Economics

Suppose that a typical firm in a monopolistically competitive industry faces a demand curve given by:

q = 60 - (1/2)p, where q is quantity sold per week.
The firm's marginal cost curve is given by: MC = 60.

1. How much will the firm produce in the short run?
2. What price will it charge?

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  1. Since it is a monopolistic product, it will be assumed everything made will be sold, and at the predicted price.
    p = selling price
    Quantity sold=quantity manufactured = q(p) =60-p/2
    Cost, C = 60 at all sales volumes
    Profit in terms of price, p
    P(p)= (selling price - cost)*quantity sold
    =(p-C)q(p)
    =(p-C)(60-p/2)
    =(p-60)(60-p/2)
    Maximize profit by setting P'(p)=0 to solve for p
    dP(p)/dp
    = d(-p^2/2+90p-3600)/dp
    = -p+90
    Setting derivative to zero,
    -p+90=0
    solve for (most profitable p)
    p=90 => product will be sold at unit price of 90.

    Production quantity
    q(p) = 60-p/2 = 60-45 = 15 units.

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