You own a bakery and the inverse demand function for your cakes is P=8-1.5Q. If the cost of producing cake is C=0.5Q, determine the profit-maximizing quantity, and the profit-maximizing price.
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- Suppose the (inverse) demand for a firm’s product is given by P = 10−2Q and the cost function is C(Q) = 2Q What is the profit-maximizing level of output and price for this firm?A firm faces a demand function D(p), for which the revenue- maximizing price is $10. The demandfunction is altered to 2D(p). What is the new revenue maximizing price?Jabari's HookNLadder is the only company selling fire engines in the fictional country of Alexandrina. Jabari initially produced four trucks, but then decided to increase production to five trucks. The following graph gives the demand curve faced by Jabari’s HookNLadder. As the graph shows, in order to sell the additional fire truck, Jabari must lower the price from $105,000 to $90,000 per truck. Notice that Jabari gains revenue from the sale of the additional engine, but at the same time, he loses revenue from the initial four engines because they are all sold at the lower price. Use the purple rectangle (diamond symbols) to shade the area representing the revenue lost from the initial four engines by selling at $90,000 rather than $105,000. Then use the green rectangle (triangle symbols) to shade the area representing the revenue gained from selling an additional engine at $90,000
- The supply function for a product is 2p − q − 60 = 0, while the demand function for the same product is (p + 20)(q + 10) = 8100. Find the market equilibrium point.Q)Suppose a small company sells speakers. The company determines that the supply function for the speakers is given by S(x)=10x+50,And the demand function for speakers is given by D(x)=5000-20x. Where x is the speaker price. How many speakers can be supplied at a price of $30?If the demand function is p=100-4q, find the level of output at which total revenue is maximum and also find the maximum revenue.
- The demand function for specialty steel products is given, where p is in dollars and q is the number of units. p = 180 3 125 − qThere are two different demand curves at your movie theaters. During the weekends, the inverse demand function is P=20-0.001Q, on weekdays, it is P=15-0.002Q. The marginal cost if 25,000 per movie. Determine prices for the weekends and weekdays.Suppose the equilibrium price in the market is $10 and the price elasticity of demand for the linear demand function at the market equilibrium is -1.25. Then we know that: demand is inelastic. marginal revenue is $2. marginal revenue is $50. demand is unit elastic.
- Elsie sells homemade lemonade. If she prices a glass of lemonade at $3, she sells 12 glasses a day. If she gives a $0.50 discount (per glass), she can sell 3 more glasses per day. Write a linear demand equation q = mp + b, where p is the price per glass, and q is the number of glasses she can sell per day. Suppose that it costs her 20 cents a glass to make lemonade. There is no fixed cost. Write down the revenue function, cost function, and profit function as functions of p. How much should she charge per glass to maximize her profit? What is the maximum profit?The demand function for small high-definition televisions is given by p = 9,000 − 55x, where p is the price, in dollars, that x televisions can be sold. The cost function (in dollars) to produce televisions is C = 3,500x + 2,000. (Simplify your answers completely.) (a)Find the revenue function, R. R = (b)Find the profit function, P. P = (c)Find how many televisions should be sold to maximize profit. televisions (d)What is the maximum profit (in dollars)? $Suppose a firm faces a demand curve for its product P=a-bQ, and the firm's cost of production and marketing are c(Q)=cQ+d, where P is price, Q is quantity and a,b,c and d are positive constants. find the following; a) The formula for profit 9(pie) in terms of Q b)The first order condition for maximum profit c)the second order condition for maximum profit