Calculate the perfectly competitive and monopoly outputs

Question

Question

1.1. Suppose a perfectly competitive industry can produce Roman candles at a constant marginal cost of RIO per unit. Once industry' is monopolized, marginal costs rise to R12 per unit because R2 per unit must be paid to lobbyists to ensure that only this firm receives a Roman candle license. Suppose the market demand for Roman candles is given by

Q_d = 1000 - 50P

And Marginal revenue curse by

MR= 20-Q/25

a. Calculate the perfectly competitive and monopoly outputs and prices

1.2 The long run total cost function for a firm producing cellphones is

TC = Q³- 40Q²- 430Q

Alice Q is the number of cellphones per week

a. What is the general shape of this total cost function?
b. Calculate the average cost function for the cellphones?
c. What shape does the graph of this function have?
d. At shape level of the cellphones output does average cost reach a minimum?
e. What is the average cost of this level of output?

1.3. Calculate the marginal cost function; show that this marginal cost curve intersects average cost at its minimum value. Graph the average and marginal cost curves for cellphones production.