Problem #1 Let’s assume a firm’s inverse demand curve and cost equation is given below: P = 175 – 2Q C = 400 + 50 Q + 0.5Q^2 Find the optimal…
Problem #1
- Let’s assume a firm’s inverse demand curve and cost equation is given below:
- P = 175 – 2Q
- C = 400 + 50 Q + 0.5Q^2
- Find the optimal quantity, price, and profit.
- With quantity on the x-axis and price on the y-axis, graph the inverse demand, marginal revenue, and marginal cost curves. Show the optimal price and quantity on the graph.
Problem #2
- You’ve been given the following total cost function:
- TC = 25 + 4Q + Q^2
- What is the marginal cost? What is the average cost?
- Using your answers from part (1), calculate the optimal quality.
Problem #3
- You’ve been hired as a new manager for a local restaurant. While the restaurant serves manythings, they are known for their wood-fired pizza and locally-sourced beer. Since both products aregenerally purchased at the same time, we consider them as complements. Thus, if you sell a lot ofpizza, you would also expect to sell a lot of beer and vice versa.
- Explain what pricing strategy, would you use to maximize profits. Use general terms for youranswer (high price, low price, etc)
- Now, let’s assume you’ve estimated the following profit function:
- ∏ = (P beer) (Q beer) + (P pizza) (Q pizza) – (C beer) (Q beer) – (C pizza) (Q pizza)
- You’ve also estimated the following equations:
- Q beer = 63 – 5(P beer) + P pizza
- Q pizza = 120 – 2(P pizza) + 2(P beer)
- C beer = 2
- C pizza = 5
- What is the profit maximizing price and quantity for pizza and beer? What is your profit? Hint: Find marginal profit with respect to P beer and P pizza, then use substitution.
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