Question

1. You are given the following demand equations:

Q 450 16P

Q 360 80P

Q 1,500 500P

a. Determine each equation’s total revenue and marginal revenue equations.

b. Plot the demand equation and the marginal and total revenue equations on a graph.

c. Use calculus to determine the prices and quantities that maximize the revenue foreach equation. Show the points of revenue maximization on the graphs that you have constructed.

2. You are given the following cost equations:

TC 1,500 300Q 25Q2 1.5Q3

TC 1,500 300Q 25Q2

TC 1,500 300Q

a. Determine each equation’s average variable cost, average cost, and marginal cost.

b. Plot each equation on a graph. On separate graphs, plot each equation’s average variable cost, average cost, and marginal cost.

c. Use calculus to determine the minimum point on the marginal cost curve.

3. Given the demand equation shown, perform the following tasks:

Q 10 .004P

a. Combine this equation with each cost equation listed in question 3. Use calculus to find the price that will maximize the short-run profit for each of the cost equations.

b. Plot the profit curve for each of the cost equations.

c. Use calculus to determine the minimum point on the marginal cost curve.

4. Given the demand equation shown, perform the following tasks:

Q 10 .004P

a. Combine this equation with each cost equation listed in question 3. Use calculus to find the price that will maximize the short-run profit for each of the cost equations.

b. Plot the profit curve for each of the cost equations.

Answer 1

Q1 :

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