OPEC can price gasoline as it wishes. Suppose that it knows how demand responds to changes in prices (p). In particular, it knows that the quantity of barrels of gasoline demanded (q) is given by the following function: $q = \alpha e^{-(1/5)p}$ where $\alpha$ is just a constant. 5. What are OPEC's revenues when $\alpha = 25$ and $q = 12$? Round your result to 1 decimal. $R(q) = $ 6. Given that the OPEC only faces a fixed cost, the total cost function is given by: $C(q) = 30$ What are OPEC's profit when $\alpha = 25$ and $q = 12$? Round your result to 1 decimal. $\pi(q) = $ 7. Solve the profit maximization problem to find the optimal quantity when $\alpha = 25$. Round your result to 1 decimal. $q^* = $
Added by Brandon H.
Close
Step 1
To find OPEC's revenues, we need to multiply the quantity demanded (q) by the price (p). We are given that q = 12 and a = 25. We can substitute these values into the demand function to find the corresponding price: q = Qe^(-1/5)p 12 = Qe^(-1/5)p To solve for p, Show more…
Show all steps
Your feedback will help us improve your experience
Aakash Goyal and 56 other Microeconomics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Suppose that you have been hired as an economic consultant concerning the world demand for oil. The demand function is $q=D(x)=63,000+50 x-25 x^{2}, \quad 0 \leq x \leq 50$ where $q$ is measured in millions of barrels of oil per day at a price of $x$ dollars per barrel. a) Find the elasticity. b) Find the elasticity at a price of 10 dollars per barrel, stating whether the demand is elastic or inelastic at that price. c) Find the elasticity at a price of 20 dollars per barrel, stating whether the demand is elastic or inelastic at that price. d) Find the elasticity at a price of 30 dollars per barrel, stating whether the demand is elastic or inelastic at that price. e) At what price is the revenue a maximum? f) What quantity of oil will be sold at the price that maximizes revenue? Compare the current world price to your answer. g) At a price of 30 dollars per barrel, will a small increase in price cause the total revenue to increase or decrease?
Sri K.
Madhur L.
(a) Production of an item has fixed costs of $\$ 10,000$ and variable costs of $\$ 2$ per item. Express the cost, $C,$ of producing $q$ items. (b) The relationship between price, $p,$ and quantity, $q,$ demanded is linear. Market research shows that 10,100 items are sold when the price is $\$ 5$ and 12,872 items are sold when the price is $\$ 4.50 .$ Express $q$ as a function of price $p$ (c) Express the profit earned as a function of $q$ (d) How many items should the company produce to maximize profit? (Give your answer to the nearest integer.) What is the profit at that production level?
Using the Derivative
Profit, Cost, and Revenue
Recommended Textbooks
Principles of Economics
Principles of Microeconomics for AP® Courses
Economics
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD