Consider the following graph of the average and marginal cost functions for a firm in a perfectly competitive market. 30 25 20 MC Р 15 10 5 AC 4 0 2 5 6 8 10 q At a price of P=10: (i) the firm's profit-maximizing quantity is 5 (ii) the average cost of production is (iii) the marginal cost of production is (iv) the firm's total profit is (v) the firm's variable profit is
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- On the graph input tool, change the number found in the Quantity Demanded field to determine the prices that correspond to the production of 0, 6, 12, 15, 18, 24, and 30 units of output. Calculate the total revenue for each of these production levels. Then, on the following graph, use the green points (triangle symbol) to plot the results. Calculate the total revenue if the firm produces 6 versus 5 units. Then, calculate the marginal revenue of the sixth unit produced. The marginal revenue of the sixth unit produced is________. Calculate the total revenue if the firm produces 12 versus 11 units. Then, calculate the marginal revenue of the 12th unit produced. The marginal revenue of the 12th unit produced is_________.A particular computing company finds that its weekly profit, in dollars, from the production and sale of x laptop computers is P(x) = -0.006x³ -0.3x² +600x-800. Currently the company builds and sells 7 laptops weekly a) What is the current weekly profit? b) How much profit would be lost if production and sales dropped to 6 laptops weekly? c) What is the marginal profit when x = 7? d) Use the answer from part (a) and (c) to estimate the profit resulting from the production and sale of 8 laptops weekly a) The current weekly profit is $ (Round to the nearest cent as needed) b) The decrease in profit is $ (Round to the nearest cent as needed.) c) The marginal profit when x=7 is $ (Round to the nearest cent as needed) CLOT d) The profit resulting from the production and sale of 8 laptops weekly is approximately $ (Round to the nearest cent as needed)The inverse demand for tea is given by P= 10 – 0.04Q, where Pis the price per a gram of tea and Qis the total number of grams of tea brought to market. There are two tea shops in the market. Shop 1's cost function is given by C = 0.01q,?, where qı is the number of grams of tea it brings to market. Shop 2's cost function is given by C2 = 0.01q2², where qp is the number of grams of tea it brings to market. Given that the two shops compete by setting output (Cournot), answer the following. a) Identify shop 1's reaction function to shop 2's output to within 2 decimal places (e.g. 0.33). 91= Number - Number 92 b) Identify shop 2's reaction function to shop 1's output to within 2 decimal places (e.g. 0.71). q2= Number Number 91 c) To within two decimal places (e.g. 0.63) what is the equilibrium output level of each shop and the equilibrium per gram price for tea. Shop 1 will produce Number grams of tea and shop 2 will produce Number grams of tea. The equilibrium market price is £ Number
- The inverse demand for tea is given by P = 8 – 0.03Q, where Pis the price per a gram of tea and Q is the total number of grams of tea brought to market. There are two tea shops in the market. Shop 1's cost function is given by C = 0.02q,?, where q, is the number of grams of tea it brings to market. Shop 2's cost function is given by C2 = 0.02q22, where q2 is the number of grams of tea it brings to %3D %3D market. Given that the two shops compete by setting output (Cournot), answer the following. a) Identify shop 1's reaction function to shop 2's output to within 2 decimal places (e.g. 0.33). 91= Number Number 92 b) Identify shop 2's reaction function to shop 1's output to within 2 decimal places (e.g. 0.71). q2= Number Number 91 c) To within two decimal places (e.g. 0.63) what is the equilibrium output level of each shop and the equilibrium per gram price for tea. Shop 1 will produce Number grams of tea and shop 2 will produce Number grams of tea. The equilibrium market price is £…2.1 A manufacturer estimates that its variable cost for manufacturing a given product is given by the following expression: C(q) = 25q² + 2000q [$] where C is the total cost and q is the quantity produced a. Derive an expression for the marginal cost of production b. Derive expressions for the revenue and the profit when the widgets are sold at marginal cost.11.2 The cost of producing x teddy bears per day at the Cuddly Companion Co. is calculated by their marketing staff to be given by the formula C(x) = 100 + 36x − 0.01x2. (a) Find the marginal cost function C'(x). C'(x) = Use it to determine how fast the cost is going up (in $) at a production level of 100 teddy bears. $ per teddy bear Compare this with the exact cost of producing the 101st teddy bear (in $). The cost is increasing at a rate of $ per teddy bear. The exact cost of producing the 101st teddy bear is $ . Thus, there is a difference of $ . (b) Find the average cost function C, and evaluate C(100) (in $). C(x) = C(100) = $ per teddy bear What does the answer tell you? The average cost of producing the first hundred teddy bears is $ per teddy bear.
- Suppose that the market for microwave ovens is a competitive market. The following graph shows the daily cost curves of a firm operating in this market. Hint: After placing the rectangle on the graph, you can select an endpoint to see the coordinates of that point.A startup software company has indicated its cost, c(x), and revenue, f(x), as given below, such that x is the number of lines of programing code (units in 1000 lines). c(x) = 80000 - 2(x-200)2 f(x) = (x-10)3 + (x+10)2 Find the marginal cost analytically, and draw its graph Find the marginal revenue analytically, and draw its graph Solve for the x point where marginal cost is equal to marginal revenue analytically. Comment why is this point significant analytically. Write the profit function and draw its graph Is the profit function concave up or concave down?you are an accountant for a manufacterer of radios. the demand function for the tablets is p= 40-4x2 where x is the number of tablets produced in millions. it costs the company $15 to make a tablet. write an equation for the manufactures profit as a function of the number of tablets produced. the company currently produces 1 million tablets and makes a profit of $21000000, but you would like to scale up production a bit, what greater number of tablets could the company produce to yield the same profit
- Q2)Tony Keonte owns a factory that manufactures Eye-Games. His weekly profit (in thousands of dollars) is given by the following function: P(x) = -4x2 + 80x- 300. Where x is the number of Eye-Games sold. a) What is the largest number of Eye-Games that the company can sell and still make profit? (25 points) b) How many Eye-Games will the firm have to produce and sell in order to maximize profit? (25 points)Joshua owns a small boat and catches lobster off the coast of Maine. His weekly cost function is TC(q) = 40 + 5q + 5q?. He sells his lobsters to the local wholesaler at the market price p (in dollars). a) Find Joshua's short-run supply function for lobsters. (Hit: In this case short-run marginal cost is the same as long-run marginal cost.) b) Find Joshua's long-run supply function for lobsters. c) Find Joshua's shutdown price and Joshua's breakeven price (the price at which profit equals zero). d) Suppose the market price is $30, calculate his profit. What will Joshua do in the long run? Explain. 1Suppose that the market for microwave ovens is a competitive market. The following graph shows the daily cost curves of a firm operating in this market. 100 90 80 ATC 70 60 50 40 30 AVC 20 10 MC 5 10 15 20 25 30 35 40 45 50 QUANTITY (Thousands of ovens) For each price in the following table, calculate the firm's optimal quantity of units to produce, and determine the profit or loss if it produces at that quantity, using the data from the graph to identify its total variable cost. Assume that if the firm is indifferent between producing and shutting down, it will produce. (Hint: You can select the purple points [diamond symbols] on the graph to see precise information on average variable cost.) Price Quantity Total Revenue Fixed Cost Variable Cost Profit (Dollars per oven) (Ovens) (Dollars) (Dollars) (Dollars) (Dollars) 25.00 1,600,000 70.00 1,600,000 $25.00 100.00 1,600,000 $35.00 If the firm shuts down, it must incur its fixed costs (FC) in the short run. In this case, the firm's…