Suppose that you estimate the following cost function for your company, v operating in a monopolistically competitive market: TC = 240Q – 12Q² + 0.2Q³ You also estimate the following demand curve for the output you are produ P = 180 – 6Q Derive the equations for average cost and marginal cost curyes

Drybar, a hair salon, has very loyal customers and faces a weekly demand for blowouts equal to qD = 1,040 – 20P. The salon has weekly total cost of TC(q)=0.05q2+20q+500. a) Ia diagram, draw drybar’s demand curve (PD). Write Drybar’s revenue as a function of the firm’s quantity. Compute the expression of Drybar’s Marginal Revenue and draw the MR curve in your. In the diagram, draw the MR curve. Note that it has twice the slope than demand. b) In the same diagram, illustrate drybar’s average total cost curve (ATC), and marginal cost curve (MC). If Drybar were a perfectly competitive firm, in the long run at what price would it sell its output? Drybar instead has market power. Suppos the firm charges all customers the same price for a blowout. c) Find the profit maximizing level of output (q*) and price (p*). Compute the price elasticity of demand at q* and show that at q* MR(q*) = p*(1+1/e) = MC(q*) i) Compute the consumer surplus created by Drybar and the profit of the firm.

Alert dont submit AI generated answer. 2. There are N consumers uniformly distributed along a linear city of unit length, served by two shops located at opposite extremities of the city. The two shops sell an identical product, for which consumers have unit demands, and they have identical constant marginal costs of 2 and no fixed costs. The cost to consumers of travelling the length of the city is 4. a) Making clear your assumptions and calculations, work out the optimal prices the shops should charge for the product, and their profits in terms of N. How does your result relate to the so-called Bertrand Paradox? b) Explain why it is optimal for the shops to locate at opposite ends of the city. c) Suppose one shop only has a marginal cost of 1, but there are no other changes to the setting. Calculate the optimal prices for the shops, and their profits in terms of N.

Tim Marlow, the owner of The Clock Works, wanted to know how many clocks he must sell in order to cover his fixed cost at a given price. Tim knew that he had a fixed cost of $20,000 for equipment, taxes, and a bank loan. He also had a unit variable cost of $20 per clock for labor, materials, and promotional costs. If the price Tim charges for each of his clocks is $40, what is his break-even point quantity?