Q) equation. I'll assume that the VC(Q) equation is then VC(Q) = Q^2 + 16Q. I'll explain all the procedures so that, in case it's different, you'll be able to solve it anyway. So:
Total cost = Q^2 + 16Q + 20
Average cost is (Total Cost)/Q:
Avg Cost = Q + 16 + 20/Q
Marginal cost is the derivative of Total cost with respect to Q:
Marginal Cost = 2Q + 16
Now, revenue is price times quantity demanded (P*Q). Since we have that P = 60 - 5Q, then:
Total Revenue = (60 - 5Q)Q = 60Q - 5Q^2
Average revenue is (Total Revenue)/Q:
Avg Revenue = 60 - 5Q
Marginal Revenue is the derivative of total revenue with respect to Q:
Marg Revenue = 60 - 10Q
Finally, profit is total revenue minus total cost:
Profit = 60Q - 5Q^2 - Q^2 - 16Q - 20 = 44Q - 6Q^2 - 20
(II) The output that maximizes total revenue can be found by ...
Purchase this Solution
Free BrainMass Quizzes
Economics, Basic Concepts, Demand-Supply-Equilibrium
The quiz tests the basic concepts of demand, supply, and equilibrium in a free market.
Basics of Economics
Quiz will help you to review some basics of microeconomics and macroeconomics which are often not understood.
Economic Issues and Concepts
This quiz provides a review of the basic microeconomic concepts. Students can test their understanding of major economic issues.
Pricing Strategies
Discussion about various pricing techniques of profit-seeking firms.
Elementary Microeconomics
This quiz reviews the basic concept of supply and demand analysis.