The market structure of the local pizza industry is best characterised by monopolistic competition. Pizza Shack is one of the producers in the local market.The market demand for Pizza Shack is: Qd = 225 – 10P.Pizza Shack’s cost function is: C(Q) = 0.15Q^2Where Q^2 refers to q squaredDetermine Pizza Shack's profit maximizing level of output and the price charged to customers.8. The market price for Pizza Shack at this level of output is
Question
The market structure of the local pizza industry is best characterised by monopolistic competition. Pizza Shack is one of the producers in the local market.The market demand for Pizza Shack is: Qd = 225 – 10P.Pizza Shack’s cost function is: C(Q) = 0.15Q^2Where Q^2 refers to q squaredDetermine Pizza Shack's profit maximizing level of output and the price charged to customers.8. The market price for Pizza Shack at this level of output is
Solution
To determine Pizza Shack's profit maximizing level of output and the price charged to customers, we need to first find the marginal cost (MC) and marginal revenue (MR).
-
The cost function is given as C(Q) = 0.15Q^2. The marginal cost (MC) is the derivative of the total cost with respect to quantity. So, MC = dC/dQ = 0.3Q.
-
The demand function is given as Qd = 225 - 10P. We can rewrite this as P = 22.5 - 0.1Q to make it easier to work with. The marginal revenue (MR) is the derivative of the total revenue (PQ) with respect to quantity. So, MR = d(PQ)/dQ = 22.5 - 0.2Q.
-
To find the profit maximizing level of output, we set MR = MC and solve for Q. So, 22.5 - 0.2Q = 0.3Q. Solving this equation gives Q = 45.
-
Substituting Q = 45 into the demand function gives the price that Pizza Shack should charge to maximize profit. So, P = 22.5 - 0.1*45 = 18.5.
Therefore, Pizza Shack's profit maximizing level of output is 45 pizzas and the price charged to customers is 18.5.
Similar Questions
Suppose you are the manager of a pizza restaurant chain. You are planning to open new outlets in Mumbai and New Delhi. You know the prices of the cheapest pizza from other outlets in each city. You are given the task of setting competitive prices for your menu.Pizza Prices in Mumbai (₹) Pizza Prices in Delhi (₹)480 500450 330350 340220 1,800350 250- 210 Question 3/4MandatoryMedianWhat is the median price for Mumbai and Delhi, respectively?₹350 and ₹335₹350 and ₹330₹220 and ₹340₹420 and ₹330
Suppose you are the manager of a pizza restaurant chain. You are planning to open new outlets in Mumbai and New Delhi. You know the prices of the cheapest pizza from other outlets in each city. You are given the task of setting competitive prices for your menu.
The monthly rent for a pizza parlor is $1,200. The average production cost per pizza is $6.75. The monthly expenses for the pizza parlor are given by the function 𝐸(𝑥)=1,200+6.75𝑥 , where x is the number of pizzas sold. For x pizzas sold, the pizza parlor's revenue is given by the function 𝑅(𝑥)=12.5𝑥 .The monthly profit of the pizza parlor is the difference between its revenue and its expenses. Which function represents the monthly profit, 𝑃(𝑥) ? A. 𝑃(𝑥)=5.75𝑥+1,200 B. 𝑃(𝑥)=5.75𝑥−1,200 C. 𝑃(𝑥)=1,200+19.25𝑥 D. 𝑃(𝑥)=6.25𝑥−1,200
The following table contains a monthly demand schedule for large, single-topping, carry-out pizzas.Price Quantity Demanded$15 A$20 25If the law of demand applies to these pizzas, then A could beGroup of answer choices30.25.0.15.
In a market there are two consumers. Each consumer has a demand curve of P = 10–0.5q. What is the market demand curve? Group of answer choicesP = 10 – QP = 10 – 0.25QP = 20 – QP = 10 – 2QP = 20 – 0.5Q
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.