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# Firm’s inverse demand curve and cost

Problem #1Let’s assume a firm’s inverse demand curve and cost equation is given below:P = 175 – 2QC = 400 + 50 Q + 0.5Q^2Find 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 #2You’ve been given the following total cost function:TC = 25 + 4Q + Q^2What is the marginal cost? What is the average cost?Using your answers from part (1), calculate the optimal quality.Problem #3You’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 pizzaQ pizza = 120 – 2(P pizza) + 2(P beer)C beer = 2C pizza = 5What 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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